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\size giant
expEYES
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	filename pics/eyes.jpg
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Experiments for
\begin_inset Newline newline
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 Young Engineers and Scientists
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website : expeyes.in
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User Manual (ver.2, Apr-2011)
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with 50 Science Experiments
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\begin_inset VSpace 0.25in
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\begin_layout Standard
\align center
PHOENIX Project
\begin_inset Newline newline
\end_inset

Inter-University Accelerator Centre
\begin_inset Newline newline
\end_inset

(A Research Centre of UGC)
\begin_inset Newline newline
\end_inset

New Delhi 110 067
\begin_inset Newline newline
\end_inset

www.iuac.res.in
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\begin_layout Standard
Preface
\end_layout

\begin_layout Standard
The PHOENIX (Physics with Home-made Equipment & Innovative Experiments)
 project was started in 2004 by Inter-University Accelerator Centre with
 the objective of improving the science education at Indian Universities.
 Development of low cost laboratory equipment and training teachers are
 the two major activities under this project.
 The first product was a general purpose interface, was also called Phoenix,
 followed by instruments like Geiger-Muller counter, Alpha spectrometer
 etc.
 The power of personal computers have been utilized for performing measurements
 and data analysis.
\end_layout

\begin_layout Standard
The new product, expEYES (Experiments for Young Engineers & Scientists),
 is meant to be a tool for learning by exploration, suitable for high school
 classes and above.
 An attempt is made to strike a balance between open ended experiments mostly
 meant for exploration and the conventional ones with some specific objective.
 We have tried optimizing the design to be simple, flexible, rugged and
 above all low cost.
 There is no need of a separate power supply since it runs on the 5 volt
 USB power, taking care of the long power failures common in many places.
 The low price makes it affordable to individuals and we hope to see students
 performing experiments outside the four walls of the laboratory, that closes
 when the bell rings.
\end_layout

\begin_layout Standard
Design of hardware developed is open and the software is released under
 GNU General Public License.
 The project has progressed due to the active participation and contributions
 from the user community and many other persons outside IUAC.
 We thank them all and also expect their continued cooperation.
 We are grateful to Prof.
 G.K.Mehta for suggesting corrections to this document.
 This is distributed under GNU Free Documentation License.
 More details and updated versions of this document are available on the
 website
\shape italic
expeyes.in
\end_layout

\begin_layout Standard
\begin_inset space ~
\end_inset


\end_layout

\begin_layout Standard
Ajith Kumar B.P.
\end_layout

\begin_layout Standard
V V V Satyanarayana
\end_layout

\begin_layout Standard
Jimson Sacharias
\end_layout

\begin_layout Standard
Deepak Munda
\end_layout

\begin_layout Standard
S.
 Venkataramanan
\end_layout

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\begin_layout Chapter
Getting Started
\end_layout

\begin_layout Section
Introduction
\end_layout

\begin_layout Standard
Performance of a student is often measured by the ability to memorize than
 the real understanding.
 As a result, most of them fail to apply what they learn in the classroom
 to things they encounter in their daily life.
 To some extent this can be corrected by learning based on exploration and
 experimenting.
 Experiments generally involve measuring and controlling physical parameters
 like temperature, pressure, velocity, acceleration, force, voltage, current
 etc.
 If the measured physical property is changing rapidly, the measurements
 need to be automated and a computer becomes a useful tool.
 For example, understanding the variation of AC mains voltage with time
 requires measuring it after every millisecond.

\end_layout

\begin_layout Standard
The ability to perform experiments with reasonable accuracy, opens up an
 entirely new path for learning science.
 Students can compare the experimental data with mathematical models and
 examine the fundamental laws governing various phenomena.
 Research scientists formulate hypotheses, design and perform experiments,
 analyze the data to check whether they agree with the theory.
 The objective of PHOENIX (Physics with Home-made Equipment and Innovative
 Experiments) project is to provide the same facilities on a smaller scale
 to the students.
 It also enables the users to develop new experiments without getting into
 the details of electronics or computer programming.
 There are several equipment and experiments developed so far.
 This document describes some experiments that can be done with the interface
 named
\shape italic
expEYES
\shape default
.
\end_layout

\begin_layout Section
The equipment
\end_layout

\begin_layout Standard
ExpEYES is interfaced and powered by the USB port of the computer.
 For connecting external signals, it has 32 Input/Output terminals, arranged
 on both sides, as shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:ExpEYES top panel"

\end_inset

.
 It can monitor and control the voltages at the terminals.
 In order to measure other parameters (like temperature, pressure etc.),
 we need to convert them in to electrical signals by using appropriate sensor
 elements.
 Even though our primary objective is to do experiments, you are advised
 to read through the brief description of the equipment given below.
\end_layout

\begin_layout Standard

\shape italic
IMPORTANT : The external voltages connected to expEYES must be within
\begin_inset Formula $\pm5V$
\end_inset

 range.

\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/top-panel.png
	lyxscale 50
	width 10cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
The ExpEYES top panel showing the external connections on both sides.
 The arrows indicates the direction of the signals.
\begin_inset CommandInset label
LatexCommand label
name "fig:ExpEYES top panel"

\end_inset

.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection
External connections
\end_layout

\begin_layout Standard
The external connections can be grouped according to their functions.
\end_layout

\begin_layout Subsubsection*
Digital Inputs (ID0 and ID1)
\end_layout

\begin_layout Standard
\align block
Software can read the voltage level applied to them.
 Any voltage less than .8
\begin_inset space ~
\end_inset

V is treated as 0 (LOW) and anything higher than 2
\begin_inset space ~
\end_inset

V is treated as 1 (HIGH).
 If the voltage input is changing between HIGH and LOW, these terminal can
 measure the frequency and duty-cycle of the connected signal.
 ExpEYES is capable of measuring time interval between voltage transitions
 on these pins with microsecond resolution.

\end_layout

\begin_layout Subsubsection*
Digital Outputs (OD0 and OD1)
\end_layout

\begin_layout Standard
Using software, we can make the voltage at these terminals 0 or 5
\begin_inset space ~
\end_inset

V.
 OD0 is transistor buffered and can drive up to 100
\begin_inset space ~
\end_inset

mA current.
 OD1 can only drive only up to 5
\begin_inset space ~
\end_inset

mA.
\end_layout

\begin_layout Subsubsection*
Signal Generators
\end_layout

\begin_layout Paragraph*
SINE
\end_layout

\begin_layout Standard
Fixed frequency sine wave generator, frequency is around 100
\begin_inset space ~
\end_inset

Hz.
 Bipolar signal output with an amplitude of around 4
\begin_inset space ~
\end_inset

V.
\end_layout

\begin_layout Paragraph*
SQR1
\end_layout

\begin_layout Standard
Can generate a square wave, swings from 0 to 5
\begin_inset space ~
\end_inset

V.
 Frequency is programmable from 15
\begin_inset space ~
\end_inset

Hz to 1
\begin_inset space ~
\end_inset

MHz.
 All intermediate values of frequency are not possible.

\end_layout

\begin_layout Paragraph*
SQR2
\end_layout

\begin_layout Standard
Can generate a square wave, swinging from 0 to 5
\begin_inset space ~
\end_inset

V.
 Frequency can be set anywhere between 0.7
\begin_inset space ~
\end_inset

Hz and 90
\begin_inset space ~
\end_inset

kHz.
 The oscillator requires an external variable resistor, 22
\begin_inset space ~
\end_inset

k
\begin_inset Formula $\Omega$
\end_inset

, for its operation.
 The frequency range is controlled by software and frequency tuning within
 the selected range is done by adjusting the resistance.
 The frequency ranges are < 25
\begin_inset space ~
\end_inset

Hz, 25 to 1
\begin_inset space ~
\end_inset

kHz, 1
\begin_inset space ~
\end_inset

kHz to 10
\begin_inset space ~
\end_inset

kHz and 10
\begin_inset space ~
\end_inset

kHz to 90
\begin_inset space ~
\end_inset

kHz.
 Entering a frequency in a particular range selects that range.
 The variable resistor is then adjusted to obtain the desired frequency.
 The actual value of the frequency is measured and displayed during adjustment.
\end_layout

\begin_layout Paragraph*
PULSE
\end_layout

\begin_layout Standard
Output frequency is 488
\begin_inset space ~
\end_inset

Hz.
 Duty cycle can be programmed from 0 to 100
\begin_inset space ~
\end_inset

% in 255 steps.
 This terminal can be configured to generate a Square wave, like SQR1.
 This feature is used by the program demonstrating interference of sound.
\end_layout

\begin_layout Subsubsection*
Analog Voltage Inputs
\end_layout

\begin_layout Paragraph*
A0 and A1
\end_layout

\begin_layout Standard
Can measure voltage within the
\begin_inset Formula $\pm5\, V$
\end_inset

 range.
 The resolution of ADC used is 12
\begin_inset space ~
\end_inset

bits.
 Voltage at these terminals can be displayed as a function of time, giving
 the functionality of a low frequency two channel oscilloscope.
\end_layout

\begin_layout Paragraph*
A2
\end_layout

\begin_layout Standard
For voltage measurement.
 Input must be within the 0 to 5
\begin_inset space ~
\end_inset

V range.
 Resolution is 12
\begin_inset space ~
\end_inset

bits.
 Voltage can be displayed as a function of time using software.
\end_layout

\begin_layout Subsubsection*
Analog Voltage Outputs
\end_layout

\begin_layout Paragraph*
BPV
\end_layout

\begin_layout Standard
Bipolar voltage output.
 Can be programmed to any value between -5
\begin_inset space ~
\end_inset

V to +5
\begin_inset space ~
\end_inset

V.
 The resolution is 12 bit, implies a minimum voltage step of around 2.5
\begin_inset space ~
\end_inset

mV.
\end_layout

\begin_layout Paragraph*
UPV
\end_layout

\begin_layout Standard
Unipolar voltage output.
 Can be programmed between 0 to +5
\begin_inset space ~
\end_inset

V.
 Cannot be used along with the current source output CS, since they share
 the same DAC output.
\end_layout

\begin_layout Paragraph*
IV
\end_layout

\begin_layout Standard
This is just the output BPV coming out through a 1
\begin_inset Formula $k\Omega$
\end_inset

 resistor.
 Used for doing I-V characteristic.
\end_layout

\begin_layout Subsubsection*
Constant Current Source (CS)
\end_layout

\begin_layout Standard
Programmable to any value from 0.05 to 2.0
\begin_inset space ~
\end_inset

mA.
 The load resistor should be chosen such that the the product
\begin_inset Formula $IR$
\end_inset

 is less than 2
\begin_inset space ~
\end_inset

V.
 Remember that CS and UPV shares the same DAC output.
\end_layout

\begin_layout Subsubsection*
Inverting Amplifiers
\end_layout

\begin_layout Standard
There are three inverting amplifiers, implemented using TL084 op-amps, denoted
 below using their input and output terminal numbers.
\end_layout

\begin_layout Paragraph*
15
\begin_inset Formula $\Rightarrow$
\end_inset

13
\end_layout

\begin_layout Standard
Input at terminal 15 and output at 13.
 Default Gain=50.
 The gain can be reduced by feeding the input through a series resistor.
 The gain is be governed by
\begin_inset Formula $G=\frac{R_{f}}{(R_{ext}+1000)}$
\end_inset

 where the internal
\begin_inset Formula $R_{f}=50000\,\Omega$
\end_inset

.
 The external series resistor is
\begin_inset Formula $R_{ext}$
\end_inset

.

\end_layout

\begin_layout Paragraph*
14
\begin_inset Formula $\Rightarrow$
\end_inset

12
\end_layout

\begin_layout Standard
Input at terminal 14 and output at 12.
 Similar to the one mentioned above.
\end_layout

\begin_layout Paragraph*
17
\begin_inset Formula $\Rightarrow$
\end_inset

18
\end_layout

\begin_layout Standard
Input at 17 and output at 18.
 Default Gain=100.
 The gain can be reduced by feeding the input through a series resistor.
 The gain is be governed by
\begin_inset Formula $G=\frac{R_{f}}{(R_{ext}+100)}$
\end_inset

 where the internal
\begin_inset Formula $R_{f}=10000\,\Omega$
\end_inset

 and the external series resistor is
\begin_inset Formula $R_{ext}$
\end_inset

.

\end_layout

\begin_layout Subsubsection*
Non-Inverting Amplifier
\end_layout

\begin_layout Standard
The input is at 21 and output at 22.
 The gain is decided by an external resistor
\begin_inset Formula $R_{g}$
\end_inset

 connected between 19 and 20 and is given by
\begin_inset Formula $Gain=1+10000/R_{g}$
\end_inset

.
 This amplifier is implemented using OP27 IC and has an offset voltage of
 around
\begin_inset Formula $30\,\mu V$
\end_inset

.
\end_layout

\begin_layout Subsubsection*
Sensor Input (SEN)
\end_layout

\begin_layout Standard
For connecting any sensor whose resistance varies with the measured parameter.
 When used with the photo-transistor.
 connect collector to this, and emitter to Ground.
 Capable of measuring the voltage and frequency.
\end_layout

\begin_layout Subsubsection*
Frequency Counters
\end_layout

\begin_layout Standard
The terminal 15 can measure the frequency of a bipolar signal (that goes
 to both negative and posiive values).
 The minimum measurable amplitude is 100
\begin_inset space ~
\end_inset

mV and the maximum is 5
\begin_inset space ~
\end_inset

V.

\end_layout

\begin_layout Standard
ID0, ID1 and SEN are capable of measuring the frequency of signals swinging
 from 0 to 5
\begin_inset space ~
\end_inset

V.

\end_layout

\begin_layout Section
Software Installation
\end_layout

\begin_layout Standard
ExpEYES can run on any computer having a Python Interpreter and a Python
 module to access the Serial port.
 The USB interface is handled by the device driver programs that presents
 the USB port as an RS232 port to the application programs.
 The communication with expEYES is done using a library written in Python
 language.
 Programs with GUI have been written for many experiments.
 There are many ways to get the software running:
\end_layout

\begin_layout Subsubsection*
The expEYES Live CD
\end_layout

\begin_layout Standard
The easiest way to get started is to boot your PC with the Phoenix Live-CD.
 From the PC BIOS, make the CD drive as the first boot device, insert the
 live CD and reboot the PC.
 A desktop will appear and you can start expEYES from the menu
\series bold
Applications
\begin_inset space ~
\end_inset

->
\begin_inset space ~
\end_inset

Science
\series default
.
 The expEYES live CD is made from GNU/Linux distribution Ubuntu 10.10.
\end_layout

\begin_layout Subsubsection*
Installing on Debian or Ubuntu GNU/Linux distributions
\end_layout

\begin_layout Standard
Install python-imaging-tk from the repository of the distribution you are
 running.
 Download
\series bold
expeyes.deb
\series default
 from
\series bold
http://expeyes.in
\series default
 and install it.
 Also install python-scipy and grace (a 2D plotting program) for full functional
ity.

\end_layout

\begin_layout Subsubsection*
For other GNU/Linux distributions
\end_layout

\begin_layout Standard
Download
\series bold
expeyes.tgz
\series default
 from
\series bold
http://expeyes.in
\series default
 and follow the instructions in the README file.
 It is important to give read/write permissions for all users on the USB
 port where expEYES is connected.
\end_layout

\begin_layout Subsubsection*
On MSWindows
\end_layout

\begin_layout Standard
Even though expEYES is Free Software and it developed using Free and Open
 software, it runs on non-free platforms also.
 To install it on MS windows, you need the following files (given on the
 CD)
\end_layout

\begin_layout Enumerate
CDM20814_Setup.exe
\end_layout

\begin_layout Enumerate
python-2.6.6.msi
\end_layout

\begin_layout Enumerate
pyserial-2.5.win32.exe
\end_layout

\begin_layout Enumerate
PIL-1.1.7.win32-py2.6.exe
\end_layout

\begin_layout Enumerate
numpy-1.6.0b2-win32-superpack-python2.6.exe
\end_layout

\begin_layout Enumerate
scipy-0.9.0-win32-superpack-python2.6.exe
\end_layout

\begin_layout Enumerate
expeyes.zip
\end_layout

\begin_layout Standard
Unzip the file
\series bold
expeyes.zip
\series default
, and double click on
\series bold
explore.py
\series default
 inside the newly created directory named EYES.

\end_layout

\begin_layout Standard
If you have expEYES liveCD, browse inside the directory named WINEYES.
 All the files mentioned above are inside that directory.
 Double click on them in the order mentioned above to install them.
 The XmGrace plotting utility is not available under MSwindows.
 Fourier transform output will be saved to disk in text format.
\end_layout

\begin_layout Section
The main GUI program
\end_layout

\begin_layout Standard
Start Applications->Science->expEYES from the menu.
 It will show a graphics window as shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Explorer screenshot"

\end_inset

, and is briefly explained below.
\end_layout

\begin_layout Itemize
Clicking on the boxes showing the terminal numbers will display help messages.
\end_layout

\begin_layout Itemize
Right Clicking on the left panel produces a pop-up menu of applications.
\end_layout

\begin_layout Itemize
The status of Digital Inputs decides the colour of the display area against
 them.
 Pale green indicates High and Gray indicates Low.
 When the input voltage swings from 0 to 5 volts, this field blinks.

\end_layout

\begin_layout Itemize
The display field against T15 may blink if an AC signal is given there.
\end_layout

\begin_layout Itemize
The Frequency display field of SEN may blink if the input is varying between
 0 and 5 volts.
 This will happen if the connected resistance is varying.
\end_layout

\begin_layout Itemize
The Buttons marked 'F' may be used for measuring the frequency, while the
 display fields are blinking.
\end_layout

\begin_layout Itemize
The values of output signals can be set by entering them in the nearby text
 box.
 Voltage, current, frequency and duty-cycle are set like this.
 Press <Enter> to set the entered value.
 If successful, the display will show a decimal point.
\end_layout

\begin_layout Itemize
SQR2 require an external resistor to function, we use a 22k
\begin_inset Formula $\Omega$
\end_inset

 variable resistor.
 The actual frequency is displayed just below the text field, where you
 set the frequency.
\end_layout

\begin_layout Itemize
State of Digital Outputs, OD0 and OD1, can be changed by using the Check
 Buttons.
\end_layout

\begin_layout Itemize
The voltages at the input terminals 23,24,25 and 26 are displayed continuously
 against them.
\end_layout

\begin_layout Standard
The GUI is made using a photograph of the device.
 Control and monitor widgets are placed on the photograph at appropriate
 places.
 Right click on the panel to get a pop-up menu of application programs for
 various experiments.
\end_layout

\begin_layout Subsubsection*
The Plot Window
\end_layout

\begin_layout Standard
The plot window on the right side works like a low frequency oscilloscope.
 The maximum sampling rate is 100
\begin_inset space ~
\end_inset

kHz only.
 You can digitise sinewaves upto 20
\begin_inset space ~
\end_inset

kHz while using only one channel and upto 10
\begin_inset space ~
\end_inset

kHz when both are enabled.
 The following controls are available.
\end_layout

\begin_layout Itemize
Horizontal scale Slider (ms/Sec).
 Set this to the minimum value and increase to view more number of cycles
 on the screen.
\end_layout

\begin_layout Itemize
Channel selection Checkboxes for A0 and A1.
\end_layout

\begin_layout Itemize
LIZ checkbox to make a Lissajous figure using A0 and A1 inputs.
\end_layout

\begin_layout Itemize
FIT checkbox to enable calculating amplitude, frequency and phase by fitting
 the data using the equation
\begin_inset Formula $V=V_{0}\sin\left(\omega t+\theta\right)+C$
\end_inset

 .
 The RMS value of the voltage and frequency are displayed.
 When both the channels are selected, the phase difference is diplayed.
\end_layout

\begin_layout Itemize
SAVE button to save the data to
\shape italic
explore.dat
\shape default
 as two column text.
\end_layout

\begin_layout Itemize
FT to do a Fourier Transform power spectrum of the data from enabled channels.
 If Xmgrace and pygrace are installed, a window is opened.
 Power spectrum is saved to
\shape italic
exploreFFT.dat
\shape default
 in text form.

\end_layout

\begin_layout Section
Basic measurements using expEYES
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/explorer.png
	lyxscale 50
	width 11cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Screen shot of Explore program.
 Arrows indicate the signal direction.
 Text fields are used for setting values.
 Buttons are provided for frequency measurements.
\begin_inset CommandInset label
LatexCommand label
name "fig:Explorer screenshot"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Before proceeding with the experiments, let us do some simple exercises
 to become familiar with expEYES.
 Boot your computer from the LiveCD, connect expEYES to the USB port and
 start the expEYES program from the menu 'Applications->Science'.
\end_layout

\begin_layout Subsection
Generate & measure voltages
\end_layout

\begin_layout Itemize
Connect BPV to A0
\end_layout

\begin_layout Itemize
Set BPV to some voltage and observe the reading at A0
\end_layout

\begin_layout Itemize
Try A1 instead of A0
\end_layout

\begin_layout Itemize
Repeat the same by connecting UPV to A2
\end_layout

\begin_layout Subsection
Observe voltage waveforms
\end_layout

\begin_layout Itemize
Connect SQR1 to A0
\end_layout

\begin_layout Itemize
Set SQR1 to 100 Hz
\end_layout

\begin_layout Itemize
Adjust the horizontal scale (ms/Div) to view 4 or 5 cycles of the square
 wave
\end_layout

\begin_layout Itemize
Repeat with other frequency values
\end_layout

\begin_layout Itemize
Connect SINE to A1 and watch both traces simultaneously
\end_layout

\begin_layout Itemize
Explore the FIT, XM and FT options.
\end_layout

\begin_layout Subsection
Measure frequency
\end_layout

\begin_layout Itemize
Connect SQR1 to ID0
\end_layout

\begin_layout Itemize
Set SQR1 to 1000
\end_layout

\begin_layout Itemize
Click on the 'F' button of ID0
\end_layout

\begin_layout Itemize
Connect SINE to T15 and measure the frequency.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
T15 will not measure the frequency of SQR1 or SQR2 outputs, because they
 do not swing below zero.
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Measure duty cycle
\end_layout

\begin_layout Itemize
Connect PULSE to ID0
\end_layout

\begin_layout Itemize
Also to A0, if you want to watch the waveform.
\end_layout

\begin_layout Itemize
Set PULSE to any value from 0 to 100
\end_layout

\begin_layout Itemize
Click on the '%' button of ID0, to measure the duty cycle.
\end_layout

\begin_layout Subsection
Setting voltage levels
\end_layout

\begin_layout Itemize
Connect OD0 to ID0
\end_layout

\begin_layout Itemize
Click on the Check button and watch ID0 display color.
\end_layout

\begin_layout Section
Experiments
\end_layout

\begin_layout Standard
A science experiment generally involves control and measurement of various
 physical parameters like temperature, pressure, voltage, current etc.
 The basic expEYES hardware can generate different kinds of electrical signals
 and measure electrical signals.
 For measuring anything other than voltage, we need to convert it using
 appropriate sensor elements.
 For example a temperature sensor will give a voltage indicating the temperature.
 Since experiments in electricity and magnetism does not require any sensor
 elements, we have more number of experiments based on electricity and magnetism.
\end_layout

\begin_layout Standard
A GUI program is provided for every experiment given in this manual.
 However, it is possible to do the same by writing few lines of code written
 in Python language.
 All the communication to expEYES is done using a Python library called

\shape italic
eyes.py
\shape default
.
 Python libraries are used for data analysis.
 If you are interested in developing new experiments based on expEYES, it
 would be a good idea to learn Python programming language.
 Almost every experiment can be extended in several ways and some hints
 are given in this direction.

\end_layout

\begin_layout Standard
The following chapters describe experiments from different topics like electrici
ty, magnetism, electronics, sound, heat, etc.
 Since the expEYES kit is meant for self learning, we have included some
 very trivial experiments in the beginning.
\end_layout

\begin_layout Chapter
Electricity
\end_layout

\begin_layout Standard
We start with the trivial task of measuring the voltage of a battery.
 Current and resistance are introduced next, followed by resistances changing
 with temperature and light.
 The concept of Alternating Current is introduced by plotting the voltage
 as a function of time.
 The behavior of circuit elements like capacitors and inductors in AC and
 DC circuits are explored, by measuring parameters like amplitude, frequency
 and phase.
 The transient response of a resistor and capacitor in series is used for
 measuring the capacitance.
 Inductance also is measured in the same manner.
 The effect of ferromagnetic materials inside an inductor in examined.
\end_layout

\begin_layout Standard
The Fourier analysis of square wave is done to study the harmonics.
 Integration and differentiation of a square wave using RC circuits also
 is explored.

\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Measuring voltage
\begin_inset CommandInset label
LatexCommand label
name "sec:Measuring-Voltage-*"

\end_inset


\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Learn to measure voltage using expEYES and get some idea about the concept
 of Electrical Ground.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/cell-volatge.png
	height 2cm

\end_inset


\begin_inset Graphics
	filename pics/drycell-voltage.png
	height 2cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Measuring the voltage of a battery
\begin_inset CommandInset label
LatexCommand label
name "fig:Measuring-drycells"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\begin_layout Itemize
1.5 Volts dry cells
\end_layout

\begin_layout Itemize
Battery holder with two connecting wires.

\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect Negative terminal of the battery to Ground.
\end_layout

\begin_layout Itemize
Positive terminal of the cell to A0.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
Voltage will be displayed on the left side of A0, as shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Measuring-drycells"

\end_inset

.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
We are measuring the potential difference between two points.
 One of them can be treated as at zero or Ground potential.
 The voltage measuring points of expEYES measure the voltage with respect
 to the terminals marked GND.
 We have connected the negative terminal of the cell to Ground.
 The positive terminal is at +3 volts with respect to the negative terminal.
\end_layout

\begin_layout Standard
Repeat the experiment by connecting the positive terminal of the cell to
 GND and the negative to A0.
 The voltage will be shown as negative.

\shape italic
Will it show correct voltage if Ground is not connected ?
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Voltage, current & resistance
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Learn about Current, Resistance and Ohm's law.
 Plot I-V curve of a resistor.
\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
The voltage across a conductor is directly proportional to current flowing
 through it.
 The constant of proportionality is called Resistance.
 This is known as Ohm's Law, expressed mathematically as
\begin_inset Formula \[
V\varpropto I\,\,\,;\,\,\,\, V=IR\,\,\,\, or\,\,\, R=\frac{V}{I}\]

\end_inset


\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\align left
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/res-measure.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/resistor_iv.png
	lyxscale 50
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
IV-characteristic of resistor
\begin_inset CommandInset label
LatexCommand label
name "fig:I-V of -resistor"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
A
\begin_inset Formula $1\, k\Omega$
\end_inset

 resistor
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect resistor from CS to Ground.
\end_layout

\begin_layout Itemize
Set the current to 0.5
\begin_inset space ~
\end_inset

mA and note down the voltage at CS.
\end_layout

\begin_layout Itemize
Change the current in .5
\begin_inset space ~
\end_inset

mA steps.
 (V should not exceed 2
\begin_inset space ~
\end_inset

V at CS)
\end_layout

\begin_layout Itemize
Right click on the Panel.
 Choose
\shape italic

\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{Resistor IV}
\end_layout

\end_inset


\shape default
 from the pop-up menu.
\end_layout

\begin_layout Itemize
Draw the graph using
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
buttonlabel{START}
\end_layout

\end_inset

 button.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features>
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
I
\begin_inset space ~
\end_inset

(mA)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
V
\begin_inset space ~
\end_inset

(volt)
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0.5
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
.508
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1.0
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1.011
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1.5
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1.5.10
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
The current source accuracy is only 1%, due to the tolerance value of the
 resistor used.
 For applications requiring higher accuracy, you can calibrate it using
 a known resistance.
 The I-V curve is shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:I-V of -resistor"

\end_inset

.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Using expEYES, we can set the current from CS (from 0.05
\begin_inset space ~
\end_inset

mA to 2
\begin_inset space ~
\end_inset

mA).
 The voltage at CS will depend on the resistance connected from the current
 source to Ground.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
 The voltage across this particular current source should not exceed 2 volts.
 Choose the load resistor and current values accordingly.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
The graph is a straight line since the voltage is directly proportional
 to current.
 The graph will not be a straight line for non-linear elements, like a diode.
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Resistances in series
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Finding the effective resistance of a series combination of resistors.
\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
For series combination of resistors, total resistance is given by
\begin_inset Formula $R=R1+R2+\cdots$
\end_inset


\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
\begin_inset Formula $560\,\Omega$
\end_inset

 and
\begin_inset Formula $1\, k\Omega$
\end_inset

 resistors
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Standard
\begin_inset Graphics
	filename schematics/res-series.png
	height 0.8cm

\end_inset


\end_layout

\begin_layout Itemize
Connect both resistors in series from CS to Ground
\end_layout

\begin_layout Itemize
Set the current to 1 mA and note down the voltage displayed at CS.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features>
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
R
\begin_inset space ~
\end_inset

(
\begin_inset Formula $\Omega)$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
V
\begin_inset space ~
\end_inset

(volts)
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
560
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
.558
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1000
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0.998
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1000+560
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1.556
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Since the current is same, the total voltage drop gives the effective resistance.
 It can be seen that it is the sum of the individual values, within the
 measurement error.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Very high resistances (
\begin_inset Formula $>10^{9}\Omega$
\end_inset

) are often implemented using series combinations.
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Resistances in parallel
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Find the effective resistance of parallel combination of resistors.
\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
For parallel combination, effective resistance is given by
\begin_inset Formula \[
\frac{1}{R}=\frac{1}{R1}+\frac{1}{R2}+\cdots\]

\end_inset


\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
Two 1
\begin_inset Formula $k\Omega$
\end_inset

 resistors
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Standard
\begin_inset Graphics
	filename schematics/res-par.png
	height 1cm

\end_inset


\end_layout

\begin_layout Itemize
Connect
\begin_inset Formula $1\, k\Omega$
\end_inset

 resistor from CS to Ground.
\end_layout

\begin_layout Itemize
Set the current to 1
\begin_inset space ~
\end_inset

mA (0.001
\begin_inset space ~
\end_inset

Ampere) and note down the voltage displayed at CS.
\end_layout

\begin_layout Itemize
Repeat the same with two resistors connected in parallel.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="2">
<features>
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $R_{connected}(\Omega)$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $V_{measured}(V)$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1000
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1.008
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1000
\begin_inset Formula $\parallel$
\end_inset

1000
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0.503
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Since we know the current, we can calculate the resistance from the measured
 voltage.
 As per the measured voltage the resistance of the parallel combination
 is
\begin_inset Formula $\frac{0.503\, V}{0.001\, A}=503\,\Omega$
\end_inset


\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Why one wants to connect resistors in parallel ?
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Measure resistance by comparison
\begin_inset CommandInset label
LatexCommand label
name "sec:Measure-resistance-by"

\end_inset


\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Learn to apply Ohm's law to find the value of an unknown resistance by comparing
 it with a known one.
\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
Voltage across a resistor is given by
\begin_inset Formula $V=IR$
\end_inset

 .
 If same amount of current is flowing through two different resistors, the
 ratio of voltages will be the same as the ratio of resistances.
\begin_inset Formula \[
I=\frac{V1}{R1}=\frac{V2}{R2}\]

\end_inset


\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
A 1
\begin_inset space ~
\end_inset


\begin_inset Formula $k\Omega$
\end_inset

 as the reference and another resistors.
 (some value from 100
\begin_inset space ~
\end_inset


\begin_inset Formula $\Omega$
\end_inset

 to 10
\begin_inset space ~
\end_inset


\begin_inset Formula $k\Omega$
\end_inset

)
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Standard
\begin_inset Graphics
	filename schematics/res-comp.png
	height 1cm

\end_inset


\end_layout

\begin_layout Itemize
Connect the unknown resistor R from UPV to A2.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
We use A2 when the voltage is in the 0 to 5V range.
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Connect 1
\begin_inset space ~
\end_inset


\begin_inset Formula $k\Omega$
\end_inset

 (R2) from A2 to Ground.
\end_layout

\begin_layout Itemize
Set UPV to 4 volts.
\end_layout

\begin_layout Itemize
Measure voltage at A2.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
Voltage at A2 = 1.244, implies voltage across the unknown resistor is
\begin_inset Formula $4-1.244=2.756$
\end_inset


\end_layout

\begin_layout Standard
Current
\begin_inset Formula $I=\frac{1.244}{1000}=1.244mA$
\end_inset


\end_layout

\begin_layout Standard
Unknown resistor value =
\begin_inset Formula $\frac{2.756}{1.244}=2.215\, k\Omega$
\end_inset


\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
What is the limitation of this method ? How do we choose the reference resistor
 ? suppose the unknown value is in Mega Ohms, what will be the voltage drop
 across a
\begin_inset Formula $1k\Omega$
\end_inset

 reference resistor ? Our voltage measurement is having a resolution of

\begin_inset Formula $\frac{1}{4095}$
\end_inset

.
\end_layout

\begin_layout Standard
We will use this method later to measure the resistance of solutions.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Voltage of a lemon cell
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Make a voltage source.
 Learn about current capability.
 Concept of internal resistance.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/lemon-cell.png
	lyxscale 120
	width 4cm

\end_inset


\begin_inset Graphics
	filename pics/lemoncellDC.png
	lyxscale 50
	width 4.6cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
(a)Copper and Zinc plates inserted into a Lemon.
 (b) The DC voltage output from the cell.
\begin_inset CommandInset label
LatexCommand label
name "fig:lemoncell"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Ripe Lemon (or some acid), thin Zinc and Copper plates.
\end_layout

\begin_layout Itemize
A 1
\begin_inset space ~
\end_inset


\begin_inset Formula $k\Omega$
\end_inset

 resistor.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Insert the zinc and copper plates into the lemon.
\end_layout

\begin_layout Itemize
Connect one plate to ground and another to A0, using two wires.
\end_layout

\begin_layout Itemize
Connect the resistor from A0 to ground.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
Voltage across the Copper and Zinc terminals will be nearly .9 volts.
 Connecting the resistor reduces it to .33 volts.
\end_layout

\begin_layout Standard
What is the internal resistance of the cell ?
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
When connected, current will start flowing through the resistor.
 But why the voltage is going down ?
\end_layout

\begin_layout Standard
It does not happen with a new dry-cell.
 Why ?
\end_layout

\begin_layout Standard
Current is the flow of charges and it has to complete the path.
 That means, current has to flow through the cell also.
 Depending on the internal resistance of the cell, part of the voltage gets
 droped inside the cell itself.
\end_layout

\begin_layout Standard
An ideal voltage source should have zero internal resistance.
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Voltage changing with time
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Introduce the concept of time dependent voltages, using a V(t) graph.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/cell-volatge.png
	width 4cm

\end_inset


\begin_inset Graphics
	filename pics/dcvoltage.png
	lyxscale 70
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Plotting DC voltage with Time
\begin_inset CommandInset label
LatexCommand label
name "fig:Graph-of-DC"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
1.5 Volts dry cells
\end_layout

\begin_layout Itemize
Battery holder with leads.

\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect Negative of the dry cell to Ground.
\end_layout

\begin_layout Itemize
Positive terminal of the cell to A0.
\end_layout

\begin_layout Itemize
Observe the graph on the right side window.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Itemize
A horizontal line appears on the Graph, Time on x-axis and voltage on y-axis.

\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Voltage is constant in time.
 A cell is a source of Direct Current (DC).
 Another type of current is called Alternating Current or AC, which changes
 the magnitude and direction with time.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Alternating current (AC)
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Learn about AC, using graphs.
 Get familiar with the sinusoidal voltage waveform.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
A piece of wire.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect SINE to A0.
\end_layout

\begin_layout Itemize
Adjust the horizontal scale to view 4 to 5 cycles.
\end_layout

\begin_layout Itemize
Enable the Checkbox 'FIT'.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/sine-a0.png
	width 2cm

\end_inset


\begin_inset Graphics
	filename pics/sinewave90hz.png
	lyxscale 50
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
AC voltage waveform from SINE
\begin_inset CommandInset label
LatexCommand label
name "fig:Sinewave"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
The waveform is shown in the figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Sinewave"

\end_inset

.
 Enable the 'FIT' option to calculate the amplitude and frequency by fitting
 the data with the equation
\begin_inset Formula $V=V_{0}\sin(2\pi ft+\theta)$
\end_inset

 , where
\begin_inset Formula $V_{0}$
\end_inset

 is the amplitude and
\begin_inset Formula $f$
\end_inset


\begin_inset space ~
\end_inset

is the frequency.

\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The voltage is changing with time.
 It goes to both negative and positive.
 One full cycle takes around 12 milli seconds, ie.
 around 90 cycles per second or 90 Hertz.
 This voltage waveform is generated by using electronic circuits.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
The frequency of the SIN output is around 90 Hz.
 It's variation is due to the 20% tolerance of the capacitors deciding the
 frequency.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
The AC mains supply coming to our houses has a frequency of 50 Hz.
\end_layout

\begin_layout Standard
What is the significance of
\begin_inset Formula $\theta$
\end_inset

 in the equation above ?
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
AC Powerline pickup
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Learn about the AC mains supply.
 Explore the phenomenon of propagation of AC through free space.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
A long piece of wire.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect one end of the wire to A0.

\end_layout

\begin_layout Itemize
Take the other end near the power line (never touch the line) and change
 the orientation of the wire until you get a good signal on the screen.
\end_layout

\begin_layout Itemize
Adjust the horizontal scale to 10 milliseconds per division.
\end_layout

\begin_layout Itemize
Enable the Checkbox 'FIT'.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/pickup.png
	width 4cm

\end_inset


\begin_inset Graphics
	filename pics/sinewave50hz.png
	lyxscale 50
	width 5cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Power line pickup
\begin_inset CommandInset label
LatexCommand label
name "fig:Power-line-pickup"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
The observed waveform is shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Power-line-pickup"

\end_inset

.
 The frequency calculated by fitting the data is 49.65 Hz
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Without making any connection, how we are getting the AC voltage from the
 mains supply ? Do this experiment with a laptop computer staying far away
 from mains supply lines.
\end_layout

\begin_layout Standard
Is it similar to the radiation from a cell phone ?
\end_layout

\begin_layout Standard
Why the frequency is differing from 50 Hz ?
\end_layout

\begin_layout Standard
We are watching the voltage picked up by the wire, it acts as an antenna
 and receives the 50 Hz radiation from the power line.
 Touching the floating end of the wire increases the pickup, you are becoming
 part of the antenna.
 The frequency
\begin_inset Formula $f$
\end_inset

 is calculated by fitting the collected data with the equation
\begin_inset Formula $V=V_{0}\sin(2\pi ft+\theta)$
\end_inset

.
\end_layout

\begin_layout Standard
Try measuring during the daytime and at midnight to compare the measured
 frequecies.
 It depends on the total load on the grid.
 If the power distribution system is really good, the frequency will remain
 constant.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
DC & AC components of a time dependent voltage
\begin_inset CommandInset label
LatexCommand label
name "sec:DC-&-AC"

\end_inset


\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Learn about the AC and DC components of a time dependent voltage.
 Separating AC and DC using a capacitor.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/sqr-a0.png
	width 2cm

\end_inset


\begin_inset Graphics
	filename pics/sqrwave2.png
	lyxscale 50
	width 3.3cm

\end_inset


\begin_inset Graphics
	filename schematics/ac-dc.png
	width 2.5cm

\end_inset


\begin_inset Graphics
	filename pics/sqrwave_dcblocked.png
	lyxscale 50
	width 3.3cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Voltage swinging between 0 and 5 volts (a) Direct connection (b) With a
 DC blocking capacitor
\begin_inset CommandInset label
LatexCommand label
name "fig:Square-wave"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
1
\begin_inset space ~
\end_inset

µF capacitor, 10
\begin_inset space ~
\end_inset

k
\begin_inset Formula $\Omega$
\end_inset

 resistor
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect SQR1 to A0 using the wire.
\end_layout

\begin_layout Itemize
Enter
\shape italic
500
\shape default
 in the Textbox of SQR1 and press Enter key.
\end_layout

\begin_layout Itemize
Adjust the horizontal scale to see several cycles.
\end_layout

\begin_layout Itemize
Insert a 1
\begin_inset space ~
\end_inset

µF between SQR1 and A0
\end_layout

\begin_layout Itemize
Connect 10
\begin_inset space ~
\end_inset

k
\begin_inset Formula $\Omega$
\end_inset

 from A0 to ground.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The observed waveforms with and without the series capacitor are shown in
 figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Square-wave"

\end_inset

.
 The voltage is swinging between 0 and 5 volts.
 After passing through the capacitor the voltage swings from -2.5 volts to
 +2.5 volts.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
What will you get if subtract a 2.5 from the y-cordinate of every point of
 the first graph.
 That is what the capacitor did.
 It did not allow the DC part to pass through.
\end_layout

\begin_layout Standard
This original voltage can be considered as a 5V AC superimposed on a 2.5V
 DC.
\end_layout

\begin_layout Standard
You may need to connect a 10
\begin_inset Formula $k\Omega$
\end_inset

 resistor from A0 to Ground to see a waveform swinging between -2.5 to +2.5
 volts.

\end_layout

\begin_layout Standard
Why the resistor is required?
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Resistance of human body
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Get some idea about the resistance of the human skin and how it varies.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
Two pieces of wire.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Set SQR1 to 500
\end_layout

\begin_layout Itemize
make a connection from SQR1 to A0, through your body
\end_layout

\begin_layout Itemize
Adjust the horizontal scale to see several cycles.
\end_layout

\begin_layout Itemize
Repeat the same by using SINE instead of SQR1.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/conduct-hand.jpg
	lyxscale 40
	width 4.1cm

\end_inset


\begin_inset Graphics
	filename pics/sqrwave_hand.png
	lyxscale 50
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Voltage after passing through the hand.
\begin_inset CommandInset label
LatexCommand label
name "fig:Square-wave-hand"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
The observed waveform is shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Square-wave-hand"

\end_inset

.
 The wave is not clean and the amplitude is reduced from 5 volts.

\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Using the method of comparison, try to calculate the resistance of the portion
 of the hand between the two wires, you were holding.
 The reference resistance is 10
\begin_inset Formula $M\Omega$
\end_inset

, internally connected from A0 to ground.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Temperature dependent resistors
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Show the dependence of resistance on temperature.
 Basic concept of a temperature sensor.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
Thermistor (NTC)
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Negative Temperature Coefficient
\end_layout

\end_inset

.
 Resistance
\begin_inset Formula $1k\Omega$
\end_inset

 at 25 degree Celsius.
\end_layout

\begin_layout Itemize
Cold water
\end_layout

\begin_layout Itemize
A candle or some other heat source.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Standard
\begin_inset Graphics
	filename schematics/ntc.png
	height 0.8cm

\end_inset


\end_layout

\begin_layout Itemize
Connect the Thermistor (NTC) from CS to ground
\end_layout

\begin_layout Itemize
Set CS to 1.0 mA
\end_layout

\begin_layout Itemize
Measure the voltage across the thermistor at different temperatures
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="3">
<features>
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Setup
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
V=IR
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $R=\frac{V}{I}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Place in cold water
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1.2
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1200
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Room Temperature
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0.935
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
935
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Why materials show electrical resistance ?
\end_layout

\begin_layout Standard
Why it depends on temperature ?
\end_layout

\begin_layout Standard
For metals, R increases with T.
 But for insulators and semiconductors it decreases.
 Why ?
\end_layout

\begin_layout Standard
What is the meaning of temperature at molecular level ?
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Light dependent resistors
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Learn about LDR.
 Measure intensity of light and its variation with distance from the source.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
A Light Dependent Resistor, LDR
\end_layout

\begin_layout Itemize
10k
\begin_inset Formula $\Omega$
\end_inset

 resistor
\end_layout

\begin_layout Itemize
A torch bulb without any reflector.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Standard
\begin_inset Graphics
	filename schematics/ldr.png
	height 0.8cm

\end_inset


\end_layout

\begin_layout Itemize
Connect LDR between UPV and A2
\end_layout

\begin_layout Itemize
set UPV to 4 volts.
\end_layout

\begin_layout Itemize
10
\begin_inset space ~
\end_inset

k
\begin_inset Formula $\Omega$
\end_inset

 resistor from A2 to ground
\end_layout

\begin_layout Itemize
Measure the voltage at A2, with no light on LDR.
\end_layout

\begin_layout Itemize
Measure it by keeping the torch bulb at a distance
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Need to be done in a dark room
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
Change the distance and note down the voltage at A2.
\end_layout

\begin_layout Itemize
Calculate the resistance by camparison as described in section
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Measure-resistance-by"

\end_inset


\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The resistance vary from 1
\begin_inset space ~
\end_inset

k
\begin_inset Formula $\Omega$
\end_inset

 to around 100
\begin_inset space ~
\end_inset

k
\begin_inset Formula $\Omega$
\end_inset

 depending on the intensity of light falling on it.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The voltage is proportional to the resistance.
 The resistance decreases with intensity of light.
 If you use a point source of light, the resistance should increase as the
 square of the distance.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Electricity through liquids, DC & AC
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Measure the resistance of liquids.
 Using both DC and AC voltages.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/water.png
	width 3.9cm

\end_inset


\begin_inset Graphics
	filename pics/DCthrough_water.png
	lyxscale 50
	width 3.6cm

\end_inset


\begin_inset Graphics
	filename pics/ACthrough_water.png
	lyxscale 50
	width 3.6cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
(a)Experimrntal setup.
 (b)Total DC voltage and voltage across the 1k
\begin_inset Formula $\Omega$
\end_inset

 resistor.
 (c) Total AC voltage and voltage across 1k
\begin_inset Formula $\Omega$
\end_inset

 resistor.
\begin_inset CommandInset label
LatexCommand label
name "fig:Current through water"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
A 100 ml beaker
\end_layout

\begin_layout Itemize
Common salt
\end_layout

\begin_layout Itemize
10k resistor
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Take some tap water in the beaker
\end_layout

\begin_layout Itemize
Connect a wire to BPV and place other end in water
\end_layout

\begin_layout Itemize
Another wire from A0 to water
\end_layout

\begin_layout Itemize
Connect 10k resistor from A0 to ground.
\end_layout

\begin_layout Itemize
Set 2.8 volts on BPV and watch the value of A0
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
If the voltage is too low use a higher resistance than 10k, otherwise use
 a lower one.
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Try changing BPV from +2.8V to -2.8V and watch the horizontal trace.
\end_layout

\begin_layout Itemize
Repeat the experiment using AC from SINE instead of DC from BPV
\end_layout

\begin_layout Itemize
Calculate the resistance as explained in section
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Measure-resistance-by"

\end_inset


\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="6">
<features>
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $V_{total}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $V_{10k\Omega}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $V_{liq}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $I=\frac{V_{10k\Omega}}{1000}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $R_{liq}=\frac{V_{liq}}{I}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
AC
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
2.6
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
2.3
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0.3
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
.23 mA
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1.3 k
\begin_inset Formula $\Omega$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
DC
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
2.6
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1.3
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1.3
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
.13 mA
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
10 k
\begin_inset Formula $\Omega$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Observed values are shown in the table
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
The values you may get could be very different depending on the ion concentratio
n and presence of impurities in the water used.
\end_layout

\end_inset

.
 The DC and AC resistances seems to be very different.
 However, when you change the polarity of BPV, the voltage across the resistor
 stays around the AC value for a while and then goes down.
 This indicates that the resistance of the liquid increases with time, may
 be due to some bubble formation.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Why the behavior is different for AC and DC ?
\end_layout

\begin_layout Standard
What are the charge carriers responsible for the flow of electricity through
 solutions ?
\end_layout

\begin_layout Standard
Is there any chemical reaction taking place ?
\end_layout

\begin_layout Standard
Try adding some common salt and repeat the measurements.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Transient Response of RC circuits
\begin_inset CommandInset label
LatexCommand label
name "sec:Capacitor-charging-&"

\end_inset


\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
In section
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:DC-&-AC"

\end_inset

, we have seen that a capacitor blocks DC but allows AC to pass through.
 In this experiment, we will explore the nature of current and voltage when
 a voltage step is applied.
 By measuring the voltage across the capacitor as a function of time, we
 can calculate the value of the capacitance.
\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
Voltage across a capacitor while charging through a resistor
\begin_inset Formula \[
V(t)=V_{0}\left(1-e^{-\frac{t}{RC}}\right)\]

\end_inset


\end_layout

\begin_layout Standard
\align left
Voltage across a capacitor while discharging through a resistor
\begin_inset Formula \[
V(t)=V_{0}e^{-\frac{t}{RC}}\]

\end_inset


\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/rc-tran.png
	width 3.2cm

\end_inset


\begin_inset Graphics
	filename pics/CR-transient-screen.png
	lyxscale 50
	width 3.8cm

\end_inset


\begin_inset Graphics
	filename pics/capacitor_linear.png
	lyxscale 50
	width 3.8cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Transient response of RC circuit.
 The third one is the charging of a capacitor through a constant current
 source.
\begin_inset CommandInset label
LatexCommand label
name "fig:Capacitor-screenshot"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
A
\begin_inset Formula $1\mu F$
\end_inset

 capacitor and a
\begin_inset Formula $1k\Omega$
\end_inset

 resistor.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the capacitor from A0 to Ground.
\end_layout

\begin_layout Itemize
Connect the resistor from A0 to OD1.
\end_layout

\begin_layout Itemize
Right click on the Panel and select
\shape italic

\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{RC Circuit}
\end_layout

\end_inset


\shape default
 from the pop-up menu
\end_layout

\begin_layout Itemize
Click on
\shape italic
\emph on

\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
buttonlabel{
\shape italic
\emph on
\lang english
0->5V STEP
\shape default
\emph default
}
\end_layout

\end_inset


\shape default
\emph default
 and
\shape italic
\emph on

\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
buttonlabel{
\shape italic
\emph on
\lang english
5->0V
\shape default
\emph default
STEP}
\end_layout

\end_inset


\shape default
\emph default
 Buttons to plot the graphs
\end_layout

\begin_layout Itemize
Adjust the horizontal scale, if required, and repeat.
\end_layout

\begin_layout Itemize
FIT the curve to extract the time constant RC.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
Applying a 0 to 5V step makes the voltage across the capacitor to rise exponenti
ally as shown in the figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Capacitor-screenshot"

\end_inset

.
 By fitting the graph we can extract the RC time constant and find the values
 of capacitance from it.

\end_layout

\begin_layout Standard
This experiment can be extended to masure die-electric constant of materials
 by making capacitors using them.
 To get the graph shown in
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Capacitor-screenshot"

\end_inset

(c), connect R from CS to A0, C from OD1 to A0, set CS to 1mA and click
 on
\shape italic
5->0V.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Why the graph is Exponential ?
\end_layout

\begin_layout Standard
A capacitor is made of two parallel metal plates separated by a thin layer
 of dielectric material.
 We have connected one plate (call it plate A) to ground and another plate
 (call it B) to OD1 via a resistor.
 Connection to A0 is for monitoring the voltage.
 Initially both plates are at zero volts.
 By clicking on
\shape italic
0->5V
\shape default
 ,we take OD1 to 5 volts.
 A current will start flowing through the resistor to plate B, due to the
 potential difference created.
 This current (flow of charge) will result in an accumulation a charge on
 plate B.
 The voltage at B will be given by
\begin_inset Formula $V=Q/C$
\end_inset

, where Q is called the capacitance.
 As more and more charge arrives, voltage at B also will increase.
 But, as per Ohm's law the current through the resistor is decided by the
 voltage difference across it.
 That mean the current will gradually decrease and reach zero when the voltage
 at plate B becomes 5 volts.
 The time for this is decided by the product RC, and is given by
\end_layout

\begin_layout Standard
\begin_inset Formula \[
V(t)=V_{0}\left(1-e^{-\frac{t}{RC}}\right)\]

\end_inset


\end_layout

\begin_layout Standard
The product RC is called the time constant of the circuit.

\shape italic

\begin_inset Foot
status collapsed

\begin_layout Plain Layout

\shape italic
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capchg.html
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Transient Response of RL circuits
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Explore the nature of current and voltage when a voltage step is applied
 to resistor and inductor in series.
 By measuring the voltage across the inductor as a function of time, we
 can calculate its value.
\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
In an RL circuit
\begin_inset Formula $V=IR+L\frac{dI}{dt}$
\end_inset

 .
 Solving this will give
\begin_inset Formula $I=I_{0}e^{-\frac{R}{L}t}$
\end_inset

 .
 The coefficient of the exponential term R/L can be extracted from the graph
 of voltage across the inductor.
 The resistance of the inductor coil should be included in the calculations,

\begin_inset Formula $R=R_{ext}+R_{L}$
\end_inset

.

\begin_inset Foot
status collapsed

\begin_layout Plain Layout
http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/esc102/node14.html
\end_layout

\end_inset


\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/rl-tran.png
	width 3.2cm

\end_inset


\begin_inset Graphics
	filename pics/LR-downstep.png
	lyxscale 50
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
LR circuit.
 Voltage across the inductor after a 5 to 0V step.
\begin_inset CommandInset label
LatexCommand label
name "fig:LR-circuit.-Voltage"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
\begin_inset Formula $1k\Omega$
\end_inset

 resistor.
\end_layout

\begin_layout Itemize
3000 turns coil, 1000 turns coil & ferrite core
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the 3000 Turns coil from A0 to Ground.
\end_layout

\begin_layout Itemize
Connect the resistor from A0 to OD1.
\end_layout

\begin_layout Itemize
Connect a wire from OD1 to A2 (for accurate measurement of total voltage)
\end_layout

\begin_layout Itemize
Right click on the Panel and select
\shape italic

\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{RL Circuit}
\end_layout

\end_inset


\shape default
 from the pop-up menu
\end_layout

\begin_layout Itemize
Click on
\shape italic
\emph on
\lang french

\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
buttonlabel{0->5V STEP}
\end_layout

\end_inset


\shape default
\emph default
\lang english
 and
\shape italic
\emph on
\lang french

\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
buttonlabel{5->0V STEP}
\end_layout

\end_inset


\shape default
\emph default
\lang english
 Buttons to plot the graphs
\end_layout

\begin_layout Itemize
Adjust the horizontal scale, if required, and repeat.
\end_layout

\begin_layout Itemize
Calculate the value of inductance
\end_layout

\begin_layout Itemize
Repeat by inserting core.
 Repeat with other coils.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The Voltage across the inductor just after a 5V to 0V step is shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:LR-circuit.-Voltage"

\end_inset

.
 The exponential curve is fitted to extract the L/R value.
 The resistance of the coil is measured by comparing it with the known external
 resistance under DC conditions.
 The inductances measured are tabulated below.
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="3">
<features>
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Coil
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Inductance (mH)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resistance (
\begin_inset Formula $\Omega$
\end_inset

)
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
3000 Turns coil
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
126
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
565
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1000 T
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
4.7
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
42
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1000T /ferrite
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
25
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
42
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The applied voltages are above zero, but the graph went to negative voltages.
 Why ?
\end_layout

\begin_layout Standard
What was the current before doing the 5->0 step ? What is back EMF ?
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Transient response of LCR circuits
\begin_inset CommandInset label
LatexCommand label
name "sec:Step-Response-ofRLC"

\end_inset


\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
The response of RL and RC circuits were done in the previous sections.
 Now we will explore the oscillatory nature by connecting L and C in series.
\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
Resonant frequency of series LC circuit =
\begin_inset Formula $\omega_{0}=\frac{1}{2\pi\sqrt{LC}}$
\end_inset

, Damping factor =
\begin_inset Formula $\frac{R}{2}\sqrt{\frac{C}{L}}$
\end_inset

, equal to 1 for critical damping.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
http://en.wikiversity.org/wiki/RLC_circuit
\end_layout

\end_inset


\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/lc-tran.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/LCRdischarge.png
	lyxscale 50
	width 3.5cm

\end_inset


\begin_inset Graphics
	filename pics/LCRdischarge_ferrite.png
	lyxscale 50
	width 3.5cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Transient response of LCR circuit.
 (a)
\begin_inset space ~
\end_inset

Setup (b)
\begin_inset space ~
\end_inset

Result with air core inductor.
 (c)
\begin_inset space ~
\end_inset

With ferrite core
\begin_inset CommandInset label
LatexCommand label
name "fig:LCR-response-setup"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
0.1uF capacitor
\end_layout

\begin_layout Itemize
3000 & 1000 Turns coil
\end_layout

\begin_layout Itemize
Ferrite core
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect Coil from OD1 to A0
\end_layout

\begin_layout Itemize
Capacitor from A0 to ground
\end_layout

\begin_layout Itemize
Right-click on Panel and select
\shape italic

\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{RLC Discharge}
\end_layout

\end_inset


\shape default
 from the menu.
\end_layout

\begin_layout Itemize
Click on Discharge.
 Adjust x-axis and repeat if required.
\end_layout

\begin_layout Itemize
FIT the graph to find the resonant frequency & Damping.
\end_layout

\begin_layout Itemize
Repeat the experiment with ferrite core inserted
\end_layout

\begin_layout Itemize
Repeat with a 1
\begin_inset Formula $k\Omega$
\end_inset

 resistor in series.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/rlc-tran.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/LCRdischarge_1k.png
	lyxscale 50
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
LCR with a 1k series resistor providing damping.
\begin_inset CommandInset label
LatexCommand label
name "fig:LCR-response-screen"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Measurements have been done using the 1000 Turns coil, with and without
 ferrite core, and the 3000 Turn coil.
 The results are tabulated below.
 The capacitance and inductance were measured by an LCR meter.
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="4">
<features>
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
C
\begin_inset Formula $\mu F$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
L mH
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $f=\frac{1}{2\pi}\sqrt{\frac{1}{LC}}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $f_{measured}(Hz)$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
.097
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
3.57
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
8552
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
8430
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
.097
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
23.2
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
3354
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
3400
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
.097
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
125
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1445
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1400
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The under damped waveform require a resistance,
\begin_inset Formula $R=\sqrt{\frac{4L}{C}}=\sqrt{\frac{4\times23.2e-3}{.097e-6}}=963$
\end_inset

 to make it critically damped.
 Result with a 1k
\begin_inset Formula $\Omega$
\end_inset

 series resistor is shown in figure .
\end_layout

\begin_layout Standard
Why the amplitude went up after inserting the ferrite core ?
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Capacitor in AC circuits
\begin_inset CommandInset label
LatexCommand label
name "sec:Capacitor-in-AC"

\end_inset


\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Explore the effect of a series capacitor in AC circuits, under steady state
 conditions.
\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
Impedance of a Capacitor
\begin_inset Formula $X_{c}=\frac{1}{2\pi fC}$
\end_inset

 , where
\begin_inset Formula $f$
\end_inset

 is the frequency in Hertz and
\begin_inset Formula $C$
\end_inset

 is the capacitance in Farads.
 Remember the working of a capacitor explained in section
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Capacitor-charging-&"

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/rc-steadystate.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/CRphaseshift-1uf560.png
	lyxscale 50
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Screenshot showing the total voltage across the RC circuit and the voltage
 across the capacitor.
 C=1 uF and R = 560
\begin_inset Formula $\Omega$
\end_inset

.
\begin_inset CommandInset label
LatexCommand label
name "fig:CRcircuit_voltages"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
1 uF capacitor
\end_layout

\begin_layout Itemize
560
\begin_inset Formula $\Omega$
\end_inset

 resistor
\end_layout

\begin_layout Itemize
A voltmeter, if you want to measure the voltage across the elements not
 directly connected to ground.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect a wire from SINE to A0
\end_layout

\begin_layout Itemize
Connect the capacitor from A0 to A1
\end_layout

\begin_layout Itemize
Connect resistor from A1 to Ground.
\end_layout

\begin_layout Itemize
Enable A1 also.
 Adjust the horizontal scale to view more than 4 cycles.
\end_layout

\begin_layout Itemize
Enable 'FIT' to show RMS voltage, Frequency etc.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The input waveform and the voltage across the resistor
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:CRcircuit_voltages"

\end_inset

.
 The voltage across the capacitor is calculated using Ohm's law, you can
 also measure it with a volt meter.

\end_layout

\begin_layout Standard
The sum of the two voltages looks like more than the total applied voltage.
\end_layout

\begin_layout Standard
Are we violating Ohm's Law ?
\end_layout

\begin_layout Standard
What mistake we are making while adding the voltages ?
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="5">
<features>
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $V_{Tot}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $V_{Res}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $I=\frac{V_{res}}{R}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $V_{cap}=IX_{c}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $V_{R}+V_{c}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
2.6
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
.8
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0.0014
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
2.4
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
3.2
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $X_{c}=\frac{1}{2\pi fC}=\frac{1}{2\pi\times93.6\times1e-6}=1712$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula $V_{c}=IX_{c}=1712\times0.0014$
\end_inset


\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
We need to account for the phase shift introduced by the capacitor
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
http://www.play-hookey.com/ac_theory/ac_rc_series.html
\end_layout

\end_inset

.
 Refer to the next section.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
AC phase shift in RC circuits
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Measure the AC voltage phase shift across the capacitor in an RC circuit.

\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
In an RC circuit, the phase shift across the inductor is given by the equation
\begin_inset Formula $\triangle\Phi=\arctan\left(\frac{X_{c}}{R}\right)$
\end_inset

, where R is the resistance and
\begin_inset Formula $X_{c}$
\end_inset

 is the capacitive reactance.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/rc-steadystate.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/CRphaseshift-1uf560.png
	lyxscale 50
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Screenshot showing phase shifts for R=560
\begin_inset Formula $\Omega$
\end_inset

 and C = 1
\begin_inset Formula $\mu F$
\end_inset

.
\begin_inset CommandInset label
LatexCommand label
name "fig:RC phaseshift"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
1 uF capacitor
\end_layout

\begin_layout Itemize
560
\begin_inset Formula $\Omega$
\end_inset

 resistor (Try other values also)
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect a wire from SINE to A0
\end_layout

\begin_layout Itemize
Connect the capacitor between A0 and A1
\end_layout

\begin_layout Itemize
Connect Resistor from A1 to Ground.
\end_layout

\begin_layout Itemize
Enable A1 also.
 Adjust the horizontal scale to view more than 4 cycles.
\end_layout

\begin_layout Itemize
Enable 'FIT' to show RMS voltage, Frequency and Phase difference.

\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The measured phase shifts are tabulated below.
 The connections and the voltage waveforms are shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:RC phaseshift"

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="5">
<features>
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
C(uF)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
R(k
\begin_inset Formula $\Omega$
\end_inset

)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Freq (Hz)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bigtriangleup\Phi$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\arctan\left(\frac{X_{c}}{X_{R}}\right)$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
560
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
93
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
71.3
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
71.9
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
where
\begin_inset Formula $X_{c}=\frac{1}{2\pi fC}$
\end_inset

 is the impedance of the capacitor, Frequency is 93Hz.

\begin_inset Formula $X_{R}$
\end_inset

 is the resistance.
\end_layout

\begin_layout Standard
Current through a capacitor leads the voltage across it by
\begin_inset Formula $90^{0}$
\end_inset

.
 Why ?
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Why the phase of the voltage advances ? Assume we have connected the AC
 to plate A and at an instance
\begin_inset Formula $t=t_{0}$
\end_inset

 the input voltage is at zero volts.
 We can see that the slope of the curve is maximum there, ie.
 the rate of change of voltage is maximum.
 The capacitor gets charged very fast at this point.
 The plate B also gathers the same charge as plate A , that is how a capacitor
 works.
 The current to plate B is flowing from ground through the resistor and
 we are measuring the IR drop across the resistor, it will be already positive
 when plate A is at zero.
 This results in the phase advance.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
AC phase shift in RL circuits
\begin_inset CommandInset label
LatexCommand label
name "sec:Inductor-in-AC"

\end_inset


\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Measure the AC voltage phase shift in an RL circuit.
\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
Impedance of an Inductor
\begin_inset Formula $X_{L}=2\pi fL$
\end_inset

 , where
\begin_inset Formula $f$
\end_inset

 is the frequency in Hertz and L is the inductance in Henry.
 In an LC circuit, the phase lag across the inductor is given by the equation
\begin_inset Formula $\triangle\Phi=\arctan\left(\frac{X_{L}}{R}\right)$
\end_inset

, where R is the resistance in Ohms.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/rl-steadystate.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/LRphaseshift-125mH-125ohm.png
	lyxscale 50
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Sine wave to LR circuit.
 Phase shift across inductor
\begin_inset CommandInset label
LatexCommand label
name "fig:LR  phaseshift-screen"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Inductor, use the solenoid coils supplied.
\end_layout

\begin_layout Itemize
560
\begin_inset Formula $\Omega$
\end_inset

 and 1
\begin_inset Formula $k\Omega$
\end_inset

 resistors
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect a wire from SINE to A0
\end_layout

\begin_layout Itemize
Connect the Inductor between A0 and A1
\end_layout

\begin_layout Itemize
Connect the 1k
\begin_inset Formula $\Omega$
\end_inset

 resistor from A1 to Ground.
\end_layout

\begin_layout Itemize
Enable A1 also.
 Adjust the horizontal scale to view more than 4 cycles.
\end_layout

\begin_layout Itemize
Enable 'FIT' to show RMS voltage, Frequency and Phase difference.

\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The measured phase shifts are shown below.
 Waveforms for the 125 mH inductor is shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:LR  phaseshift-screen"

\end_inset

.
 The resistance of the inductor also should be included while calculating
 the phase shift.
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="4">
<features>
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
L(mH)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $R=R_{coil}+R_{ext}$
\end_inset

(
\begin_inset Formula $\Omega$
\end_inset

)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bigtriangleup\Phi=\arctan\left(\frac{X_{L}}{X_{R}}\right)$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bigtriangleup\Phi_{measured}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
125
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
565 + 560
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
3.71
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-3.8
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
25
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
42 + 560
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1.39
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-1.4
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Current through an inductor lags by
\begin_inset Formula $90^{0}$
\end_inset


\begin_inset Foot
status collapsed

\begin_layout Plain Layout
http://www.play-hookey.com/ac_theory/ac_inductors.html
\end_layout

\end_inset

.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
If you do not know the value of an inductor, you can use this experiment
 to determine it from the phase shift observed with a known resistor value.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Ferromagnetic material inside inductor
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Observe the effect of ferromagnetic materials inside a solenoid coil inductor.
\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
Self Inductance of a solenoid is given by
\begin_inset Formula $L=\frac{\mu N^{2}A}{l}$
\end_inset

 , where N is the number of turns, A is the cross sectional area,
\begin_inset Formula $\mu$
\end_inset

 is the permeability of the surrounding media and
\begin_inset Formula $l$
\end_inset

 is the length.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/rl-steadystate-ferrite.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/LRphaseshift_ferrite.png
	lyxscale 50
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
LR circuit.
 Effect of Ferrite core.
\begin_inset CommandInset label
LatexCommand label
name "fig:Ferrite_LR-screen"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
1000 turns coil
\end_layout

\begin_layout Itemize
1
\begin_inset Formula $k\Omega$
\end_inset

 resistor (You can use other values also)
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect as explained in
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Inductor-in-AC"

\end_inset


\end_layout

\begin_layout Itemize
Insert an ion rod into the coil and observe the changes
\end_layout

\begin_layout Itemize
Repeat with the 3000 turns coil.

\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The phase shift increased from 3.7 to 11.6 by inserting the ferrite core.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The phase shift went from 3.7 to 11.6 degrees, around 3 times increase in
 the Inductance.
 However, in this case it will be wrong to assume that the permeability
 of the core is 3 Why ? (look at the geometry)
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
RC Integration & Differentiation
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Integrate and differentiate a squarewave using and RC circuit.

\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/RCinteg.png
	width 4cm

\end_inset


\begin_inset Graphics
	filename pics/RCdiff.png
	width 4cm

\end_inset


\begin_inset Graphics
	filename pics/triwave_diff.png
	width 1.6cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
(a)RC Intergrator (b)RC Differentiator (c) Square wave, integrated and different
iated.
\begin_inset CommandInset label
LatexCommand label
name "fig:RC-Integ-diff"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
For the circuit shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:RC-Integ-diff"

\end_inset

(a)
\end_layout

\begin_layout Standard
\begin_inset Formula \[
V_{out}=\frac{1}{RC}\int V_{in}dt\]

\end_inset


\end_layout

\begin_layout Standard
and for the one in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:RC-Integ-diff"

\end_inset

(b)
\begin_inset Formula \[
V_{out}=RC\frac{dV_{in}}{dt}\]

\end_inset


\end_layout

\begin_layout Standard
Figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:RC-Integ-diff"

\end_inset

(c) shows a square wave, with it's integrated and differentiated outputs.
 It is easy to understand as the triagular wave differentiated twice.
 The constant positive slope of triangular wave gives the positive horizontal
 part of the square wave.
 Differentiating the square wave gives spikes at the rising and falling
 edges.
 These are ideal cases.

\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
1uF capacitor
\end_layout

\begin_layout Itemize
1
\begin_inset Formula $k\Omega$
\end_inset

 resistor
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Standard
\begin_inset Graphics
	filename schematics/rc-integ.png
	height 0.8cm

\end_inset


\begin_inset space ~
\end_inset


\begin_inset space ~
\end_inset


\begin_inset space ~
\end_inset


\begin_inset Graphics
	filename schematics/rc-diff.png
	height 0.8cm

\end_inset


\end_layout

\begin_layout Itemize
Connect a wire from SQR1 to A0
\end_layout

\begin_layout Itemize
Connect R from SQR1 to A1
\end_layout

\begin_layout Itemize
Connect C from A1 to Ground.
\end_layout

\begin_layout Itemize
Enable A1.
 Adjust the horizontal scale to view more than 4 cycles.
\end_layout

\begin_layout Itemize
Set SQR1 to 20Hz, 100Hz and 1kHz and view the waveforms.
\end_layout

\begin_layout Itemize
Interchange the positions of R and C to watch differentiation.
\end_layout

\begin_layout Itemize
Click on the Button
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
buttonlabel{
\lang english
FT
}
\end_layout

\end_inset

 to view a Fourier Transform.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/squarewave_interg20hz.png
	lyxscale 50
	width 3.6cm

\end_inset


\begin_inset Graphics
	filename pics/squarewave_interg1khz.png
	lyxscale 50
	width 3.6cm

\end_inset


\begin_inset Graphics
	filename pics/squarewave_diff20hz.png
	lyxscale 50
	width 3.6cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
(a) Integration at 20Hz (b)Integration at 1kHz (c) Differentiation at 20Hz.
 For all cases R=1k
\begin_inset Formula $\Omega$
\end_inset

 and C=1uF
\begin_inset CommandInset label
LatexCommand label
name "fig:Effect-of-RCon squarewave"

\end_inset

.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Integration observed at 20Hz and 1kHz are shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Effect-of-RCon squarewave"

\end_inset

, using an RC of 1 milliseconds.
 At 20Hz, the squarewave passes through the cpacitor with a small distortion.

\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
When the time period becomes comparable with the RC value, the waveform
 becomes triangular.
 The differentiation can only be shown at lower frequency since capturing
 the narrow spike require a fast oscilloscope.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Fourier Analysis
\begin_inset CommandInset label
LatexCommand label
name "sec:Fourier-Transform-**"

\end_inset


\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Learn about Fourier Transform of a signal.
 Time and Frequency domain representations.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
A piece of wire.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect SINE to A0
\end_layout

\begin_layout Itemize
Adjust the horizontal scale to view several cycles.
\end_layout

\begin_layout Itemize
Click on FT to do a Fourier tarnsform
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Itemize
The sinewave and it's Fourier transform are shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Sine-wave-and"

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/sinewave.png
	lyxscale 50
	width 6cm

\end_inset


\begin_inset Graphics
	filename pics/sine90hz-fft.png
	lyxscale 15
	width 5cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
(a)Sine wave.
 (b) Frequency spectrum by Fourier transform.
\begin_inset CommandInset label
LatexCommand label
name "fig:Sine-wave-and"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The original display was showing the amplitude as a function of time, and
 therefore is called the time domain representation of the signal.
 In the Fourier transform plot, frequency is on the x-axis and the y-axis
 shows the relative strength of the frequency components of the signal.
 This is called the frequency domain representation of the signal.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
http://en.wikipedia.org/wiki/Fourier_transform
\end_layout

\end_inset

In this case there is only one dominant peak.
 The small peak at three times the fundamental frequency is a measure of
 distortion of our sine wave.

\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Harmonics of a square wave
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Explore the harmonic content of a square wave using Fourier Transform .
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
A piece of wire.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect terminal 6 (SQR1) to 26 (A0)
\end_layout

\begin_layout Itemize
Enter 100 on the text field near SQR1 and press Enter key.
\end_layout

\begin_layout Itemize
Enable the Yellow Checkbox A0 on the right side window.

\end_layout

\begin_layout Itemize
Adjust the horizontal scale to 10 milliseconds per division.
\end_layout

\begin_layout Itemize
Press A0-FT
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/sqr1000Hz.png
	lyxscale 50
	width 5.5cm

\end_inset


\begin_inset Graphics
	filename pics/sqr1000Hz-fft.png
	lyxscale 15
	width 5.5cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Squarewave and it's Fourier transform
\begin_inset CommandInset label
LatexCommand label
name "fig:Squarewave-and-it's"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
A new window opens displaying a trace as shown in figure .
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Fourier series decomposes any periodic function or periodic signal into
 the sum of a set of simple oscillating functions, namely sines and cosines.
 A square wave function can be represented as
\begin_inset Formula $f(\theta)=sin(\theta)+\frac{sin(3\theta)}{3}+\frac{sin(5\theta)}{5}+\cdots$
\end_inset

.
 In the Fourier transform of a square wave of frequency
\begin_inset Formula $f$
\end_inset

 , there will be a
\begin_inset Formula $3f$
\end_inset

 component (having an amplitude of one third of
\begin_inset Formula $f$
\end_inset

 ),
\begin_inset Formula $5f$
\end_inset

 component (amplitude one fifth) etc.
 as shown in the figure
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Chapter
Electricity & Magnetism
\end_layout

\begin_layout Standard
Electromagnetic induction is demonstrated using a moving magnet and a coil
 powered by an AC voltage.
 Working of transformer is demonstrated using two coils.
 A simple AC generator, capable of generating multi-phase output, is made
 using a rotating magnet.
\end_layout

\begin_layout Section
Electromagnetic induction
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Explore the voltage induced across a coil by a changing magnetic field.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/EMinduction-photo.jpg
	lyxscale 50
	width 5.8cm

\end_inset


\begin_inset Graphics
	filename pics/em_induction.png
	lyxscale 50
	width 4.9cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Voltage induced on a coil by a moving magnet.
\begin_inset CommandInset label
LatexCommand label
name "fig:EM Induction"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Small cylindrical magnets.

\end_layout

\begin_layout Itemize
3000 Tunrns coil and a paper tube to guide the magnet.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the coil from A0 to Ground.
\end_layout

\begin_layout Itemize
From Panel right-click and open
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{EM Induction}
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Click on
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
buttonlabel{
\lang english
Start Scanning
}
\end_layout

\end_inset

.
 A horizontal trace should appear
\end_layout

\begin_layout Itemize
Drop the magnet through the coil until a trace is caught.
\end_layout

\begin_layout Itemize
Repeat the process by changing the parameters like magnet strength, speed
 etc.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The result is shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:EM Induction"

\end_inset

.
 The amplitude inceases with the speed of the magnet.
 From the graph, we can find the time taken by the magnet to travel through
 the coil.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The second peak is bigger than the first peak.
 Why ? Where will be the magnet at the zero crossing of the induced voltage?
\end_layout

\begin_layout Standard
Drop the magnet from different heights and plot the voltage vs square root
 of the height.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
A simple AC generator
\begin_inset CommandInset label
LatexCommand label
name "sec:A-simple-AC"

\end_inset


\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Measure the frequency and amplitude of the voltage induced across a solenoid
 coil by a rotating magnet.
 Gain some understanding about the AC generators by looking at the output
 and the drawbacks of the setup.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/ac-gen.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/ACgen-output-30pct.png
	lyxscale 50
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Voltage output of the AC generator with different speeds of rotation of
 the magnet
\begin_inset CommandInset label
LatexCommand label
name "fig:AC generator output"

\end_inset

.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
A magnet , D = 10 mm, L = 10 mm
\end_layout

\begin_layout Itemize
DC motor
\end_layout

\begin_layout Itemize
3000 Turns coil
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the DC motor to PULSE (T10), mount the magnet horizontally.
\end_layout

\begin_layout Itemize
Connect the coil from A0 to ground
\end_layout

\begin_layout Itemize
Hold the coil perpendicular to the axis of rotation of the motor, close
 to the magnet.
 Be careful not to touch it.
\end_layout

\begin_layout Itemize
Set PULSE to 10 (% duty cycle)
\end_layout

\begin_layout Itemize
Measure the frequency & amplitude by enabling FIT.
\end_layout

\begin_layout Itemize
Repeat by changing PULSE to 20 , 30 and 40 (NOT beyond that)
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The voltage output is shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:AC generator output"

\end_inset

.
 The speed of the motor is nearly proportional to the duty cycle (from 20%
 to 40%)
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Connect another coil to A1 and bring that also near the magnet to view a
 two phase AC waveform.
 You can change the relative phase by changing the angular positions of
 the coils.
\end_layout

\begin_layout Standard
Bring another shorted coil near the magnet to observe the change in frequency.
 The shorted coil is drawing energy from the generator and the speed get
 reduced.

\end_layout

\begin_layout Standard
The magnetic field in this generator is very weak.
 The resistance of the coil is very high and trying to draw any current
 from it will drop most of the voltage across the coil itself.

\begin_inset Foot
status collapsed

\begin_layout Plain Layout
It would be safer to power the motor from a separate variable voltage power
 supply (<3 volts).
 The PULSE output is NOT meant for this job, we are almost short circuiting
 an output pin of the micro-controller.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Mutual induction, transformer
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Demonstrate mutual induction between two coils, working of the transformer.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/transformer.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/mutual_induction.png
	lyxscale 50
	width 3.4cm

\end_inset


\begin_inset Graphics
	filename pics/mutual_induction_Ecore_1kload.png
	lyxscale 50
	width 3.4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Mutual Induction between two coils.(a) Connections (b) using a ferrite rod
 (c) using two E shaped cores
\begin_inset CommandInset label
LatexCommand label
name "fig:Mutual-Induction-between"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Two coils, each having 3000 turns.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the first coil from SINE to ground.
\end_layout

\begin_layout Itemize
A wire from SINE to A0, for monitoring the input wave form.
\end_layout

\begin_layout Itemize
Second coil from A1 to Ground.
\end_layout

\begin_layout Itemize
Align coils and insert the ferrite rod through them.
\end_layout

\begin_layout Itemize
Enable A1 and FIT
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The applied waveform and the induced waveform are shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Mutual-Induction-between"

\end_inset

.
 A changing magnetic filed is causing the induced voltage.
 In the previous two experiments, the changing magnetic field is created
 by the movement of permanent magnets.
 In the present case the changing magnetic field is created by a time varying
 current.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The output should have been in phase with the input as per the theory.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
http://sound.westhost.com/xfmr.htm
\end_layout

\end_inset

However, this is not happening if the coupling is not enough.

\end_layout

\begin_layout Standard
With more ferrite material, the phase shift is as expected from the theory.
\end_layout

\begin_layout Standard
Try doing this experiment using a squarewave of 100 Hz, 1000 Hz etc.
 Connect a 1k
\begin_inset Formula $\Omega$
\end_inset

 resistor from secondary to ground to reduce the ringing.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Electromagnet, solenoid coil
\begin_inset CommandInset label
LatexCommand label
name "sec:Magnetic-Effect-of"

\end_inset


\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Demonstrate the magnetic effect of electric current, using a solenoid coil
 and permanent magnet.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/coil-magnetpendulum-photo.JPG
	lyxscale 50
	width 5cm

\end_inset


\begin_inset Graphics
	filename pics/solenoid_field.jpg
	lyxscale 40
	width 6cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
(a) Current carrying solenoid repelling a permanent magnet.
 (b)Magnetic field of a current carrying solenoid
\begin_inset CommandInset label
LatexCommand label
name "fig:Solenoid Magnetic-field"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Solenoid coil.
\end_layout

\begin_layout Itemize
Two Button shaped magnets
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the solenoid from OD0 to Ground.
\end_layout

\begin_layout Itemize
Make a pendulum using a paper strip and the magnets.
\end_layout

\begin_layout Itemize
Hang the pendulum near the solenoid as shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Solenoid Magnetic-field"

\end_inset


\end_layout

\begin_layout Itemize
Take OD0 to HIGH and observe the force
\end_layout

\begin_layout Itemize
Reverse the direction of the pendulum
\end_layout

\begin_layout Itemize
Place the pendulum on the other side of the coil.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The solenoid behaves just like a bar magnet.
 Hang the pendulum magnet near the coil and change the direction of current
 by interchanging the wires connected to OD0 and ground
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The magnetic field of a solenoid coil is shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Solenoid Magnetic-field"

\end_inset

.
 The direction of field depends on the direction of the current.

\end_layout

\begin_layout Standard
Find the direction of winding of the solenoid from the above observations.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Eddy current braking
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Demonstrate the effect of eddy currents by moving a conductor perpendicular
 to a magnetic field.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
DC motor
\end_layout

\begin_layout Itemize
Annular disc of aluminium
\end_layout

\begin_layout Itemize
magnet 10mm x 10mm
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Fix the disc on the motor using a cello-tape
\end_layout

\begin_layout Itemize
Connect motor between PULSE and Ground
\end_layout

\begin_layout Itemize
Set PULSE to 30%
\end_layout

\begin_layout Itemize
Bring the magnet close to the disc surface
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The speed of rotation reduces when magnet is brought near the surface of
 the disc.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Eddy currents are created when a conductor experiences changes in the magnetic
 field.
 If either the conductor is moving through a steady magnetic field, or the
 magnetic field is changing around a stationary conductor, eddy currents
 will occur in the conductor.

\end_layout

\begin_layout Chapter
Sound
\end_layout

\begin_layout Standard
Sound is generated from electrical signals and frequency of sound is measured
 by converting it back into electrical signal.
 Reflection and interference of sound are explored.
 Velocity of sound is measured by observing the phase shift of digitized
 sound with distance.

\end_layout

\begin_layout Section
Generating sound
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
To find some answer to questions like:
\end_layout

\begin_layout Itemize
What is a description of sound?
\end_layout

\begin_layout Itemize
What are the characteristics of sound waves?
\end_layout

\begin_layout Itemize
How is sound created and detected?
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
Loudspeaker
\end_layout

\begin_layout Itemize
Piezo electric disc
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the 150
\begin_inset Formula $\Omega$
\end_inset

 speaker from SQR1 to GND
\end_layout

\begin_layout Itemize
Set SQR1 to 1000.

\end_layout

\begin_layout Itemize
Listen to the sound.

\end_layout

\begin_layout Itemize
Change the frequecy to note the difference in the sound generated.
\end_layout

\begin_layout Itemize
Repeat the same using Piezo disc also
\end_layout

\begin_layout Itemize
Right Click and open
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{Music}
\end_layout

\end_inset

 from the menu
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Itemize
The pitch of sound produced depends on the frequency.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
How the loudspeaker is making sound? When the AC voltage is applied, the
 diaphragm of the speaker moves back and forth.
 In one forward movement, it pushes against the air in front of it and creates
 a compressed or high pressure region.
 Next it moves backward creating a low pressure region just behind the high
 pressure region created earlier, and completed one cycle.
 In the next forward movement, another high pressure region is created and
 it pushes the high and low pressure regions created by the last cycle.
 This process is repeated and the alternate high and low pressure regions
 travels forward.
 This is sound.
\end_layout

\begin_layout Standard
Generating different frequencies creates music.
 However the richness is provided by the right amount of harmonics for each
 frequency, something that we cannot control in this setup.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Frequency of sound
\begin_inset CommandInset label
LatexCommand label
name "sec:Sound Frequency"

\end_inset


\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Measure the frequency of sound by converting it in to an electrical signal.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/sound-freq.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/sound3012hz.png
	lyxscale 50
	width 3.5cm

\end_inset


\begin_inset Graphics
	filename pics/sound2000hz.png
	lyxscale 50
	width 3.5cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Digitizing sound.(a)Connections (b) Frequency is 3012 Hz (c) 2000 Hz.
\begin_inset CommandInset label
LatexCommand label
name "fig:Digitized sound screen"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Microphone assembly
\end_layout

\begin_layout Itemize
Piezo disc
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the microphone between T15 & T16.
 Bias resistor to UPV
\end_layout

\begin_layout Itemize
Connect amplifier output (T13) to A0
\end_layout

\begin_layout Itemize
Set 5 volts on UPV.
\end_layout

\begin_layout Itemize
Connect Speaker from SQR1 to Ground.
\end_layout

\begin_layout Itemize
Set SQR1 to 3000 Hz and fix the speaker facing it
\end_layout

\begin_layout Itemize
Watch the waveform and adjust the timebase
\end_layout

\begin_layout Itemize
Enable FIT to measure the frequency
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="2">
<features>
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
freq.
 set
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
freq.
 measured
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
3012.0
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
3011.94
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
2000
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
2000.46
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
By fitting the digitized data, we are able to extract the frequency information.
 However, the waveform looks cleaner near 3000 Hz.
 This is because the resonant frequency of the speaker is near 3000 Hz.
\end_layout

\begin_layout Standard
The output of 2000 Hz contains the 6000 Hz component.
 Click on FT to view the Power specta and compare both.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Sound waves creates pressure variations in the medium through which it travels.
 The microphone generates a voltage is proportional to the pressure.
 Since this signal is very small, we amplify it 50 times before digitizing
 it.
 The voltage variations are in tune with the pressure variations.
 You can consider the microphone as a pressure sensor, but working only
 for time varying pressures.

\end_layout

\begin_layout Standard
Repeating the experiment will give results that may look strange at first
 sight.
 Powering by 100 Hz will give you a frequency of around 3900 Hz, but with
 a small amplitude.
 Resonance is again the reason.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Velocity of sound
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Calculate the velocity of sound by measuring the air pressure variation
 with distance.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/sound-vel.png
	width 4cm

\end_inset


\begin_inset Graphics
	filename pics/sound_waves.png
	lyxscale 80
	width 6.2cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
(a)Experimental setup (b) Schematic of the propagation of sound waves, and
 the variation of microphone output with pressure.

\begin_inset CommandInset label
LatexCommand label
name "fig:Sound-waves"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Piezo disc
\end_layout

\begin_layout Itemize
Microphone assembly
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the Piezo from SQR1 to Ground
\end_layout

\begin_layout Itemize
Connect the microphone assembly and set UPV to 5 volts.
\end_layout

\begin_layout Itemize
Connect Amplifier output to A0 and SQR1 to A1
\end_layout

\begin_layout Itemize
Right click and Start
\shape italic

\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{Velocity of Sound}
\end_layout

\end_inset


\shape default
from the menu
\end_layout

\begin_layout Itemize
Keep the Piezo on the edge of a piece of soft cloth, facing the microphone
\end_layout

\begin_layout Itemize
Adjust the distance to make the waveforms in phase
\end_layout

\begin_layout Itemize
Slide it away to make the waveform out of phase, without moving the cloth.
\end_layout

\begin_layout Itemize
Measure the distance from the edge of the cloth to the current position.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/sound_inphase.png
	lyxscale 50
	width 5.4cm

\end_inset


\begin_inset Graphics
	filename pics/sound_outofphase.png
	lyxscale 50
	width 5.4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Sound amplitude captured at half wave length apart.
\begin_inset CommandInset label
LatexCommand label
name "fig:Sound-amplitude-captured"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
The amplitude of sound captured at two points is shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Sound-amplitude-captured"

\end_inset

.
 The squarewave is the voltage driving the piezo electric disc.
 To change the phase of the sinusoidal wave, the microphone output, by 180
 degrees ( half wavelength) the microphone is moved by 4.3 cm.
 The velocity of sound is given by
\begin_inset Formula $v=f\lambda=4000*2*0.043=344$
\end_inset

 meter per second.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Sound travels as a series of compressions and rarefactions.
 The lower part of figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Sound-waves"

\end_inset

 shows the High and Low pressure regions along the direction of travel of
 the sound wave.
 The pressure as a function of time at any stationary point on the path
 is given by the microphone output, as shown in the upper part of figure

\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Sound-waves"

\end_inset


\end_layout

\begin_layout Standard
We can display the pressure variation at any point with respect to the variation
 at the starting point.
 The relative phase of the two waveforms changes when you move the microphone.
 Moving by one wavelength changes the phase by 360 degrees.
 We have moved half wavelength to makethe phase differ by 180 degrees.
 The velocity of sound can be calculated by multiplying the frequency and
 the measured wavelength.
\end_layout

\begin_layout Standard
Why use the folded soft cloth cloth ? Why not do it on a hard surface ?
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Reflection of sound
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Study the nature of sound reflection from a hard surface
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
Microphone assembly
\end_layout

\begin_layout Itemize
Piezo electric disc, powered by SQR1.
\end_layout

\begin_layout Itemize
A 10cm x 10cm hard sheet, plastic or cardboard.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the Microphone as explained in section
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Sound Frequency"

\end_inset


\end_layout

\begin_layout Itemize
Connect the Piezo from SQR1 to Ground.
\end_layout

\begin_layout Itemize
Fix the mic and buzzer facing the same direction
\end_layout

\begin_layout Itemize
Watch the amplitude of A0.
\end_layout

\begin_layout Itemize
Keep a piece of paper in front and capture again.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
Sound is getting reflected from a hard surface.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Change the orientation of reflector and observe the changes.
 How does it compare with the reflection of light from a mirror (or rather
 from a white sheet of paper)
\end_layout

\begin_layout Standard
Try the reflection from a soft surface like cloth or sponge.
\end_layout

\begin_layout Standard
The effect of reflection is what forced us to use the cloth surface in the
 previous experiment.
 Try placing a hard surface parallel to the direction of sound to see the
 effect of it on the phase difference.
 The sound travelling directly interfere with the part reflected from the
 hard surface results in phase change at the microphone.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Interference of sound
\begin_inset CommandInset label
LatexCommand label
name "sec:Interference-of-sound"

\end_inset


\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Study the interference of sound from two individual sources
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/sound-beats.png
	width 5cm

\end_inset


\begin_inset Graphics
	filename pics/sound_beats.png
	lyxscale 40
	width 6cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Beats created using two nearby frequencies.
\begin_inset CommandInset label
LatexCommand label
name "fig:SoundBeats"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Condenser microphone
\end_layout

\begin_layout Itemize
Two Piezo electric discs, powered by SQR1 and PULSE.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Make connections as shown in the figure.
\end_layout

\begin_layout Itemize
Right Click and start
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{Interference of Sound}
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Set SQR1 to 4200 Hz and PULSE to 3800 Hz
\end_layout

\begin_layout Itemize
Adjust distances to get clear beat pattern.
\end_layout

\begin_layout Itemize
Repeat with other values of frequencies.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The individual frequencies are 4201.7 Hz and 3816.8, differing by 384.9 Hz.
 From figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:SoundBeats"

\end_inset

 it can be seen that one wave envelope is around 2.65 mS, ie.
 a frequency of around 380 Hz.
 Wavelength is the distance between two minimum pressure points.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The relative strength of the individual frequency components can be measured
 by taking a Fourier transform of the output.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Analysing Music
\begin_inset Foot
status open

\begin_layout Plain Layout
Contributed by jithinbp at gmail.com
\end_layout

\end_inset


\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
Guitar with someone who knows how to use it
\end_layout

\begin_layout Itemize
Microphone assembly
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the microphone between T15 & T16
\end_layout

\begin_layout Itemize
Bias to UPV and set it to 5 volts
\end_layout

\begin_layout Itemize
Play different notes and click on FT to take the Fourier transform
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The results are shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Fourier-analysis-of Music"

\end_inset

.
 Base string E is used.
 Ratio between notes is given by
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="8">
<features>
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Sa
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Re
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Ga
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Ma
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Pa
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Dha
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Ni
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Sa
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
9/8
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
5/4
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
4/3
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
3/2
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
5/3
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
15/8
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
2
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/sariga.png
	lyxscale 50
	width 6cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Fourier analysis of musical notes.
\begin_inset CommandInset label
LatexCommand label
name "fig:Fourier-analysis-of Music"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Velocity, using ultrasound
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Measure the velocity of sound from the time of flight of ultrasound bursts.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/40kHz-piezo-photo.jpg
	lyxscale 50
	width 4cm

\end_inset


\begin_inset Graphics
	filename schematics/ultra-sound.png
	width 3cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
(a)Experimental setup (b) Connections
\begin_inset CommandInset label
LatexCommand label
name "fig:Ultrasound"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
40 kHz piezo transmitter and receiver
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the Transmitter Piezo from OD1 to Ground
\end_layout

\begin_layout Itemize
Receiver from T15 to Ground.
\end_layout

\begin_layout Itemize
Right click and open
\shape italic

\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{40 kHz Piezo TOF}
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Place the Transmitter and receiver facing each other at 5 cm
\end_layout

\begin_layout Itemize
Measure Time of Travel
\end_layout

\begin_layout Itemize
Repeat at 6 and 7 cm also
\end_layout

\begin_layout Itemize
Calculate velocity of sound from the differences in distance and time
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features>
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Distance
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Time(usec)
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
4
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
223
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
5
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
253
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
6
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
282
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
In this experiment, we use a pair of 40 kHz piezo electric crystals to study
 the propagation of sound in air.
 We apply a 5 volts pulse, 13 microseconds wide, to the transmitter piezo
 to make it undergo mechanical vibrations to generate a 40 kHz sound wave
 burst.
 The receiver piezo kept at a distance converts this sound waves back into
 an electrical signal.
 It is amplified and the time interval between the pulse and the arrival
 of the waves at the receiver is measured.

\end_layout

\begin_layout Standard
To eliminate systematic errors like the response time of the transmitter,
 amplifier delays etc., we use the difference in time with change in distance.

\begin_inset Formula $0.02/(0.000282-0.000223)=338m/sec$
\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Forced Oscillations of Piezo-electric crystal
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Study the behavior of a Piezo-electric disc at various excitation frequencies.
 This is just an exploration.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
Piezo disc
\end_layout

\begin_layout Itemize
Microphone assembly
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the Piezo from SQR1 to Ground
\end_layout

\begin_layout Itemize
Connect the microphone to T15, T16 and T31
\end_layout

\begin_layout Itemize
Right click and open
\shape italic

\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{Interference of Sound}
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Place the Tansmitter and receiver facing each other
\end_layout

\begin_layout Itemize
Set NS (number of samples) to 800
\end_layout

\begin_layout Itemize
Tick SQR1, set it to 200
\end_layout

\begin_layout Itemize
Tick START
\end_layout

\begin_layout Itemize
Adjust distance and click on FFT
\end_layout

\begin_layout Itemize
Change SQR1 to 500, Disable and Enable START
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The resonant frequency of the Piezo crystal is around 3600 Hz, where it
 gives maximum amplitude as shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Piezo-Sound-output"

\end_inset

(a).
 When the excitation frequency is 100 Hz, the piezo gets a kick every 5
 milli seconds, as shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Piezo-Sound-output"

\end_inset

(b), ie.
 at rising and falling edges of the exciting squarewave.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status collapsed

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/piezo-3600hz.png
	lyxscale 50
	width 5cm

\end_inset


\begin_inset Graphics
	filename pics/piezo-100hz.png
	lyxscale 50
	width 5cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Sound output from Piezo (a)Excitation frequency 3625 Hz (b) Excitation frequency
 100 Hz
\begin_inset CommandInset label
LatexCommand label
name "fig:Piezo-Sound-output"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status collapsed

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/piezo-fft-100hz.png
	lyxscale 70
	width 5cm

\end_inset


\begin_inset Graphics
	filename pics/piezo-fft-500hz.png
	lyxscale 70
	width 5cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Fourier power spectrum of the sound from Piezo disk.
 (a)Excited by 100 Hz (b)Excited by 500 Hz.
\begin_inset CommandInset label
LatexCommand label
name "fig:Piezo-Fourier-spectrum"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The Fourier power spectrum shows that the output is amplitude modulated.
 The resonant frequency peak has sidebands at twice the driving frequency.
 This behavior is seen only at lower excitation frequencies.
\end_layout

\begin_layout Standard
It may be interesting to repeat this study using a variable frequency sine
 wave instead of the square wave.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Chapter
Electronics
\end_layout

\begin_layout Standard
The non-linear elements like diodes and transistors are studied by drawing
 their characteristic curves and making simple circuits to demonstrate their
 functioning.
 Photo-transistor is used for transparency measurements, optical signal
 transmission and for timing the mechanical movements.
 Amplitude and Frequency modulation are explored.
\end_layout

\begin_layout Section
Half wave rectifier, PN junction
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Learn the working of a PN junction diode.
 Making DC from a sinusoidal AC.
 Filtering to reduce the AC component.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/half-wave.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/diode-halfwave.png
	lyxscale 50
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Diode as a half wave rectifier.
\begin_inset CommandInset label
LatexCommand label
name "fig:Diode-rectifier"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
1N4148 diode, 1 k
\begin_inset Formula $\Omega$
\end_inset

 resistor
\end_layout

\begin_layout Itemize
1 uF and 100 uF capacitors.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect SINE to A0
\end_layout

\begin_layout Itemize
Diode from A0 to A1
\end_layout

\begin_layout Itemize
Load resistor from A1 to Ground
\end_layout

\begin_layout Itemize
View the waveform on A0 and A1
\end_layout

\begin_layout Itemize
Add different values of filter capacitors from A1 to ground
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/diode-halfwave-1uF.png
	lyxscale 50
	width 5cm

\end_inset


\begin_inset Graphics
	filename pics/diode-halfwave-100uF.png
	lyxscale 50
	width 5cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Rectifier with Filter.
 (a) 1 uF (b) 100 uF.
\begin_inset CommandInset label
LatexCommand label
name "fig:Rectifier-with-Filter"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
The negative half is removed by the diode as shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Diode-rectifier"

\end_inset

.
 Also notice that the voltage in the positive half is reduced by around
 0.7 volts, the knee voltage of a silicon diode.
 A load resistor is required for the proper operation of the circuit, it
 could be more than 1k
\begin_inset Formula $\Omega$
\end_inset

 but do NOT use very low values since our AC source can drive only up to
 5 mA current.
\end_layout

\begin_layout Standard
The effect of a capacitor is shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Rectifier-with-Filter"

\end_inset

.
 We can see that the capacitor charges up and then during the missing cycle
 it maintains the voltage.
 The remaining AC component is called the ripple in the DC.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Can we use very large capacitance to reduce the ripple ?
\end_layout

\begin_layout Standard
During what part of the cycle current flows through the diode ?
\end_layout

\begin_layout Standard
Amount of peak current is decided by what ?
\end_layout

\begin_layout Standard
Do not get the impression that you can reduce ripple by increasing the capacitan
ce.
 During the rising part of the positive half cycle, the capacitive reactance
 decides the current through the diode, and in practical circuits it should
 not exceed diode limits.

\end_layout

\begin_layout Standard
Practical circuits use full wave rectifier or bridge rectifier.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
180
\begin_inset Formula $^{0}$
\end_inset

out of phase sine waves
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
To demonstrate the working of a fullwave rectifier using two diodes, we
 need two AC waveforms differing by 180 degree in phase.
 We do this by inverting the output of SINE using an inverting amplifier.
 The gain is made near unity by feeding the amplifier input through a 10k
\begin_inset Formula $\Omega$
\end_inset

 series resistor.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
We can also generate two out of phase waveforms by placing two coils on
 the opposite side of the rotating magnet, explained in section
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:A-simple-AC"

\end_inset

.
\end_layout

\end_inset


\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status collapsed

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/sine-180deg.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/sine-two-180deg.png
	lyxscale 50
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Inverting Amplifier making 180
\begin_inset Formula $^{0}$
\end_inset

out of phase sine wave.
\begin_inset CommandInset label
LatexCommand label
name "fig:Inverting-Amplifier-making"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
10 k
\begin_inset Formula $\Omega$
\end_inset

 resistor
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect as shown in the figure
\end_layout

\begin_layout Itemize
View the waveforms on A0 and A1
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The result is shown in the figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Inverting-Amplifier-making"

\end_inset

.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The amplitudes are not exactly equal.
 The gain is given by
\begin_inset Formula $G=\frac{10000}{10000+100}$
\end_inset

.

\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Diodes, Fullwave rectifier
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Make a fullwave rectifier from two AC waveforms differing by 180 degree
 in phase.

\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/full-wave.png
	width 4cm

\end_inset


\begin_inset Graphics
	filename pics/diode-fullwave.png
	lyxscale 50
	width 5.7cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Full wave rectifier using two diodes.
\begin_inset CommandInset label
LatexCommand label
name "fig:Diode-fullwave-rectifier-1"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Two 1N4148 diodes
\end_layout

\begin_layout Itemize
1 k
\begin_inset Formula $\Omega$
\end_inset

 and 10 k
\begin_inset Formula $\Omega$
\end_inset

 resistors
\end_layout

\begin_layout Itemize
1 uF and 100 uF capacitor.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect SINE to A0
\end_layout

\begin_layout Itemize
Connect SINE to T17 through a 10k
\begin_inset Formula $\Omega$
\end_inset

 resistor.
\end_layout

\begin_layout Itemize
One Diode from A0 to A1
\end_layout

\begin_layout Itemize
Another Diode from T18 to A1
\end_layout

\begin_layout Itemize
1k
\begin_inset Formula $\Omega$
\end_inset

 resistor from A1 to Ground
\end_layout

\begin_layout Itemize
View the waveform on A0 and A1
\end_layout

\begin_layout Itemize
Add Capacitor from A1 to ground
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The result is shown in the figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Diode-fullwave-rectifier-1"

\end_inset

.
 Adding capacitors to reduce the ripple is left as an exercise to the user.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
This is only to demonstrate the working of a full wave rectifier.
 You cannot draw only draw few milli amperes of current from this circuit.
\end_layout

\begin_layout Standard
Why fullwave rectifier is superior to halfwave rectifier ?
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Diode I-V characteristic
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Draw the I-V Characteristic of diode.
 Examine the Diode equation.
\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
The IV characteristic of an ideal PN junction diode is given by equation
\begin_inset Formula \[
I=I_{0}\left(e^{\frac{qV}{kT}}-1\right)\]

\end_inset


\end_layout

\begin_layout Itemize
\begin_inset Formula $I_{0}$
\end_inset

 ,Reverse saturation current
\end_layout

\begin_layout Itemize
q , Charge of electron
\end_layout

\begin_layout Itemize
k, Boltzmann constant
\end_layout

\begin_layout Itemize
T, Absolute temperature
\end_layout

\begin_layout Standard
For practical (non-ideal) diode, the form used is.
\begin_inset Formula \[
I=I_{0}\left(e^{\frac{qV}{nkT}}-1\right)\]

\end_inset


\end_layout

\begin_layout Standard
where
\begin_inset Formula $n=1$
\end_inset

 for an ideal diode.
 For practical diodes it varies from 1 to 2.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/diode-iv.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/diode_4148.png
	lyxscale 40
	width 3.7cm

\end_inset


\begin_inset Graphics
	filename pics/diode_zener_iv.png
	lyxscale 40
	width 3.7cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Diode IV characteristic curves for 1N4148 and a 3.3 volts zener diode.
\begin_inset CommandInset label
LatexCommand label
name "fig:Diode-IV-characteristic"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Diodes 1N4148 and a 3.3 volts Zener diode (To see the reverse biased curve).
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the 1N4148 diode from I-V to Ground.
 (N side to ground)
\end_layout

\begin_layout Itemize
Connect IV to A0 by a wire.
\end_layout

\begin_layout Itemize
Right Click and select
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{Diode IV}
\end_layout

\end_inset

 from the menu.
\end_layout

\begin_layout Itemize
Click on START to draw the characteristic curve.
\end_layout

\begin_layout Itemize
Click on FIT to calculate the Diode Ideality factor.
\end_layout

\begin_layout Itemize
Replace 1N4148 with the Zener diode.
\end_layout

\begin_layout Itemize
Enable the ZENER Checkbox and click
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
buttonlabel{START}
\end_layout

\end_inset

.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The curves obtained are shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Diode-IV-characteristic"

\end_inset

.
 The value of n for 1N4148 is 1.93 and for the zener it is 1.5.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
We have calculated the value of
\begin_inset Formula $n$
\end_inset

 by fitting the experimental data with the equation.
 The ideality factor of the Zener is calculated fitting the forward biased
 part of the data only.
\end_layout

\begin_layout Standard
Repeat the experiment by heating the diode to different temperatures.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Light emitting diodes, LED
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Plot IV curves for LEDs of different wavelengths.
 Relate to Plank's constant.
\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
Energy of photon from is given by
\begin_inset Formula $E=h\nu=hc/\lambda$
\end_inset

 .
 This energy is equal to the energy of an electron that overcomes the junction
 barrier and is given by
\begin_inset Formula $E=eV_{0}$
\end_inset

.
 So Plank's constant
\begin_inset Formula $h=eV_{0}\lambda/c$
\end_inset

 , where
\begin_inset Formula $\lambda$
\end_inset

 is the wavelength of light from the LED,
\begin_inset Formula $e$
\end_inset

 the charge of electron and
\begin_inset Formula $c$
\end_inset

 the velocity of light.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/diode-iv.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/diode-LED-iv.png
	lyxscale 50
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
IV characteristics of Blue & Green LEDS
\begin_inset CommandInset label
LatexCommand label
name "fig:LED IV-char"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Red, Blue, Green and Yellow LEDs.
 All with clear glass cover, ie.
 not colored.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Right click on the Panel and open
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{LED IV}
\end_layout

\end_inset

 from the popup menu.
\end_layout

\begin_layout Itemize
Connect the diodes from I-V to Ground, one by one, and plot the graph.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The observed characteristics are shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:LED IV-char"

\end_inset

.
 The linear part of the curve is fitted to find the x-intercept point, and
 it is 1.788 for the red LED
\begin_inset Formula $(\lambda=660nm)$
\end_inset

, which gives
\begin_inset Formula \[
h=\frac{1.6e-19\times1.788\times600e-9}{3e-8}=6.29e-34\]

\end_inset


\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard

\shape italic
Note: This need to be done more accurately.
 Compare the ratio of voltages with wavelength to estimate the accuracy
 of measurements.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Transistor CE characteristic
\begin_inset CommandInset label
LatexCommand label
name "sec:Transistor-CE-Characteristic"

\end_inset


\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Plot the CE characteristic curve of a transistor.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
2N2222 transistor, 200
\begin_inset Formula $k\Omega$
\end_inset

 resistor, wires
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Solder two small wires to the collector.

\end_layout

\begin_layout Itemize
Solder the resistor to the base.
\end_layout

\begin_layout Itemize
Connect Base to UPV (0 to 5V output)
\end_layout

\begin_layout Itemize
Collector to IV, and to A0 for voltage monitoring
\end_layout

\begin_layout Itemize
emitter to Ground
\end_layout

\begin_layout Itemize
Right-click on Panel and open
\shape italic

\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{Transistor CE}
\end_layout

\end_inset


\shape default
 from the menu
\end_layout

\begin_layout Itemize
Enter the Bias supply voltage to the base and
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
buttonlabel{START}
\end_layout

\end_inset

.
 Repeat for different Vb.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/tran-ce.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/tran_ce.png
	lyxscale 50
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Transistor common emitter characteristics
\begin_inset CommandInset label
LatexCommand label
name "fig:Transistor-common-emitter"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\begin_layout Standard
The characteristic curves for different base currents are shown in figure

\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Transistor-common-emitter"

\end_inset

.

\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
We are connecting the Collector to a I-V , which is connected internally
 to BPV.
 The base current is set by setting the voltage at one end of the 200 k
\begin_inset Formula $\Omega$
\end_inset

 resistor, the other end is connected to the transistor base.
 The value of base current is calculated by
\end_layout

\begin_layout Standard
\begin_inset Formula \[
I_{b}=\frac{V_{bias}-0.6}{200\times10^{3}}\times10^{6}\mu A\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Transistor amplifier (CE)
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Demonstrate the working of a transistor amplifier in common emitter configuratio
n.
 The operating point is set by changing the bias voltage, using UPV.
 An AC signal is generated using the loudspeaker as a microphone and this
 input is given to the base through DC blocking capacitor.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/tran-amp.png
	width 4cm

\end_inset


\begin_inset Graphics
	filename pics/tran_amp2V.png
	lyxscale 50
	width 3.4cm

\end_inset


\begin_inset Graphics
	filename pics/tran_amp4V.png
	lyxscale 50
	width 3.4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Transistor amplifier at different operating points.(a) Setup (b)
\begin_inset Formula $Bias=2V$
\end_inset

 (c)
\begin_inset Formula $Bias=4V$
\end_inset


\begin_inset CommandInset label
LatexCommand label
name "fig:Transistor-amplifier-at"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Transistor holder with 200
\begin_inset Formula $k\Omega$
\end_inset

 resistor and
\begin_inset Formula $.1\mu F$
\end_inset

 capacitor at the Base.
\end_layout

\begin_layout Itemize
Small Loudspeaker, to be used as a microphone
\end_layout

\begin_layout Itemize
Piezo disk, to generate sound.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Transistor Collector to IV and A0
\end_layout

\begin_layout Itemize
Connect Transistor Base to UPV
\end_layout

\begin_layout Itemize
Piezo Disc to SQR1 and set SQR1 to 3000 Hz
\end_layout

\begin_layout Itemize
Small loudspeaker to Base through the 0.1
\begin_inset Formula $\mu F$
\end_inset

 capacitor, other end Ground.
\end_layout

\begin_layout Itemize
Set Bias voltage on UPV.
 Try values from 1V to 5V.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The collector voltage for different base voltages are shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Transistor-amplifier-at"

\end_inset

.

\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Remember that the voltage gain is not same as the transistor
\begin_inset Formula $\beta$
\end_inset

 , but it depends on the resistance in the collector circuit.
 In our setup the the collector is connected to 5V through a 1k
\begin_inset Formula $\Omega$
\end_inset

 resistor.
\end_layout

\begin_layout Standard
Why do we need to feed the input through a capacitor ? Why not connect the
 signal directly ? Try short circuiting the capacitor by a piece of wire,
 while observing the trace.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Photo-transistor
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Understand the photo transistor.
 Draw the CE characteristic
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/phtran-ce.png
	width 4cm

\end_inset


\begin_inset Graphics
	filename pics/photo-tran_ce.png
	lyxscale 50
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
CE characteristic of photo-transistor.
\begin_inset CommandInset label
LatexCommand label
name "fig:CE-char phototran"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Photo transistor (base lead removed) and wires
\end_layout

\begin_layout Itemize
white LED
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Transistor Emitter to ground and Collector to IV and A0
\end_layout

\begin_layout Itemize
LED from SQR2 to ground
\end_layout

\begin_layout Itemize
Right-click on Panel and open
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{Photo-Transistor CE}
\end_layout

\end_inset

 from the menu
\end_layout

\begin_layout Itemize
Place a light source 5 cm away from the Transistor
\end_layout

\begin_layout Itemize
Click on
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
buttonlabel{START}
\end_layout

\end_inset

, to draw the CE curve
\end_layout

\begin_layout Itemize
Repeat by changing the distance between light source and transistor
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The characteristic curves for different light intensities are shown in figure.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The base current is decided by the intensity of light.

\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Opto-electric signal transmission
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Demonstrate the transmission of signals through optical media.
 Electrical signals are connected into light at the transmitter and converted
 back into electrical signals at the receiver.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/opto-tran.png
	width 4cm

\end_inset


\begin_inset Graphics
	filename pics/phototran_sqr_received.png
	lyxscale 50
	width 5cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
The waveform at the photo-transistor collector
\begin_inset CommandInset label
LatexCommand label
name "fig:Phototransistor output"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
LED and Photo transistor.
\end_layout

\begin_layout Itemize
Fiber optic cable.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect LED from SQR2 to ground.
\end_layout

\begin_layout Itemize
Connect the 22k resistor of SQR2
\end_layout

\begin_layout Itemize
Phototransistor emitter to ground and collector to SEN (T23)
\end_layout

\begin_layout Itemize
Connect SEN to A0
\end_layout

\begin_layout Itemize
Set SQR2 to 100 Hz
\end_layout

\begin_layout Itemize
Place the LED facing the phototransistor and adjust the waveform
\end_layout

\begin_layout Itemize
Enable FIT option to calculate the frequency by fitting the data.
\end_layout

\begin_layout Itemize
Get a more accurate frequency measurement by clicking on 'Measure Freq'
\end_layout

\begin_layout Itemize
Repeat the experiment by changing the frequency.
\end_layout

\begin_layout Itemize
Use the Fiber Optic cable to guide the light from LED to the transistor.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The output of the phototransistor for 500 Hz signal to the LED is shown
 in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Phototransistor output"

\end_inset

.
 The frequency calculated by curve fitting is very close to 500.
 The frequency measurement done internally gives the correct value.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The electrical signal is converted into light signal by the LED.
 Light is transmitted to the photo-transistor and it is converted back into
 the electrical signal.
 It can be seen that, the shape of the waveform is slightly rounded but
 the frequency information is preserved.
 This demonstrates the advantage of digital signal transmission over the
 analog.

\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Amplitude & Frequency Modulation
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Study amplitude and frequency modulation of a signal.
 Analyse the AM output mathematically to see the sidebands.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/AM-photo.jpg
	lyxscale 30
	width 6cm

\end_inset


\begin_inset Graphics
	filename pics/AMcarr-and-sig400x20.png
	lyxscale 50
	width 5cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Amplitude modulation.(a)Experimental setup (b) Modulating signal along with
 the modulated output.
\begin_inset CommandInset label
LatexCommand label
name "fig:Amplitude-modulation"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Phoenix Analog Box.
 It has a sine wave generator (around 100 Hz) whose amplitude can be controlled
 using a DC control voltage.
 It also has a 4kHz sine wave generator that has Amplitude and Frequency
 controls.
 We use the UPV output of expEYES to controll the amplitude of the 100 Hz
 generator.
 Its output is monitored on A0 and also given to the Amplitude Modulating
 input of the second oscillator.
 The amplitude of the second oscillator is given to A1.
\end_layout

\begin_layout Standard
You can capture these waveforms, separately or togetther.
 The number of samples and the time gap between samples can be specified
 by the user.
 The depth of modulation is decided by the amplitude of the modulating signal.
\end_layout

\begin_layout Standard
Analog box also allows you to set the frequency of the modulating signal
 between 100 to 300Hz but we are not using this feature here.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the Grounds of Analog Box and expEYES
\end_layout

\begin_layout Itemize
UPV to AC of the 100 Hz oscillator
\end_layout

\begin_layout Itemize
100 Hz output to A0 and AM input
\end_layout

\begin_layout Itemize
Modulated output to A1
\end_layout

\begin_layout Itemize
Select A0 and A1
\end_layout

\begin_layout Itemize
Capture 400 samples with 20 microsecond interval
\end_layout

\begin_layout Itemize
Select A1 only
\end_layout

\begin_layout Itemize
Capture 1800 samples with 40 usec interval
\end_layout

\begin_layout Itemize
Click on Power Spectrum to do a Fourier transform
\end_layout

\begin_layout Itemize
To do FM connect 100 Hz output to the FM input of the other generator.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
A carrier signal having a frequency of around 4kHz is modulated by a sinewave
 of around 100 Hz.
 A small portion of the output (400 points with 20 usec gap) along with
 the modulating signal is shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Amplitude-modulation"

\end_inset

(b).
 Power spectrum is calculated using Fourier transform.
 To get better results a larger sample (1800 samples with 40 usec gap) is
 taken for this purpose.

\end_layout

\begin_layout Standard
Frequency modulation also done, just changing the signal connection from
 AM to FM input.
 The FM output is shown in figure
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/AMfft-1800x40.png
	lyxscale 15
	width 5.4cm

\end_inset


\begin_inset Graphics
	filename pics/FMcarr-and-sig500x10-2V.png
	lyxscale 50
	width 5.5cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
(1)Power spectrum of AM output.
 Generated from 1800 data points with 40 microseconds time interval in between.(2
) The FM output
\begin_inset CommandInset label
LatexCommand label
name "fig:Amplitude-FT"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The two sidebands are clearly obtained on both sides of the carrier peak,
 separated by the modulating frequency.
\end_layout

\begin_layout Standard
The AM output looks similar to the sound beats we obtained in section
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Interference-of-sound"

\end_inset

, but taking a power spectrum of beats gives two peaks corresponding to
 the individual frequencies.
 How do they differ inspite of the similar looks ?
\end_layout

\begin_layout Chapter
Mechanics, Optics & Heat
\end_layout

\begin_layout Standard
Resonance phenomena is studied using a driven pendulum.
 Value of acceleration due to gravity is measured using time of flight method
 and also by using a pendulum.
\end_layout

\begin_layout Section
Resonance of a driven pendulum
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Demonstrate the resonance of a driven pendulum.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
Solenoid and pendulum made of button magnets, same as in section
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Magnetic-Effect-of"

\end_inset


\end_layout

\begin_layout Itemize
22 k
\begin_inset Formula $\Omega$
\end_inset

 potentiometer
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect solenoid from SQR2 to Ground.
\end_layout

\begin_layout Itemize
Connect the 22K variable resistor of SQR2.
\end_layout

\begin_layout Itemize
Hang the pendulum near the solenoid as shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Solenoid Magnetic-field"

\end_inset


\end_layout

\begin_layout Itemize
Set SQR2 to 10 Hz, and adjust the resistor to reduce frequency until the
 pendulum amplitude goes up .
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
When SQR2 reaches the resonant frequency of the pendulum, the amplitude
 goes up due to resonance.
 A 5.2 cm (from the center of the magnet to the axis of oscillation) long
 pendulum resonated at around 2.3 Hz, almost tallying with its calculated
 natural frequency.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The resonant frequency of the pendulum can be calculated by assuming it
 as a simple pendulum and using
\end_layout

\begin_layout Standard
\begin_inset Formula \[
f=\frac{1}{T}\,\,\,\,\, where\,\,\,\,\, T=2\pi\sqrt{\frac{\ell}{g}}\]

\end_inset


\end_layout

\begin_layout Standard
where
\begin_inset Formula $\ell$
\end_inset

 is the distance from the center of the magnet to the point of suspension
 and
\begin_inset Formula $g$
\end_inset

 is the acceleration due to gravity.

\end_layout

\begin_layout Standard
Repeat the experiment by changing the length of the pendulum.

\begin_inset Foot
status collapsed

\begin_layout Plain Layout
SQR2 cannot go below 0.7 Hz
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Value of 'g', Rod pendulum
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Measure the period of oscillations of a rod pendulum using a light barrier
 and calculate the value of acceleration due to gravity.
\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
Period of oscillation of a uniform rod about one end is given by
\begin_inset Formula \[
T=2\pi\sqrt{\frac{2\ell}{3g}}\]

\end_inset


\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/rodpend-photo.jpg
	lyxscale 30
	width 3.2cm

\end_inset


\begin_inset Graphics
	filename schematics/rodpend.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/rodpend-ghist.png
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Measuring the period of a rod pendulum using Light Barrier, to calculate
 the value of 'g'.
\begin_inset CommandInset label
LatexCommand label
name "fig:Rod Pendulum"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Light Barrier, made of LED and photo-transistor
\end_layout

\begin_layout Itemize
Rod Pendulum
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the LED from SQR2 to Ground
\end_layout

\begin_layout Itemize
Photo-transistor collector to SEN and emitter to ground
\end_layout

\begin_layout Itemize
Right click on the panel and start
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{Rod Pendulum}
\end_layout

\end_inset

 from the popup menu
\end_layout

\begin_layout Itemize
Measure and enter the length of the pendulum
\end_layout

\begin_layout Itemize
Oscillate the pendulum and click on
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
buttonlabel{START}
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Can make a histogram using XmGrace.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The time period (in milli seconds to match the vertical range with value
 of 'g') and the calculated value of 'g' are plotted, as shown in figure

\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Rod Pendulum"

\end_inset

.
 It also shown a histogram of the 20 readings.

\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The calculated value of 'g' is around 972.5
\begin_inset Formula $cm/sec^{2}$
\end_inset

, showing a systematic error of around 8.5 .
 The random error is less than 0.1 % .
 The reason for the systematic error could be due to the following reasons.
 The length is measured from the knife edge to the bottom and used in the
 formula.
 But there is a small mass projecting above the knife edge that is not included
 in the calculation.
 Another reason is that the pendulum may not be exactly vertical in the
 resting position.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Oscillations of a pendulum
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
To study the nature of oscillations of a pendulum.
 An angle encoder is required for measuring the angular displacement as
 a function of time.
 We will try to measure the angular velocity as a function of time, since
 it can be done using an inexpensive DC motor.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/pendulum-photo.jpg
	lyxscale 40
	width 5.5cm

\end_inset


\begin_inset Graphics
	filename pics/pendulum-osc.png
	lyxscale 50
	width 5.5cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Nature of oscillations of a pendulum.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
A small DC motor with a pendulum attached to its axis.
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Attach some sort of rigid pendulum to the axis of the motor.
\end_layout

\begin_layout Itemize
Connect the termainal of the DC motor between T17 and Ground
\end_layout

\begin_layout Itemize
Connect T18 to A0
\end_layout

\begin_layout Itemize
Right click and start
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{Pendulum Waveform}
\end_layout

\end_inset

 from the menu.
\end_layout

\begin_layout Itemize
Oscillate the pendulum and START digitizing
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The observed waveform is shown in figure.
 Fitting it with equation
\begin_inset Formula $A=A_{0}sin\left(\omega t+\theta\right)*\exp\left(-dt\right)+C$
\end_inset

, using Xmgrace gave an angular frequency of 10 Hz.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The pendulum should be made with a heavy bob and a light weight rod connecting
 it to the axis of the motor.
 I was in a hurry to finish this writeup and just used a screwdriver and
 a magnet to attach it to the motor axis.
 The DC motor acts like a generator in this case.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Value of 'g' by time of flight
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Measure the time of flight of a body falling under gravity from a known
 height and calculate the value of acceleration due to gravity.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/gravity-tof-photo.jpg
	lyxscale 40
	width 5cm

\end_inset


\begin_inset Graphics
	filename schematics/g-tof.png
	width 3cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Gravity by measuring the time of flight.The iron ball is held by the lectromagnet.
\begin_inset CommandInset label
LatexCommand label
name "fig:Gravity-by-TOF"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Electromagnet (1000 Turns coil with iron core)
\end_layout

\begin_layout Itemize
150
\begin_inset Formula $\Omega$
\end_inset

 Loudspeaker
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Fix the Electromagnet on a stand
\end_layout

\begin_layout Itemize
Connect it to OD0 and Ground
\end_layout

\begin_layout Itemize
Connect speaker between T15 & T16
\end_layout

\begin_layout Itemize
Right Click and start
\shape italic

\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{Gravity TOF}
\end_layout

\end_inset


\shape default
from the menu.
\end_layout

\begin_layout Itemize
Click on
\shape italic
Attach the Ball
\shape default
to energize the magnet.

\end_layout

\begin_layout Itemize
Enter the height from the bottom side of the ball to the floor
\end_layout

\begin_layout Itemize
Click on Measure TOF
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="3">
<features>
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Height
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Time
\begin_inset Formula $t$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $g=\frac{2h}{t^{2}}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
35
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
.269
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
967.4
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
25
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
.228
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
961.8
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The calculated values is less than the actual value.
 Why ?
\end_layout

\begin_layout Standard
We measure the time from making a 5->0 volts transition at OD0 to the appearance
 of few millivolts at the loudspeaker output.
 The magnetic effect will not vanish instantly and the circuit delays are
 also need to be accounted.
\end_layout

\begin_layout Standard
If you apply a correction of 2 milliseconds to the first reading, the result
 is
\begin_inset Formula $70/.267^{2}=981.9$
\end_inset

.
 This shows the accuracy required for mesuring the time of flight.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Temperature measurement, PT100
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Record the temperature of a liquid by using a Platinum Resistance Thermometer

\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
Resistance of a PT100 element is related to the temperature by the equation
\begin_inset Formula \[
R_{T}=R_{0}\left[1+AT+BT^{2}\right]\]

\end_inset


\end_layout

\begin_layout Standard
where
\begin_inset Formula $A=3.9083e-3$
\end_inset

 and
\begin_inset Formula $B=-5.775e-7$
\end_inset


\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/cooling-water-photo.jpg
	lyxscale 50
	width 3.5cm

\end_inset


\begin_inset Graphics
	filename schematics/pt100.png
	width 3cm

\end_inset


\begin_inset Graphics
	filename pics/cooling-water-pt100.png
	lyxscale 50
	width 3.5cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Cooling curve of water measured using PT100 sensor.

\begin_inset CommandInset label
LatexCommand label
name "fig:Cooling-curve-water"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\begin_layout Itemize
PT100 sensor element
\end_layout

\begin_layout Itemize
330 Ohm resistor
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect PT100 from CS to Ground
\end_layout

\begin_layout Itemize
Connect CS to T21 (Non-inverting amplifier input)
\end_layout

\begin_layout Itemize
Connect T22 (amplifier OUTPUT) to A2
\end_layout

\begin_layout Itemize
Connect the gain control resistor between T19 & T20
\end_layout

\begin_layout Itemize
Right click and start
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{PT100 Sensor}
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Enter the resistance value
\end_layout

\begin_layout Itemize
Select the total time and time interval between measurements
\end_layout

\begin_layout Itemize
Press
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
buttonlabel{START}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Calibration is required for better accuracy.
 Keep the sensor on ice and click on
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{Freezing Point}
\end_layout

\end_inset

.
 Immerse the sensor in boiling water and click on
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{Boiling Point}
\end_layout

\end_inset

.
 After that click on
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{Calibrate}
\end_layout

\end_inset

.
 Once the calibration is done the temperature is calculated using the calibratio
n constants.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
Cooling curve of water is shown in figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Cooling-curve-water"

\end_inset

 .
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
PT100 is a platinum element having a resistance of 100
\begin_inset Formula $\Omega$
\end_inset

 at zero degree celcius.
 The resistance varies with temperature and tables are available to correlate
 the resistance and temperature.
 Our program sets a current of 1mA through PT100 and measures the voltage
 drop across it.
 The voltage is amplified for inceasing the resolution.

\end_layout

\begin_layout Standard
The program reads the amplifier output voltage.
 Voltage across PT100 is calculated by dividing this voltage by the gain
 of the amplifier (
\begin_inset Formula $G=1+\frac{10000}{Rg}$
\end_inset

).
 Since the current is known the resistance and hence the temperature can
 be calculated.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Temperature Controller
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Implement a temperature controller using the LM35 sensor.
 A transistor is user as a controllable heater.
 LM35 is kept pressed to the transistor body with some heat conducting paint
 in between.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename schematics/temp-control.png
	width 5cm

\end_inset


\begin_inset Graphics
	filename pics/temp-con.png
	lyxscale 40
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Temperature measurement using LM35.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
LM35 sensor
\end_layout

\begin_layout Itemize
2N2222 Transistor
\end_layout

\begin_layout Itemize
10 k
\begin_inset Formula $\Omega$
\end_inset

 and 2.4k
\begin_inset Formula $\Omega$
\end_inset

 resistors
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect LM35 and the transistor as shown in the figure
\end_layout

\begin_layout Itemize
Join the plastic bodies of LM35 and 2N2222 using heat conducting compound.
\end_layout

\begin_layout Itemize
Use an external 12 volts DC power supply
\end_layout

\begin_layout Itemize
Right click and start
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{Temp Controller}
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Set the temperature setpoint and the base voltage (UPV)
\end_layout

\begin_layout Itemize
Press
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
buttonlabel{START}
\end_layout

\end_inset

 .
 The vertical scale will be 0 to setpoint + 10 deg.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
Temperature as a function of time is plotted.

\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The temperature is kept within
\begin_inset Formula $\pm$
\end_inset

0.5 degree of the setpoint.
 LM35 has only that much resolution.
 The time variation depends on the heat conductivity of the transistor and
 LM35 body and the collector current.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Stroboscope
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
An object executing periodic motion will appear stationary when it is illuminate
d with a light pulse of the same frequency.
 The simple reason is that the object is illuminated every time when it
 reaches the same point.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/stroboscope-photo.jpg
	lyxscale 30
	width 5cm

\end_inset


\begin_inset Graphics
	filename schematics/strobo.png
	width 4.5cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Stroboscope using flashing LED.
 The AC voltage picked up by the coil due to the rotating magnet is used
 for cross checking the speed of rotation
\begin_inset CommandInset label
LatexCommand label
name "fig:Stroboscope"

\end_inset

.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
LED
\end_layout

\begin_layout Itemize
DC motor
\end_layout

\begin_layout Itemize
3000 turns coil
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect motor from PULSE to Ground
\end_layout

\begin_layout Itemize
Connect LED from SQR2 to Ground
\end_layout

\begin_layout Itemize
Connect the 22k resistor for SQR2
\end_layout

\begin_layout Itemize
Set Pulse to 20 %
\end_layout

\begin_layout Itemize
Set SQR2 to 20
\end_layout

\begin_layout Itemize
Adjust the resistor until the motor axis appears nearly stationary
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
As you adjust SQR2, the movement of the disc on the axis of the motor appears
 to slow down and then at some point reverses the direction of motion.
 Note down the frequency at the direction reversal.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
How the RPM of a car engine adjusted ?
\end_layout

\begin_layout Standard
When viewed in a pulsed light source of frequency 11 Hz, a motor rotating
 clockwise at 10 rotations per second will look like rotating anti-clockwise
 once a second.
 During stopping and starting, the ceiling fans some times looks like rotating
 backwards, in the light of fluorescent tubes.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Speed of rotation of a motor
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Learn about making sensors to detect mechanical movements.
 Use a photo-transistor to find the rotational speed of a motor.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/motor-rpm-photo.jpg
	lyxscale 40
	width 4cm

\end_inset


\begin_inset Graphics
	filename schematics/motor-rps.png
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Measuring the speed of rotation of a motor using light barrier.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Photo-transistor
\end_layout

\begin_layout Itemize
LED
\end_layout

\begin_layout Itemize
Small DC motor
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Attach a paper leaf to the Motor
\end_layout

\begin_layout Itemize
Connect motor to PULSE
\end_layout

\begin_layout Itemize
Connect LED from SQR2 to Ground
\end_layout

\begin_layout Itemize
Set SQR2 to zero
\end_layout

\begin_layout Itemize
Connect phototransistor collector to SEN
\end_layout

\begin_layout Itemize
Emitter to ground
\end_layout

\begin_layout Itemize
Position the LED and phototransistor such that the leaf moves between them
\end_layout

\begin_layout Itemize
set PULSE to different duty cycle values to rotate the motor at different
 speeds.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The rotations per second observed for different duty cycle values are given
 below.
 Except for the first reading speed is proportional to the duty cycle, ie.
 the power given to the motor.
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
<features>
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
PULSE %
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
SEN Freq.
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
9.8
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
5.6
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
20
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
14.4
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
29.8
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
21.4
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
40
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
28.2
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
The observed values can be cross checked by using a magnet and coil as explained
 in section
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:A-simple-AC"

\end_inset

 or by using the stroboscope explained in the previous section.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Transparency Measurement
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Compare the transmission of light through different semi transparent materials.
\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/light-thru-paper-photo.JPG
	lyxscale 50
	width 4cm

\end_inset


\begin_inset Graphics
	filename schematics/light-bar.png
	width 4cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Light transmission measurement using photo transistor
\begin_inset CommandInset label
LatexCommand label
name "fig:Light-transmission-measurement"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Photo-transistor, LED and 10 k
\begin_inset Formula $\Omega$
\end_inset

 resistor
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the Photo-transistor collector to SEN and Emitter to Ground.
\end_layout

\begin_layout Itemize
Connect the LED from SQR2 and Set SQR2 to 0
\end_layout

\begin_layout Itemize
Right click and start the
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
menuitem{CRO}
\end_layout

\end_inset

 from the menu.
 Select the SEN.
\end_layout

\begin_layout Itemize
Place the LED facing the transistor and note down the voltage.
\end_layout

\begin_layout Itemize
Place some semitransparent material in between and see the difference.
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The voltage decreases with the intensity of light falling on the photo-transisto
r.
 Try LEDs of different color and compare the results.
 Try the transmission of red light through RED and GREEN foils with the
 same thickness.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Standing waves on a String
\end_layout

\begin_layout Subsection*
Objective
\end_layout

\begin_layout Standard
Study standing waves on a stretched thread excited by a relay coil.
 The tension on the thread is varied by changing the suspended mass.
\end_layout

\begin_layout Subsection*
Theory
\end_layout

\begin_layout Standard
Velocity of wave propagation in a string is given by
\begin_inset Formula $v=\sqrt{\frac{T}{\mu}}$
\end_inset

, where T is the tension and
\begin_inset Formula $\mu$
\end_inset

 is the linear mass density.
 The velocity
\begin_inset Formula $v=f\lambda$
\end_inset

 .
 On a vibrating string, the fundamental harmonic has only two nodes, at
 both ends, and the length of the string
\begin_inset Formula $L=\lambda/2$
\end_inset

.
 Fundamental frequency
\begin_inset Formula $f_{0}=\frac{v}{2L}=\frac{1}{2L}\sqrt{\frac{T}{\mu}}$
\end_inset


\end_layout

\begin_layout Subsection*
Equipment
\end_layout

\begin_layout Itemize
A relay coil with amplifier, powered by 12 AC adapter
\end_layout

\begin_layout Itemize
22k potentiometer
\end_layout

\begin_layout Subsection*
Procedure
\end_layout

\begin_layout Itemize
Connect the Grounds of expEYES and the vibrating string accessory.
\end_layout

\begin_layout Itemize
Connect SQR2 to the relay amplifier input of the amplifier.
\end_layout

\begin_layout Itemize
Connect 22k pot and set SQR2 to 30 Hz
\end_layout

\begin_layout Itemize
Set the suspended mass to 30 gm
\end_layout

\begin_layout Itemize
Adjust 22k to get the standing wave fundamental (single loop)
\end_layout

\begin_layout Subsection*
Observation
\end_layout

\begin_layout Standard
The frequency is proportional to the square of tension applied, within experimen
tal errors.
\end_layout

\begin_layout Subsection*
Discussion
\end_layout

\begin_layout Standard
Make the string such that one half of it has double the linear mass density
 than the other half.
 Watch the higher order modes.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Chapter*
Appendix A : Accessories
\end_layout

\begin_layout Standard
Every experiment require something to be connected to expEYES interface.
 It could be just a peice of wire or a set of sensors.
 The standard accessory set is sufficient to perform most of the experiments
 described in this manual.
 There are some other accessories available presently and their number is
 likely to grow.
 The standard accessory set available along with expEYES contains the following
 components.
 The values of the parameters, like inductance, specified are nominal, measured
 from random samples.

\end_layout

\begin_layout Paragraph*
Crocodile Clips with wires
\end_layout

\begin_layout Standard
If the connection to any terminal is changed many times during an experiment,
 it is easier to make the connection using the crocodile clip provided.
\end_layout

\begin_layout Paragraph*
Microphone assembly
\end_layout

\begin_layout Standard
A condenser microphone with a biasing resistor and a DC blocking capacitor.
 It should be fixed to T16 & T15, with the wire conneted to UPV.
 The capacitor lead goes to T15.
\end_layout

\begin_layout Paragraph*
3000 Turns Coil (2)
\end_layout

\begin_layout Standard
Inductance
\begin_inset Formula $\approx$
\end_inset

 125 mH, Resistance
\begin_inset Formula $\approx$
\end_inset

 560
\begin_inset Formula $\Omega$
\end_inset

 , made from insulated copper wire 44 SWG.
 These coils are be used for studying inductance, electromagnetic induction
 etc.

\end_layout

\begin_layout Paragraph*
1000 Turns coil
\end_layout

\begin_layout Standard
Inductance
\begin_inset Formula $\approx$
\end_inset

 4 mH, Resistance
\begin_inset Formula $\approx$
\end_inset

 45
\begin_inset Formula $\Omega$
\end_inset

 , made from insulated copper wire 40 SWG.
 With the ferrite rod inserted, the Inductance increases to around 25 mH.
\end_layout

\begin_layout Paragraph*
Electromagnet (with iron core)
\end_layout

\begin_layout Standard
Inductance
\begin_inset Formula $\approx$
\end_inset

 20 mH, Resistance
\begin_inset Formula $\approx$
\end_inset

 45
\begin_inset Formula $\Omega$
\end_inset

 , made from insulated copper wire 40 SWG.
 This coil has iron core fixed inside and used as an electromagnet in some
 experiments.
 50 cm long leads are provided.
\end_layout

\begin_layout Paragraph*
Piezo Electric Discs (2)
\end_layout

\begin_layout Standard
Resonant frequency is around 4000 Hz.
 Can be energized by SQR1, SQR2 or PULSE outputs.
 Discs are enclosed in a plastic shell that forms a cavity, that enhances
 the amplitude of sound produced.
\end_layout

\begin_layout Paragraph*
Loud Speaker (big)
\end_layout

\begin_layout Standard
The resistance of the speaker is 150
\begin_inset Formula $\Omega$
\end_inset

 , different from the commonly available 8
\begin_inset Formula $\Omega$
\end_inset

 speakers.
 Can be powered by SQR1, SQR2 or PULSE.
\end_layout

\begin_layout Subsubsection*
Loudspeake (small)
\end_layout

\begin_layout Standard
This is a low impedance speaker, but more rugged.
 We will use it as a microphone also in some experiments.
\end_layout

\begin_layout Paragraph*
DC Motor
\end_layout

\begin_layout Standard
Fixed on a metallic base.
 Should be powered by a DC voltage less than 3 volts.
 In some experiments, we power the motor with the PULSE output, with a duty
 cycle less than 40%.
 It is safer to connect a diode in series when the motor is powered from
 the terminal PULSE.
\end_layout

\begin_layout Paragraph*
Transistor Holder
\end_layout

\begin_layout Standard
A three pin socket to insert transistors to plot the characteristic curve,
 200
\begin_inset Formula $k\Omega$
\end_inset

 at base.
\end_layout

\begin_layout Paragraph*
Permanent Magnets
\end_layout

\begin_layout Itemize
10mm diameter & 10 mm length
\end_layout

\begin_layout Itemize
12 mm diameter & 1.5 mm length
\end_layout

\begin_layout Itemize
5 mm diameter & 10 mm length
\end_layout

\begin_layout Subsubsection*
Other Items
\end_layout

\begin_layout Itemize
22 k potentiometer, used for SQR2.
\end_layout

\begin_layout Itemize
Holder for two dry cells.
\end_layout

\begin_layout Itemize
Aluminium Disc with center hole.
\end_layout

\begin_layout Itemize
Mild Steel ball, D= 10 mm
\end_layout

\begin_layout Itemize
Ferrite rod, D = 6 mm, L = 20 mm
\end_layout

\begin_layout Itemize
Ferrite Rod, D = 12 mm, L = 50 mm
\end_layout

\begin_layout Itemize
5mm LEDS : RED, BLUE, GREEN
\end_layout

\begin_layout Itemize
10 mm white LED, with leads
\end_layout

\begin_layout Itemize
Capacitors : 100uF, 47uF, 10 uF, 1uF and 0.1 uF
\end_layout

\begin_layout Itemize
Resistors : 100
\begin_inset Formula $\Omega$
\end_inset

, 200
\begin_inset Formula $\Omega$
\end_inset

, 330
\begin_inset Formula $\Omega$
\end_inset

, 560
\begin_inset Formula $\Omega$
\end_inset

, 1
\begin_inset Formula $k\Omega$
\end_inset

, 10
\begin_inset Formula $k\Omega$
\end_inset

 and 100
\begin_inset Formula $k\Omega$
\end_inset


\end_layout

\begin_layout Itemize
Diode : 1N4148
\end_layout

\begin_layout Itemize
Zener Diode, 3.3 volts
\end_layout

\begin_layout Itemize
Transistor : 2N2222
\end_layout

\begin_layout Itemize
15 cm wire - 5 pcs
\end_layout

\begin_layout Itemize
8 cm wire - 5 pcs
\end_layout

\begin_layout Itemize
Screwdriver
\end_layout

\begin_layout Itemize
LDR
\end_layout

\begin_layout Itemize
Thermistor
\end_layout

\begin_layout Subsection*
Light Barrier and Rod Pendulum
\end_layout

\begin_layout Standard
The light barrier can be used for timing mechanical movements.
 A light beam falling on a photo-transistor is intercepted and the time
 intervals are measured.
 Can be used for finding the speed of rotation of a motor, period of oscillation
s of a pendulum etc.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pics/light-bar-rodpend-photo.jpg
	lyxscale 30
	width 3.7cm

\end_inset


\begin_inset Graphics
	filename pics/40kHz-piezo-photo.jpg
	lyxscale 40
	width 3.7cm

\end_inset


\begin_inset Graphics
	filename pics/standing-wave-app-photo.jpg
	lyxscale 30
	width 3.6cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
(a) Light Barrier and Rod Pendulum (b)40 kHz Piezo Transmitter and Receiver.
 (c) Vibrating string apparatus.
\begin_inset CommandInset label
LatexCommand label
name "fig:Light-Barrier-and"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection*
Ultrasound Piezo Tranceiver
\end_layout

\begin_layout Standard
The 40 kHz ultra-sound Piezo-electric transmitter and receiver can be used
 for studying sound.
 The velocity of sound can be found by measuring the time of flight of a
 sound packet from the transmitter to receiver.
 The 40 kHz signal cannot be viewed properly using the expEYES oscilloscope
 feature, you need a higher frequency CRO to view the signals properly.
\end_layout

\begin_layout Subsection*
Vibrating String Apparatus
\end_layout

\begin_layout Standard
This is powered by 12 volts DC and driven by a signal from SQR2.
 The amplified SQR2 drives a relay coil and a string attached to the relay
 contact vibrates.
 Standing waves can be formed by adjusting the tension and frequency of
 vibration.
\end_layout

\end_body
\end_document
