Practical Work Book Lca

EE Department Linear Circuit Analysis
PRACTICAL WORK BOOK

For The Course
EE-111 Linear Circuit Analysis
For
B.E. Electrical Engineering
Group Members
Degree Syndicate
Complied By: Checked By:

Lab. Engineer Bahzad Zaib Assistant Professor Zubair Ahmad
CEME (NUST), Rawalpindi 1

DEPARTMENT OF ELECTRICAL ENGINEERING

College of Electrical & Mechanical Engineering (CEME), NUST-Pakistan
LIST OF EXPERIMENTS
S.NO. TITLE OF EXPERIMENT Page No.
01 Introduction: Basic Concepts and Lab Equipment. 04
02 Experimental Verification of OHM’s Law. 20
03 Verification of Current & Voltage Divider Rule. 25
04 Experimental Verification of Nodal Analysis. 30
05 Experimental Verification of Mesh Analysis. 35
06 Experimental Verification of Superposition Theorem. 40
07 Study of Star and Delta Connections of Resistances. 44
Experimental Verification of Star-Delta Transformation.
08 Experimental Verification of Thevenin’s Theorem. 48
09 Study of Maximum Power Transfer Theorem & its 52

Experimental Verification for a Network.
10 Verification of Reciprocity Theorem. 57
11 Implementation of Inverting Amplifier & Non-Inverting 61

Amplifier (OP AMP Applications).

12 Implementation of Unity Gain Follower & Summing 66

Amplifier (OP AMP Applications).
13 Transient Analysis & Time Constant Determination for an 72

RC circuit.
14 Experimental Verification of Norton’s Theorem. 80
Note: PSICE solution for the task of each lab to be submitted with lab reports.
LABORATORY WORK ESSENTIALS
COMPONENTS
● Resistances –fixed (Ω) 50 x 2,80 x 2, 100 x 2, 120 x 2,390 x 2,430 x 2, 1k x 6,

2.2k x 5, 2.5k x 3, 5k x 2, 10k x 2, 100k x 4, 20k x 4.
● Resistances –variable (Ω) 1k x 2, 2k x 2, 5k x 2, 10k x 2
● Capacitor-fixed 1uF x 2
● IC’s LM741 x 2
EQUIPMENTS
● Digital Multi Meter
● Oscilloscope
● DC Power Supplies

● Bread Board
● Function Generator
SOFTWARES
Nil
EXPERIMENT NO – 01
INTRODUCTION: BASIC CONCEPTS & LAB EQUIPMENT
OBJECTIVE:
- To know and understand basic function of laboratory equipment.
- To become familiar with the correct ways of operating lab instruments.
THEORY:
A few tools are required for basic electronics work. Most of these tools are inexpensive and easy
to obtain.
Digital multi-meter:
First and foremost in your tool collection is a multi-meter. This is an electrical instrument
designed to measure voltage, current, resistance, and often other variables as well. Multi-meters
are manufactured in both digital and analog form. A digital multi-meter is preferred for precision
work, but analog meters are also useful for gaining an intuitive understanding of instrument
sensitivity and range.

Solder-less bread-board:
Also essential is a solder-less breadboard, sometimes called a prototyping board, or proto-board.
This device allows you to quickly join electronic components to one another without having to
solder component terminals and wires together.
The internal structure / layout of solder less bread-board can be depicted as:
we can think of a breadboard as a board that can be divided in 2 functional areas:

– the power strip(s) (in the drawing above A and D)
– the component grid(s) (in the drawing above B and C)
Most breadboards have at least 2 “component grids” (B and C), separated at exactly the distance
between the two pin sides of a DIP IC package between B and C. The pins of the component
grids (B and C) are connected vertically, per column. The grids B and C are not connected with
each other
Bench Top Power Supply:

Bench Top Power Supplies are used for general design, repair, instructional, or testing purposes
and includes both Fixed and Variable output supplies. It is provided with 3 terminals for
connection purposes: positive, negative and ground. The digital display shows the values of
voltage which is adjusted by coarse adjustment and fine adjustment knobs.

Oscilloscope:
The main purpose of an oscilloscope is to graph an electrical signal as it varies over time. Most
scopes produce a two-dimensional graph with time on the x-axis and voltage on the y-axis.
Controls surrounding the scope’s screen allow you to adjust the scale of the graph, both
vertically and horizontally – allowing you to zoom in and out on a signal. There are also controls
to set the trigger on the scope, which helps focus and stabilize the display.
In addition to those fundamental features, many scopes have measurement tools, which help to
quickly quantify frequency, amplitude, and other waveform characteristics. In general a scope
can measure both time-based and voltage-based characteristics:
› Timing characteristics:
Frequency and period – Frequency is defined as the number of times per second a waveform
repeats. And the period is the reciprocal of that (number of seconds each repeating waveform
takes). The maximum frequency a scope can measure varies, but it’s often in the 100’s of MHz
(1E6 Hz) range.
Duty cycle – The percentage of a period that a wave is either positive or negative (there are both
positive and negative duty cycles). The duty cycle is a ratio that tells you how long a signal is
“on” versus how long it’s “off” each period.
Rise and fall time – Signals can’t instantaneously go from 0V to 5V, they have to smoothly rise.
The duration of a wave going from a low point to a high point is called the rise time, and fall
time measures the opposite. These characteristics are important when considering how fast a
circuit can respond to signals.
› Voltage characteristics:
Amplitude – Amplitude is a measure of the magnitude of a signal. There are a variety of
amplitude measurements including peak-to-peak amplitude, which measures the absolute
difference between a high and low voltage point of a signal. Peak amplitude, on the other hand,
only measures how high or low a signal is past 0V.
Maximum and minimum voltages – The scope can tell you exactly how high and low the voltage
of your signal gets.

Mean and average voltages – Oscilloscopes can calculate the average or mean of your signal, and
it can also tell you the average of your signal’s minimum and maximum voltage.
Oscilloscope Usage:
Here are some of the important oscilloscope buzzwords you should be familiar with before
turning it on.
Key Oscilloscope Specifications
Some scopes are better than others. These characteristics help define how well you might expect
a scope to perform:
› Bandwidth – Oscilloscopes are most commonly used to measure waveforms which have a
defined frequency. No scope is perfect though: they all have limits as to how fast they can see a
signal change. The bandwidth of a scope specifies the range of frequencies it can reliably
measure.
› Digital vs. Analog – As with most everything electronic, o-scopes can either be analog or
digital. Analog scopes use an electron beam to directly map the input voltage to a display. Digital
scopes incorporate microcontrollers, which sample the input signal with an analog-to-digital
converter and map that reading to the display. Generally analog scopes are older, have a lower
bandwidth, and less features, but they may have a faster response (and look much cooler).
› Channel Amount – Many scopes can read more than one signal at a time, displaying them all
on the screen simultaneously. Each signal read by a scope is fed into a separate channel. Two to
four channel scopes are very common.
› Sampling Rate – This characteristic is unique to digital scopes, it defines how many times per
second a signal is read. For scopes that have more than one channel, this value may decrease if
multiple channels are in use.
› Rise Time – The specified rise time of a scope defines the fastest rising pulse it can measure.
The rise time of a scope is very closely related to the bandwidth. It can be calculated as Rise
Time = 0.35 / Bandwidth.
› Maximum Input Voltage – Every piece of electronics has its limits when it comes to high
voltage. Scopes should all be rated with a maximum input voltage. If your signal exceeds that

voltage, there’s a good chance the scope will be damaged.

› Resolution – The resolution of a scope represents how precisely it can measure the input
voltage. This value can change as the vertical scale is adjusted.
› Vertical Sensitivity – This value represents the minimum and maximum values of your vertical,
voltage scale. This value is listed in volts per div.
› Time Base – Time base usually indicates the range of sensitivities on the horizontal, time axis.
This value is listed in seconds per div.
› Input Impedance – When signal frequencies get very high, even a small impedance (resistance,
capacitance, or inductance) added to a circuit can affect the signal. Every oscilloscope will add a
certain impedance to a circuit it’s reading, called the input impedance. Input impedances are
generally represented as a large resistive impedance (>1 MΩ) in parallel (||) with small
capacitance (in the pF range). The impact of input impedance is more apparent when measuring
very high frequency signals, and the probe you use may have to help compensate for it.
Anatomy of An Oscilloscope
While no scopes are created exactly equal, they should all share a few similarities that make
them function similarly. On this page we’ll discuss a few of the more common
systems of an oscilloscope: the display, horizontal, vertical, trigger, and inputs.
The Display
An oscilloscope isn’t any good unless it can display the information you’re trying to test, which
makes the display one of the more important sections on the scope.
Every oscilloscope display should be criss-crossed with horizontal and vertical lines called divisions. The
scale of those divisions are modified with the horizontal and vertical systems. The vertical system is
measured in “volts per division” and the horizontal is “seconds per division”. Generally, scopes will
feature around 8-10 vertical (voltage) divisions, and 10-14 horizontal (seconds) divisions.
Older scopes (especially those of the analog variety) usually feature a simple, monochrome display,

though the intensity of the wave may vary. More modern scopes feature multicolor LCD screens, which
are a great help in showing more than one waveform at a time.
Many scope displays are situated next to a set of about five buttons – either to the side or below the
display. These buttons can be used to navigate menus and control settings of the scope.
Vertical System
The vertical section of the scope controls the voltage scale on the display. There are
traditionally two knobs in this section, which allow you to individually control the vertical
position and volts/div.
The more critical volts per division knob allow you to set the vertical scale on the screen. Rotating the
knob clockwise will decrease the scale, and counter-clockwise will increase. A smaller scale – fewer volts
per division on the screen – means you’re more “zoomed in” to the waveform.
The display on the GA1102, for example, has 8 vertical divisions, and the volts/div knob can select a
scale between 2mV/div and 5V/div. So, zoomed all the way in to 2mV/div, the display can show
waveform that is 16mV from top to bottom. Fully “zoomed out”, the scope can show a waveform
ranging over 40V. (The probe, as we’ll discuss below, can further increase this range.)
The position knob controls the vertical offset of the waveform on the screen. Rotate the knob clockwise,
and the wave will move down, counter-clockwise will move it up the display. You can use the position
knob to offset part of a waveform off the screen.
Using both the position and volts/div knobs in conjunction, you can zoom in on just a tiny part of the
waveform that you care about the most. If you had a 5V square wave, but only cared about how much it
was ringing on the edges, you could zoom in on the rising edge using both knobs.

Horizontal System
The horizontal section of the scope controls the time scale on the screen. Like the vertical system, the
horizontal control gives you two knobs: position and seconds/div.
The seconds per division (s/div) knob rotates to increase or decrease the horizontal scale. If you rotate
the s/div knob clockwise, the number of seconds each division represents will decrease – you’ll be
“zooming in” on the time scale. Rotate counter-clockwise to increase the time scale, and show a longer
amount of time on the screen.
Using the GA1102 as an example again, the display has 14 horizontal divisions, and can show
anywhere between 2nS and 50s per division. So zoomed all the way in on the horizontal scale, the scope
can show 28nS of a waveform, and zoomed way out it can show a signal as it changes over 70 seconds.
The position knob can move your waveform to the right or left of the display, adjusting the
horizontal offset.
Using the horizontal system, you can adjust how many periods of a waveform you want to see. You can
zoom out, and show multiple peaks and troughs of a signal:
Or you can zoom way in, and use the position knob to show just a tiny part of a wave:

Trigger System
The trigger section is devoted to stabilizing and focusing the oscilloscope. The trigger tells the
scope what parts of the signal to “trigger” on and start measuring. If your waveform is periodic,
the trigger can be manipulated to keep the display static and unflinching. A poorly triggered
wave will produce seizure-inducing sweeping waves like this:
The trigger section of a scope is usually comprised of a level knob and a set of buttons to select the
source and type of the trigger. The level knob can be twisted to set a trigger to a specific voltage point.

A series of buttons and screen menus make up the rest of the trigger system. Their main purpose is to
select the trigger source and mode. There are a variety of trigger types, which manipulate how the
trigger is activated:
› An edge trigger is the most basic form of the trigger. It will key the oscilloscope to start measuring
when the signal voltage passes a certain level. An edge trigger can be set to catch on a rising or falling
edge (or both).
› A pulse trigger tells the scope to key in on a specified “pulse” of voltage. You can specify the duration
and direction of the pulse. For example, it can be a tiny blip of 0V -> 5V -> 0V, or it can be a seconds-long
dip from 5V to 0V, back to 5V.
› A slope trigger can be set to trigger the scope on a positive or negative slope over a specified amount
of time.
› More complicated triggers exist to focus on standardized waveforms that carry video data,
like NTSC or PAL. These waves use a unique synchronizing pattern at the beginning of every frame.
You can also usually select a triggering mode, which, in effect, tells the scope how strongly you feel
about your trigger. In automatic trigger mode, the scope can attempt to draw your waveform even if it
doesn’t trigger. Normal mode will only draw your wave if it sees the specified trigger. And single
mode looks for your specified trigger, when it sees it it will draw your wave then stop.
The Probes
An oscilloscope is only good if you can actually connect it to a signal, and for that you need
probes. Probes are single-input devices that route a signal from your circuit to the scope. They
have a sharp tip which probes into a point on your circuit. The tip can also be equipped with
hooks, tweezers or clips to make latching onto a circuit easier. Every probe also includes
a ground clip, which should be secured safely to a common ground point on the circuit under
test.
While probes may seem like simple devices that just latch onto your circuit and carry a signal to the
scope, there’s actually a lot that goes into probe design and selection.
Optimally, what a probe needs to be is invisible – it shouldn’t have any effect on your
signal under test. Unfortunately, long wires all have intrinsic inductance, capacitance, and resistance, so,
no matter what, they’ll affect scope readings (especially at high frequencies).
There are a variety of probe types out there, the most common of which is the passive

probe, included with most scopes. Most of the “stock” passive probes are attenuated. Attenuating
probes have a large resistance intentionally built-in and shunted by a small capacitor, which helps to
minimize the effect that a long cable might have on loading your circuit. In series with the input
impedance of a scope, this attenuated probe will create a voltage divider between your signal and the
scope input.
Most probes have a 9MΩ resistor for attenuating, which, when combined with a standard 1MΩ input
impedance on a scope, creates a 1/10 voltage divider. These probes are commonly called 10X
attenuated probes. Many probes include a switch to select between 10X and 1X (no attenuation).
Attenuated probes are great for improving accuracy at high frequencies, but they will also reduce the
amplitude of your signal. If you’re trying to measure a very low-voltage signal, you may have to go with a
1X probe. You may also need to select a setting on your scope to tell it you’re using an attenuated
probe, although many scopes can automatically detect this.
Beyond the passive attenuated probe, there are a variety of other probes out here. Active probes are
powered probes (they require a separate power source), which can amplify your signal or even pre-
process it before it get to your scope. While most probes are designed to measure voltage, there are
probes designed to measure AC or DC current. Current probes are unique because they often clamp
around a wire, never actually making contact with the circuit.

Using an Oscilloscope
The infinite variety of signals out there means you’ll never operate an oscilloscope the same way
twice. But there are some steps you can count on performing just about every time you test a
circuit. We’ll show an example signal, and the steps required to measure it.
Probe Selection and Setup

First off, you’ll need to select a probe. For most signals, the simple passive probe included with
your scope will work perfectly fine.
Next, before connecting it to your scope, set the attenuation on your probe. 10X – the most
common attenuation factor – is usually the most well-rounded choice. If you are trying to
measure a very low-voltage signal though, you may need to use 1X.
Connect the Probe and Turn the Scope On

Connect your probe to the first channel on your scope, and turn it on. Have some patience
here, some scopes take as long to boot up as an old PC.
When the scope boots up you should see the divisions, scale, and a noisy, flat line of a
waveform.
The screen should also show previously set values for time and volts per div. Ignoring those scales for
now, make these adjustments to put your scope into a standard setup:
› Turn channel 1 on and channel 2 off.
› Set channel 1 to DC coupling.
› Set the trigger source to channel 1 – no external source or alternate channel triggering.
› Set the trigger type to rising edge, and the trigger mode to auto (as opposed to single).
› Make sure the scope probe attenuation on your scope matches the setting on your probe (e.g. 1X,
10X).
For help making these adjustments you can consult scope’s user’s manual.

Testing the Probe

Let’s connect that channel up to a meaningful signal. Most scopes will have a built-in frequency
generator that emits a reliable, set-frequency wave – on the GA1102CAL there is a 1kHz square
wave output at the bottom-right of the front panel. The frequency generator output has two
separate conductors – one for the signal and one for ground. Connect your probe’s ground
clip to the ground, and the probe tip to the signal output.
As soon as you connect both parts of the probe, you should see a signal begin to dance around your
screen. Try fiddling with the horizontal and vertical system knobs to maneuver the waveform around the
screen. Rotating the scale knobs clockwise will “zoom into” your waveform, and counter-clockwise
zooms out. You can also use the position knob to further locate your waveform.
If your wave is still unstable, try rotating the trigger position knob. Make sure the trigger isn’t higher
than the tallest peak of your waveform. By default, the trigger type should be set to edge, which is
usually a good choice for square waves like this.
Try fiddling with those knobs enough to display a single period of your wave on the screen.
Or try zooming way out on the time scale to show dozens of squares.

Compensating an Attenuated Probe

If your probe is set to 10X, and you don’t have a perfectly square waveform as shown above,
you may need to compensate your probe. Most probes have a recessed screw head, which you
can rotate to adjust the shunt capacitance of the probe.
Try using a small screwdriver to rotate this trimmer, and look at what happens to the waveform.
Adjust the trimming cap on the probe handle until you have a straight-edged square wave.
Compensation is only necessary if your probe is attenuated (e.g. 10X), in which case it’s critical.
Probing, Triggering, and Scaling Tips

Once you’ve compensated your probe, it’s time to measure a real signal! Go find a signal source
e.g. frequency generator and start.
The first key to probing a signal is finding a solid, reliable grounding point. Clasp your ground
clip to a known ground, sometimes you may have to use a small wire to intermediate between
the ground clip and your circuit’s ground point. Then connect your probe tip to the signal under
test. Probe tips exist in a variety of form factors – the spring-loaded clip, fine point, hooks, etc.
– try to find one that doesn’t require you to hold it in place all the time.

Once your signal is on the screen, you may want to begin by adjusting the horizontal and vertical scales
into at least the “ballpark” of your signal. If you’re probing a 5V 1kHz square wave, you’ll probably want
the volts/div somewhere around 0.5-1V, and set the seconds/div to around 100µs (14 divisions would
show about one and a half periods).
If part of your wave is rising or falling of the screen, you can adjust the vertical position to
move it up or down. If your signal is purely DC, you may want to adjust the 0V level near the bottom of
your display.
Once you have the scales ball parked, your waveform may need some triggering. Edge
triggering – where the scope tries to begin its scan when it sees voltage rise (or fall) past a set point – is
the easiest type to use. Using an edge trigger, try to set the trigger level to a point on your waveform
that only sees a rising edge once per period.
Now just scale, position, trigger and repeat until you’re looking at exactly what you need.
Measure Twice, Cut Once

With a signal scoped, triggered, and scaled, it comes time to measure transients, periods, and
other waveform properties. Some scopes have more measurement tools than others, but
they’ll all at least have divisions, from which you should be able to at least estimate the
amplitude and frequency.
Many scopes support a variety of automatic measurement tools, they may even constantly
display the most relevant information, like frequency. To get the most out of your scope, you’ll
want to explore all of the measure functions it supports. Most scopes will calculate frequency,
amplitude, duty cycle, mean voltage, and a variety of other wave characteristics for you
automatically.

Using the scope’s measure tools to find VPP, VMax, frequency, period and duty cycle
A third measuring tool many scopes provide is cursors. Cursors are on-screen, movable
markers which can be placed on either the time or voltage axis. Cursors usually come in pairs, so you can
measure the difference between one and the other.
Measuring the ringing of a square wave with cursors.
Once you’ve measured the quantity you were looking for, you can begin to make adjustments to your
circuit and measure some more! Some scopes also
support saving, printing, or storing a waveform, so you can recall it and remember those good old times
when you scoped that signal.
To find out more about what your scope can do, consult its user’s manual!
Voltmeter Usage:
A multi-meter is an electrical instrument capable of measuring voltage, current, and resistance.
Digital multi-meters have numerical displays, like digital clocks, for indicating the quantity of
voltage, current, or resistance. Analog multi-meters indicate these quantities by means of a
moving pointer over a printed scale.
Some digital multi-meters are auto-ranging. An auto-ranging meter has only a few

selector switch (dial) positions. Manual-ranging meters have several different selector positions
for each basic quantity: several for voltage, several for current, and several for resistance.
In order to measure voltage of a battery set your multi-meter’s selector switch to the
highest-value ‘DC volt’ position available. Auto-ranging multi-meters may only have a single
position for DC voltage, in which case you need to set the switch to that one position. Touch the
red test probe to the positive (+) side of a battery, and the black test probe to the negative (-) side
of the same battery. The meter should now provide you with some sort of indication. Reverse the
test probe connections to the battery if the meter’s indication is negative (on an analog meter, a
negative value is indicated by the pointer deflecting left instead of right).
If your meter is a manual-range type, and the selector switch has been set to a high-
range position, the indication will be small. Move the selector switch to the next lower DC
voltage range setting and reconnect to the battery. The indication should be stronger now, as
indicated by a greater deflection of the analog meter pointer (needle), or more active digits on the
digital meter display. For the best results, move the selector switch to the lowest-range setting
that does not ‘over-range’ the meter. An over-ranged analog meter is said to be ‘pegged,’ as the
needle will be forced all the way to the right-hand side of the scale, past the full-range scale
value. An over-ranged digital meter sometimes displays the letters ‘OL’, or a series of dashed
lines. This indication is manufacturer-specific.
Ohmmeter Usage:
Be sure to never measure the resistance of any electrically ‘live’ object or circuit. In other words,
do not attempt to measure the resistance of a battery or any other source of substantial voltage
using a multi-meter set to the resistance (ohms) function, failing to heed this warning will likely
result in meter damage and even personal injury.
Connect the meter’s test probes across the resistor as such, and note its indication on the
resistance scale:

If the needle points very close to zero, you need to select a lower resistance range on the Meter.
If you are using a digital multi-meter, you should see a numerical figure close to 10 shown on the
display, with a small ”k” symbol on the right-hand side denoting the metric prefix for ”kilo”
(thousand). Some digital meters are manually-ranged, and require appropriate range selection
just as the analog meter. If yours is like this, experiment with different range switch positions
and see which one gives you the best indication.
Ammeter Usage:
Current is the measure of the rate of electron ‘flow’ in a circuit. It is measured in the unit of the
Ampere, simply called ‘Amp’, (A).
The most common way to measure current in a circuit is to break the circuit open and insert an
‘ammeter’ in series (in-line) with the circuit so that all electrons flowing through the circuit also
have to go through the meter. Because measuring current in this manner requires the meter be
made part of the circuit, it is a more difficult type of measurement to make than either voltage or
resistance.
Some digital meters, like the unit shown in the illustration, have a separate jack to insert the red
test lead plug when measuring current. Other meters, like most inexpensive analog meters, use
the same jacks for measuring voltage, resistance, and current.

OHM’S LAW
(EXPERIMENTAL VERIFICATION OF OHM’S LAW)
OBJECTIVE:
- To verify ohm’s law experimentally.
APPARATUS:
1. DC power supply.
2. Three resistances of different values
3. Connecting wires
4. Digital multi meter (DMM) / Voltmeter / Ammeter
THEORY:
Ohm’s Law:
When current I flows through a resistor, then the potential difference V (often simply called
voltage) between its terminals is proportional to I as in equation (1), where R is the resistance.
Basic Equation: V = R · I (1)
Combinations of Resistors:
When two or more resistors ( R1, R2, R3,…) are connected in series (Fig. 1) then this
combination is equivalent to a single resisto of resistance Req given by (2).
Basic Formula: Req = R1 + R2 + R3+. . . . . (2)
When two or more resistors are connected in parallel (Fig. 2) then the equivalent resistance Req
is given by (3).
Basic Formula: Req = 1 + 1 + 1 + 1 . . . (2)
R1 R2 R3

PROCEDURE & OBSERVATIONS:

Part I: Ohm’s Law
› Make sure that the DC power supply is off and unplugged. Make sure that the regulating
knobs are in minimum positions. Your instructor will explain to you the operation of DC power
supply, the ammeter and the voltmeter.
› Construct the circuit as in Fig. 3a, using the resistor marked R1 in your sample. Use the dc
ammeter scale and make sure that + and – markings are exactly as in Fig. 3a
› Set the voltmeter scale to dc volts scale. Attach connectors to your voltmeter (or DMM as
voltmeter. suggestion: use a red connector for the + terminal and a black one for -). Connect the
+ terminal to point B (where the current enters the resistor) and the other one to point A.
› Make sure all connections are tight. If you have a faulty connector, immediately hand it to your
instructor.
Note: Call your instructor to check your circuit. Do not proceed without his or her permission.
› After your instructor’s approval, prepare on your data sheet your first table, as shown. Plug in
the power supply. With the regulating knob(s) in Min position, turn the power “ON”.
Turn slowly the regulating knob(s) and watch both the ammeter and the voltmeter readings to
increase (if not, turn off the power at once and call your instructor).Keep doing this until the
ammeter reaches 50mA or the voltmeter reaches 5 volts whichever comes first. Record the
current I and the voltage V to three significant digits, by estimating fractions of smallest
divisions on the scales.
Resistor R1 Resistor R2 Resistor R3
I (mA) V (volts) I (mA) V (volts) I (mA) V (volts)

› Decreasing the current, record I and V four more times (a total of 5 readings), in roughly equal
intervals. The lowest current should be 5 to 10 mA.
› Repeat the last two steps for your resistors R2 and R3, with maximum current close to 50 mA
but using the finest voltmeter scale possible for each given resistor.
› Turn the power “OFF”, and record:
- The uncertainties in your readings on all scales of ammeter and voltmeter which you have
used.
- The zero readings of your ammeter: these are their readings when they are completely
disconnected from any circuits. They should be close to zero, but not necessarily exactly so.
Procedure Part II: Combinations of Resistors

› Connect all three resistors R1 , R2 , R3 in series and use the DC volt scale on the voltmeter.
Record 5 runs as before. (Note: your maximum current may be less than 50 ma because the
voltage must not exceed 10mvolts).
› Connect all these resistors in parallel. Again, use the DC voltmeter scale, with the maximum
current close to 50 mA. Record 5 runs, as before.
› Estimate (from your data in Part I) the values of R1 , R2 , R3 . Take the two higher
resistances (record which ones you are using) and connect them in parallel. Connect this
combination in series with the remaining resistor. Record 5 runs, as usual.
R1 , R2 , R3 R1 , R2 , R 3 R1 , R2 , R3
in Series in Parallel

2 Parallel in Series with

3rd
I (mA) V (volts) I (mA) V (volts) I (mA) V (volts)
Graphical Results
› Using graph paper, plot V vs. I for each of your resistors R1, R2, R3. Draw the line of best fit
in each case and (from the slope) determine the resistance in ohms, 3 significant digits. Display
all calculations on the graph sheet.
R1= R2= R3=
› Using graph paper, plot V vs. I for each of the three combinations. Determine Req for each
case, as in (1) above.
› From your results in (1) calculate the predicted (= theoretical) values of Req for each of the
three combinations. Display the calculations clearly.

› Summarize your results in the table shown. For % discrepancies use the predicted values as
more reliable (that is, refer to them as if they were exact).
%
COMBINATION PREDICTED R MEASURED R
DISCR.
ALL IN SERIES
ALL IN PARALLEL
SERIES &
PARALLEL


DIVIDER RULES
(VERIFICATION OF CURRENT DIVIDER RULE & VOLTAGE DIVIDER RULE)
OBJECTIVE:
- Verify the divider rules for voltage (VDR) and current (CDR).
THEORY:
The Voltage Divider Rule (VDR) states that the voltage across an element or across a series
combination of elements in a series circuit is equal to the resistance of the element or series
combination of elements divided by the total resistance of the series circuit and multiplied by the
total impressed voltage:
The Current Divider Rule (CDR) states that the current through one of two parallel branches is
equal to the resistance of the other branch divided by the sum of the resistances of the two
parallel branches and multiplied by the total current entering the two parallel branches. That is,
APPARATUS:
1. Power Supply 2. Resistances 3. Digital Multi-Meter (DMM)
4. Connecting Wires 5. Bread Board
PROCEDURE:
Part 1: Voltage Divider Rule (VDR)
Construct the circuit

› Without making any calculations, what value would you expect for the voltage across each
resistor? Explain your reasoning.
› Calculate V1 using the VDR with the measured resistor values. Measure V1 and determine the
percent difference between the theoretical and experimental results. How do they compare?
› If R2 = R3, then the VDR states the V2 = V3 and V1 = V2 + V3. Measure voltages V2 and V3,
and comment on the validity of these statements.

› Using VDR, calculate the voltage Vab. Measure Vab and determine the percent difference
between the theoretical and experimental results. How do they compare?
› Remove resistor R2 to construct the following open circuit:

› Using the measured resistor values, calculate the voltages V1, V2, and Vopen using VDR.
Measure voltages V1, V2, and Vopen with the DMM and calculate the percent differences.
Explain the reasoning.
Part 2: Current Divider Rule (CDR)

Construct the circuit

› Without making any calculations, what value would you expect for the current through each of
the resistors? Explain your reasoning.
› Calculate the currents I1, I2, and I3 using the CDR from the measured value of Is. Measure the
currents I1, I2, and I3.

› Based on these measurements, are your conclusions of earlier part verified? Use a percent
difference to compare the theoretical and experimental results.
› Set the maximum current coming from the power supply at 200 mA via a short. Place a short
circuit across the 10kΩ-resistor to construct the following circuit:
Part 3: Challenge Circuit

Construct the circuit below:

› Calculate the voltages V1, V2, V3 and V4 using the VDR with measured resistor values.
Measure the voltages V1, V2, V3 and V4 and use a percent difference to compare the calculated
and measured results. How do they compare?
› Using the results of earlier part, calculate the voltage Vab using KVL.
› Measure the voltage Vab and use a percent difference to compare the calculated and measured
results. How do they compare? Is the voltage Vab equal to V1 – V3? Equal to V2 – V4? Explain
your reasoning?
› Suppose now that a short is placed across the terminal points ab. Calculate the current Iab
through the short. Measure the current Iab and use a percent difference to compare the theoretical
and experimental results. How do they compare?
Note: Use separate sheet for the findings of above part!
NODAL ANALYSIS
(EXPERIMENTAL VERIFICATION OF NODAL ANALYSIS)
OBJECTIVE:
- To analyze a circuit and to determine the unknown parameters of the circuit
THEORY:
Under this method the following procedure is adopted:

Assume the voltage of different independent nodes.

› Write the equations for each node as per Kirchhoff’s Current Law.
› Solve the above equations to get the node voltages.
› Calculate the branch current from the values of node voltages.
Let us consider the circuit shown in the figure below. L and M are two
independent nodes. M can be taken as a reference node. Let the voltage of node L (with respect
to M) be VL.
Using Kirchoff‘s Law we get,

I1+I2=I3
Ohm’s law gives,
I1= V1 / R1= (E1-VL) / R1,
I2=V2/R2 = (E2-VL) / R2,
I3 =VL / R3
(E1-VL)/R1 + (E2-VL)/R2= VL/R3
Rearranging the terms we get,
VL (1/R1+1/R2+1/R3)-E1/R1-E2/R2=0
It may be noted that the above nodal equation contains the following terms:
› The node voltage multiplied by the sum of all the conductances connected to that node. This
term is positive.
› The node voltage at the other end of each branch (connected to this node) multiplied by the
conductance of the branch. These terms are negative.
› In this method of solving a network the no of equations required for the solution is one less
than the no of independent nodes in the network
In general the nodal analysis yields similar solutions.
APPARATUS:
1. Two DC power supplies.

2. Five resistances of different values

3. Connecting wires
4. Digital multi meter (DMM)
PROCEDURE:
› Construct the circuit shown in Figure below:
Figure
› Pick the resistances. Also verify their resistance by meter and record it in table.
› Solve given circuit for the unknowns before moving to the circuit for measured values.
› Set the DC supply E1=10V and E2=5V.
› Measure the currents through resistances R1, R2, R3, R4 & R5 and record it in table.
› Also measure voltages across each resistor.
› Now set the DC supply E1=5V and E2=7V.
› Repeat all steps and record the values
Note: Use measured values of resistances for all calculations. Make these calculations on the space provided.
OBSERVATIONS & CALCULATIONS:


Resistors R1 R2 R3 R4 R5
Rated Values
Measured
Values
For E1=10V and E2=5V
Voltages VR1 VR2 VR3 VR4 VR5
Calculated
Values
Measured
Values
Percentage
Difference
Currents IR1 IR2 IR3 IR4 IR5
Calculated
Values
Measured
Values

Percentage
Difference
E1=5V and E2=7V
Voltages VR1 VR2 VR3 VR4 VR5
Calculated
Values
Measured
Values
Percentage
Difference
Currents IR1 IR2 IR3 IR4 IR5
Calculated
Values
Measured
Values
Percentage
Difference
Challenge: Swap the resistors R1 with R4, R5 with R2 and repeat all above steps to determine
unknown voltages and currents both theoretically and practically.
Note: Use separate sheets for analysis of above problem.
ANSWER THE FOLLOWING QUESTIONS

(a). What is a node?
(b). Calculate the equivalent resistance.

(c). Solve the following circuit for power dissipation (P=VI) across R1, R2 and R3.
(d). What do you meant by a super node?

Note: Use separate sheets for answering above questions.
MESH ANALYSIS
(EXPERIMENTAL VERIFICATION OF MESH ANALYSIS)

OBJECTIVE:
- To analyze a two Mesh circuit and to determine the current in each branch of the circuit
THEORY:
The mesh analysis is a systematic way of applying KVL around each mesh of a circuit and
describes the branch voltages in terms of the mesh currents. This will give us a set of equations
that we solve together to find the mesh currents. Once we find the mesh currents we can use
them to calculate any other currents or voltages of interest.
We know from KVL the algebraic sum of voltages around a close loop is zero so considering the
circuit shown below and applying KVL in each loop (mesh):
While writing equations for

Applying KVL to mesh 1
- E1 + I1R1 + (I1 - I2) R2 = 0
I1 (R1 + R2) - I2R2 = E1 (1)
Applying KVL to mesh 2
- E2 + (I2 - I1) R2 + I2R3 = 0
I2 (R2 + R3) - I1R2 = E2 (2)
Solving above two equations, values of unknowns can easily be calculated.

R1 + R2 −R2 I1 E1
[ ][ ]=[ ]
−R2 R2 + R3 I2 E2
APPARATUS:
1. Two DC power supplies.
2. Three resistances of different values

3. Connecting wires
4. Digital multi meter (DMM)
PROCEDURE:
› Construct the circuit shown in Figure below:
› Pick the resistances. Also verify their resistance by meter and record it in table.
› Solve given circuit for the unknowns before moving to the circuit for measured values.
› Set the DC supply E1=12V and E2=5V.
› Measure the currents through resistances R1, R2 & R3 and record it in table.
› Also measure voltages across each resistor.
› Now set the DC supply E1=5V and E2=12V.
› Repeat all steps and record the values


Resistors R1 R2 R3
Rated Values
Measured Values
For E1=12V and E2=5V
Voltages VR1 VR2 VR3
Calculated Values
Measured Values
Percentage Difference
Currents IR1 IR2 IR3
Calculated Values
Measured Values
E1=5V and E2=12V
Voltages VR1 VR2 VR3
Calculated Values

Measured Values
Currents IR1 IR2 IR3
Calculated Values
Measured Values
Challenge: Swap the resistors R1 with R3 and repeat all above steps to determine unknown
voltages and currents both theoretically and practically.

(a). What is the difference between a loop and a mesh?
(b). What is an ideal voltage source? How is it different from real voltage source?

(c). What is an ideal current source? How is it different from real current source?
(d). Solve the following circuit for power dissipation across R1, R2 and R3.
(e). What do you meant by a super mesh?

SUPERPOSITION THEOREM
(EXPERIMENTAL VERIFICATION OF SUPERPOSITION THEOREM)

OBJECTIVE:
- To verify super position theorem in DC circuits.
THEORY:
The superposition principle states that:
“The current through or voltage across, any resistive branch of a multisource network is the
algebraic sum of the contribution due to each source acting independently.”
When the effect of one source is considered, the others are replaced by their internal resistances.
This principle permits one to analyze circuits without restoring to simultaneous equations.
Superposition is effective only for linear circuit relationship. Non-linear effects, such as power,
which varies as the square of the current or voltage, cannot be analyzed using this principle.
Applying Superposition
› Step 1: In a network containing multiple independent sources, each source can be applied
independently with the remaining sources turned off.
› Step 2: To turn off a voltage source, replace it with a short circuit, and to turn off a current
source, replace it with an open circuit.
› Step 3: When the individual sources are applied to the circuit, all the circuit laws and
techniques we have learned, or will learn, can be applied to obtain a solution.
›Step 4:The results obtained by applying each source independently are then added together
algebraically to obtain a solution.
APPARATUS:
1- DMM
2- 2 DC Power Supplies,
3- Resistances (1k Ω, 2k Ω, 430 Ω)
PROCEDURE:
› Make all necessary calculations as per table I. Use measured values of resistances in
calculations.
› Construct the network of Fig-I, where R1 = 1 k Ω, R2 = 430 Ω, R3 = 2 k Ω. Verify the
resistances using DMM.
Figure-I
› Using superposition and measured resistance values, calculate the currents indicated in
observation Table (a), for the network of Fig-1. Next to each magnitude include a small arrow to

indicate the current direction for each source and for the complete network.
› Energize the network of Fig-1 and measure the voltages indicated in observation table b,
calculate current in Table (b) using Ohm’s Law. Indicate the polarity of the voltages and
direction of currents on Fig-1.
› Construct the network of Fig -2. Note that source E2 has been removed.
Figure-II
› Energize the network of Fig -2 and measure the voltages indicated in Table (c). Calculate
currents using Ohm’s Law.
› Now construct the network of Fig -3. Note that source E1 has been removed.
Figure-III
› Energize the network of Fig -3 and measure the voltages indicated in Table (d). Calculate
currents using Ohm’s Law.
› Using the results of above steps, determine the power delivered to each resistor and insert in
Table (e).
Resistors Nominal Values Measured Values
R1 1kΩ
R2 430kΩ
R3 2kΩ

(a). Calculated Values for the network of Fig I

Due to E1 Due to E2 Algebraic Sum ( ∑ )
I1= I1= I1=
I2= I2= I2=
I3= I3= I3=
(b). Measured Values for the network of Fig I

V1 V2 V3 I1 I2 I3
(c). Measured Values for the network of Fig II

V1 V2 V3 I1 I2 I3
(d). Measured Values for the network of Fig III

V1 V2 V3 I1 I2 I3
(e). Power Absorbed (use measured values of I and V)

Due to E1 Due to E2 Sum of Columns 1&2 E1 & E2 acting
simultaneously
Challenge: Give the complete analysis of above discussed problem with E1 & E2’s polarities
reversed!


(a). If Is=18A, R1= 6Ω, R2=4Ω and R3=3Ω, the current I3 (in Amp) is calculated as:
(b). What are the limitations of Superposition Theorem?

(c). Calculate current through R3 using superposition theorem in the figure below.
(d). Find the current drawn from a 115 V line by a DC electric motor that delivers 1hp. Assume
100% efficiency of operation.

STAR & DELTA CONNECTION OF RESITANCES
(EXPERIMENTAL VERIFICATION OF STAR-DELTA TRANSFORMATION)
OBJECTIVE:
- To understand the significance of star-delta transformation in circuit solving.
THEORY:
In many circuit applications, we encounter components connected together in one of two ways to
form a three-terminal network: the “Delta,” or Δ (also known as the “Pi,” or π) configuration,
and the “Y” (also known as the “T”) configuration.
It is possible to calculate the proper values of resistors necessary to form one kind of network (Δ
or Y) that behaves identically to the other kind, as analyzed from the terminal connections alone.
That is, if we had two separate resistor networks, one Δ and one Y, each with its resistors hidden
from view, with nothing but the three terminals (A, B, and C) exposed for testing, the resistors
could be sized for the two networks so that there would be no way to electrically determine one
network apart from the other. In other words, equivalent Δ and Y networks behave identically.
There are several equations used to convert one network to the other:

APPARATUS:
1. Eleven resistances of different values
2. DMM
3. Breadboard
4. DC Power Supply
PROCEDURE:
› Select resistances randomly and measure their values.
› Using star-delta transformations, calculate value of Req(calculated) for the circuit below.
› Construct the circuit shown above. For voltage source being set to V (source) = 15V, determine
the total current I (total) in the circuit using DMM and calculate

Req (measured_1) = V (source) / I (total)

› Disconnect the above circuit by removing voltage source and measure the value of Req
(measured_2) using DMM as an ohm meter,
› Compare measured and calculated values.

R1 R2 R3 R4 R5 R6 R7

Req(calculated)
Req (measured_1)
Difference
Req(calculated)
Req (measured_2)
Difference
Challenge: Repeat the above procedure by interchanging R3 to R5 and R8 to R9 in original

circuit. Make all calculations and measurements involved.


(a). What is the significance of star-delta transformation approach?
(b). For the circuit shown below determine the value of total current when voltage source is set to
18V.
(c) Determine the equivalent resistance between the terminals A & B of network shown below.

THEVENIN'S THEOREM
(EXPERIMENTAL VERIFICATION OF THEVENIN'S THEOREM)
OBJECTIVE:
- To Verify Thevenin Theorem by finding its Thevenin’s Equivalent Circuit.
THEORY:
Any linear circuit is equivalent to a single voltage source (Thevenin's Voltage) in series with
single equivalent resistance (Thevenin’s Equivalent Resistances).
Applying Thevenin’s Theorem:
› Step 1: Remove the load and find voltage across the open-circuit terminals, Vth. All the circuit
analysis techniques presented can be used to compute this voltage.
› Step 2: Determine the Thevenin equivalent resistance of the network at the open terminals with
the load removed. Three different types of circuits may be encountered in determining the
resistance, Rth.
- If the circuit contains only independent sources, they are made zero by replacing the voltage
sources with short circuits and the current sources with open circuits. Rth is then found by
computing the resistance of purely resistive network at the open terminals.
- If the circuit contains only dependent sources, an independent voltage or current source is
applied at the open terminals and the corresponding current or voltage at these terminals is
measured. The Voltage/Current ratio at the terminals is the Thevenin equivalent resistance. Since
there is no energy source the open circuit voltage is zero in this case.
- If the circuit contains both the independent and dependent sources, the open circuit terminals
are shorted and the short-circuit current between these terminals is determined. The ratio of the
open circuit voltage to short circuit current is the resistance Rth.
› Step 3: If the load is now connected to the Thevenin equivalent circuit, consisting of Vth in
series with Rth, the desired solution can be obtained.
APPARATUS:
1. DMM
2. Power Supply
3. Resistances (120Ω, 1k Ω, 390Ω)
PROCEDURE:
› Calculate measured values of resistances.
› Reduce the circuit by calculating the Thevenin equivalent resistance across the terminals A &

B.
› Calculate the Thevenin equivalent voltage across terminals “A” and “B” for 5V, 10V, 15V.
› Pertaining to circuit in figure III, calculate values of IL for different values of RL.
› Now construct circuit in figure I, measure the value of Vth by removing RL.
› Construct circuit in figure II to have measured value of Rth.
› Construct circuit in figure III to determine measured values of IL for different values of RL.
Figure-I
Figure-II
Figure-III
R1 R2 R3
Vs Vth Rth RL IL

5V 1kΩ
22kΩ
10V 1kΩ
22kΩ
15V 1kΩ
22kΩ
Table. Calculated Values
Vs Vth Rth RL IL
5V 1kΩ
22kΩ
10V 1kΩ
22kΩ
15V 1kΩ
22kΩ
Table. Measured Values
Challenge: Replacing 1kΩ resistances by 2.2kΩ and keeping all other things same, redo the
above analysis.


(a). Use Thevenin’s Theorem to find the current through the 5Ω resistance in the circuit diagram
shown below.
(b).What is the importance of Thevenin’s Theorem in circuit analysis?

(c). Discuss the limitations of Thevenin’s Theorem.
(d) A light bulb draws 0.5A current at the input voltage of 230V. Determine the resistance of the
filament and also the power dissipated.
Note: Use separate sheets for answering above questions

MAXIMUM POWER TRANSFER THEOREM
(EXPERIMENTAL VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM
FOR A NETWORK)
OBJECTIVE:
- To prove maximum power transfer theorem practically.
THEORY:
The power transferred from a source supply source to load is at its maximum when the resistance
of the load is equal to the internal resistance of the source. In other words “A resistive will be
consuming maximum power from the supply when the load resistance is equal to the equivalent
(Thevenin) resistance.”
A graph of RL against P is shown in figure below, the maximum value of power occurs at RL=
Rth.

APPARATUS:
1. DMM
2. Power Supply
3. Resistances: fixed (2.2kΩ, 1kΩ), variable (5kΩ)
PROCEDURE:
› Connect the circuit shown in the figure below.
› From the circuit it can be noted that Rth is fixed resistance of value 2.2kΩ but RL is variable
of value 5kΩ.
› Set the value of Vth = 10 V.
› Change the value of RL in steps as shown in table.
› Measure the voltage VL and current IL and record it in table.
› Plot the graph of power vs. load resistance (RL).
› Using graph estimate P max (practical).
› Use P max = Vth²/ 4Rth to have the value of P max (theoratical).

› Repeat above steps by using Rth = 1kΩ.

PART (I)
For Vth = 10 V, Rth = 2.2kΩ
RL IL VL Power = IL x VL
0.3kΩ
0.6kΩ
0.9kΩ
1.5kΩ
2.2kΩ
2.5kΩ
3.0kΩ
3.3kΩ
3.6kΩ
4.0kΩ
P max (theoratical)
P max (practical)
Difference

PART (II)
For Vth = 10V, Rth = 1kΩ
RL IL VL Power = IL x VL
0.3kΩ
0.6kΩ
0.9kΩ
1.5kΩ
2.2kΩ
2.5kΩ
3.0kΩ
3.3kΩ
3.6kΩ
4.0kΩ
P max (theoratical)
P max (practical)
Difference

Challenge: For Rth = 1kΩ +2.2kΩ, estimate maximum power transferred to the circuit
practically. Also compare it with theoretical value.

(a). What is meant by load matching?
(b). Find the value of RL for maximum power transfer in the network shown below. Also
calculate the maximum power that can be transferred to this load.

RECIPROCITY THEOREM
(EXPERIMENTAL VERIFICATION OF RECIPROCITY THEOREM)
OBJECTIVE:
- To verify reciprocity theorem experimentally.
THEORY:
The reciprocity theorem states that “The current I in any branch of a network, due to a single
voltage source E anywhere else in a network, will equal the current through the branch in which
current I was originally measured”. The reciprocity theorem is thus applicable only to single
source networks. It is, therefore, not a theorem employed in a multi source networks. In other
words, the location of voltage source and the resulting current may be interchanges without a
change in current. The precaution is to be taken that the polarity of voltage source has the same
correspondence with the direction of branch current in that position.

Figure (1)
In the network of the figure (a), the current I due to voltage source E was determined. If the
position of each is interchanged as shown in figure (b), the current I will be of same value as
indicated. To demonstrate the validity of this statement and theorem, consider the network of
figure (a) with the values of elements assigned there.
The total resistance is
Figure (2)
For the network of the figure (b) which corresponds to that of figure (a), we find

which agrees with value of I calculated above.

APPARATUS:
1. DMM
2. Power Supply
3. Resistors
PROCEDURE:
› Consider the following circuit for practical purpose.
Figure (3)
› Make connections as shown in figure 3 (a). Calculate the values of I and IT and write it in table
(1) for different values of E.
› Measure IT and I and write it in table (I).
› Make connections in figure 3(b).Calculate the values of IT and I and record in table (2).
› Measure IT and I and writ it in table (II).
› Compare calculated values and measured values of currents in both the cases and comment on
the result.
R1 R2 R3 R4

Calculated Values Measured Values

IT I IT I
E =2.5V
E =7.5V
E =5V
E =10V
TABLE-I
(values for original circuit)
Calculated Values Measured Values

IT I IT I
E =2.5V
E =7.5V
E =5V
E =10V
TABLE-II
(values after changing position of source)


(a). What are the limitations of Reciprocity Theorem?
(b). Show that Reciprocity Theorem is applicable for the network shown in figure below.

OPERATIONAL AMPLIFIER APPLICATIONS
(IMPLEMENTATION OF INVERTING AMPLIFIER & NON-INVERTING AMPLIFIER)
OBJECTIVE:
-To gain experience with operational amplifier.
-To study the use of OP-AMP as an inverting amplifier & non-inverting amplifier.
THEORY:
The operational amplifier is an extremely efficient and versatile device. Its applications span the
broad electronic industry filling requirements for signal conditioning, special transfer functions,
analog instrumentation, analog computation, and special systems design. The analog assets of
simplicity and precision characterize circuits utilizing operational amplifiers. The precision and
flexibility of the operational amplifier is a direct result of the use of negative feedback.
Generally speaking, amplifiers employing feedback will have superior operating characteristics
at a sacrifice of gain.
The op-amp is a very high gain amplifier with inverting and non-inverting inputs. It can
be used to provide much smaller but exact gain set by external resistors or to sum more than one
input, each having a desired voltage gain.
As an inverting amplifier the resistors are connected to the inverting input as shown in figure 1
with output voltage:
Figure 1

A non inverting amplifier is provided by a circuit of figure 2 with output voltage given by:
Figure 2
APPARATUS:
1. LM 741 IC (OP-AMP) 2. Resistances (fixed) 100k, 20k Ω 3. Oscilloscope
4. DC power Supply 5. Digital Multi Meter (DMM) 6. Connecting wires
PROCEDURE, OBSERVATIONS & CALCULATIONS:

PART (1) – INVERTING AMPLIFIER:
Figure 3
› Set the circuit in accordance with the figure 3.

› Using function generator, apply the input of value 1V, rms and f= 10 kHz and sketch the input
using oscilloscope.
› Keeping the values of Ro and Ri equal to 100k and 20k, calculate the voltage gain (Vo/Vi)
using .
› Using DMM/oscilloscope measure the output voltage Vo determine the measured voltage gain

(Av).
› Compare the voltage gains of step (c) and (d).
› Sketch the output waveform.
› Record all the readings in table below.
Input Wave Form

1V, rms
(f=10kHz)
Value of Ro 100k
Value of R1 20k
Calculated Voltage Gain

(Vo/Vi)
Output Voltage (Vo)
Measured Voltage Gain (Av)
Difference of Gains

Output Waveform
PART (2) – NON INVERTING AMPLIFIER:
Figure 4
› Set the circuit in accordance with the figure 4.
› Using function generator, apply the input of value 1V, rms and f=10kHz and sketch the input
using oscilloscope.
› Keeping the values of Ro and R1 equal to 100k and 20k, calculate the voltage gain (Vo/Vi)
using .
› Using DMM/oscilloscope measure the output voltage Vo determine the measured voltage gain
(Av).
› Compare the voltage gains of step (c) and (d).

Input Wave Form

1V, rms
(f=10kHz)
Value of Ro 100k
Value of R1 20k
Calculated Voltage Gain

(Vo/Vi)
Output Voltage (Vo)
Measured Voltage Gain (Av)
Difference of Gains

Output Waveform
OPERATIONAL AMPLIFIER APPLICATIONS
(IMPLEMENTATION OF UNITY GAIN FOLLOWER & SUMMING AMPLIFIER)

OBJECTIVE:
-To gain experience with operational amplifier.
-To study the use of OP-AMP as a unity gain follower & summing amplifier.
THEORY:
The operational amplifier is an extremely efficient and versatile device. Its applications span the
broad electronic industry filling requirements for signal conditioning, special transfer functions,
analog instrumentation, analog computation, and special systems design. The analog assets of
simplicity and precision characterize circuits utilizing operational amplifiers. The precision and
flexibility of the operational amplifier is a direct result of the use of negative feedback.
Generally speaking, amplifiers employing feedback will have superior operating characteristics
at a sacrifice of gain.
Connecting the output back to the inverting input as in figure 1 provides a gain of unity.
Figure 1
More than one input can be connected through separate resistors as shown in figure 2 with the
output voltage then:

figure 2
APPARATUS:
1. LM 741 IC (OP-AMP) 2. Resistances (fixed)100K Ω x2, 20k Ω 3. Oscilloscope
4. DC power Supply 5. Digital Multi Meter (DMM) 6. Connecting wires
PROCEDURE, OBSERVATIONS & CALCULATIONS:

PART (1) – UNITY GAIN FOLLOWER:
Figure 3
› Set the circuit in accordance with the figure3 .

› Using function generator, apply the input of value 2V, rms and f= 10 kHz and sketch the intput
using oscilloscope.
› Using DMM measure the output voltage Vo .

Input Wave Form

2V, rms
(f=10kHz)
Calculated Output Voltage

(Vo)
Measured Output Voltage (Vo)
Output Waveform
PART (2) – SUMMING AMPLIFIER:

Figure 4
› Set the circuit in accordance with the figure .

› Using function generator, apply the inputs of value 1V, rms and f=10kHz and sketch the inputs
using oscilloscope.
› Keeping the values of Ro= R1 equal to 100k and R2=20k, calculate the output voltage using
.
› Measure and record the output voltage.
› Compare the voltages gains of step (c) and (d).
Input Wave Form

1V, rms
(f=10kHz)
V1=V2
Value of Ro 100k
Value of R1 100k

Value of R2 20k
Calculated Output Voltage

(Vo)
Measured Output Voltage
Difference of Voltages
Output Waveform


(a). Write the characteristics of an ideal operational amplifier?
(b). If v1 = 1V and v2 = 2V, find vo in the circuit below:

RC CIRCUIT ANALYSIS
(TRANSIENT ANALYSIS & TIME CONSTANT DETERMINATION)
OBJECTIVE:
-To analyze RC series circuit.
-To study quantitatively the rate at which capacitor charges or discharges.
THEORY:
Suppose we have a circuit as given above. We connect the switch to point A at time t = 0.
Kirchhoff Law tells us that the sum of voltage differences around a closed loop must be zero.




APPARATUS:
1. Capacitor 1µF 2. Resistances (fixed) 100k 3. Oscilloscope
4. Function Generator 5. Digital Multi Meter (DMM) 6. Connecting wires
PROCEDURE:
In this experiment we will try to verify properties of an RC circuit by using a square wave
generator in place of a battery and switch. The output of a square wave generator alternates
between two different voltages separated by a potential difference V.
When the output is at higher potential the capacitor is charging up. When the output switches to
lower potential, the capacitor discharges. The capacitor then alternates between charging and
discharging cycles in accordance with output of a square wave generator.
The charging cycle should be described by Equation 2 and discharging cycle by Equation 4.

› Connect the circuit as shown in figure above.

› Using function generator, apply the square wave input.
› Observe the output waveform (across capacitor) on oscilloscope.
› Adjust the frequency to such a value such that the capacitor is sufficiently charged and
discharged alternatively. This can simply be done by reducing the frequency using frequency
setting knob of function generator.
› Determine the value Vmax (max. voltage up to which a capacitor can be charged) from display
at oscilloscope screen.
› Find the value of voltage corresponding to Time Constant by using V (Time Constant) = 0.63 x
Vmax
› Now look for the value in seconds on Time Scale corresponding to the voltage determined in
step
› This value will be equal to the Time Constant (measured)
› Calculate the theoretical value of time constant by using
Time Constant (Calculated) = RxC.
› Compare the values of Time Constant (Calculated) and Time Constant (measured).
› Also draw the waveforms for input and output.
Vmax
V (Time Constant)
Time Constant (Calculated)
Time Constant (Measured)
Difference

Input Waveform (square wave)
Output Waveform (across capacitor)


(a). It is assumed that after 4-5 time constants the capacitor is fully charged. Prove
mathematically.
(b). Show that ohm x farad = second.
(c). How can you identify the leads/ terminals of an electrolytic capacitor? (hint: the one used in
lab)

NORTON’S THEOREM
(EXPERIMENTAL VERIFICATION OF NORTON’S THEOREM)
OBJECTIVE:
- To verify Norton’s Theorem experimentally.
APPARATUS:
1. Resistors 2. Power Supply 3. DMM
4. Connecting wires

THEORY:
To simplify the solutions of the complicated net works, many network theorems were developed.
Norton’s theorem is one of them. The statement of this theorem is that
“ The current ( IL) in a load impedance, connected to two terminals A &B of a network
of generators and linear impedances is same if this load impedance is connected to a constant
current generator, whose generated current ( IN ) is equal to the short circuit current between the
terminals A and B, in parallel with an impedance ( RN ) equal to the impedance of the net work
between the same two terminals A and B, when the generators in the net work have been
replaced by their internal impedances.”
Figure-1 is the network containing number of generators and linear impedances. IN is

the short circuit (Norton’s) current between A& B. RN is the (Norton’s) impedance
between A & B, when the source is replaced by its internal impedance.
The load current IL is given by:
Where IN = Norton’s Current, RL = Load Resistance & RN = Norton’s Resistance
PROCEDURE:
› The voltage source is disconnected and the terminals are short circuited by assuming that the
internal impedance of the voltage source is zero. And the resistance across A & B is measured
after removing the load RL. This resistance is the Norton’s resistance RN.
› Now the voltage source or battery is connected. The current between A & B is measured. This
is the short circuit current and is called as Norton’s current ( IN ).
› Now the load resistor RL is connected in its place in series with a milli-ammeter or a multi
meter and the current IL through the load is measured. Similarly, the IN and IL are
measured for different source voltages (V). The values V, IN and IL are noted in the
table-1.
› The circuit is replaced by a constant current source IN with a parallel resistor, whose
value is equal to RN. This is the Norton’s equivalent circuit.
› Now the load RL is also connected in series with a milli-ammeter between A & B. Then the
current IL1 through the load RL is measured for different values of IN measured in the table-1.
The IN and IL1 values are noted in the table-2.
› It is observed that for same values of IN in tables1 and 2, the IL and IL1 are equal. Also
calculate the IL values using the above formula. These values are also equal to ILl Values.

Table-I
RN measured across the terminals A and B
Source Voltage V IN measured Load Current IL

Table-II
RN computed
RL Load Resistance
IN Computed Load Current IL1 Load Current IL (from Calculated IL

table I)


(a). Can we covert a circuit’s Norton’s into its Thevenin’s equivalent? If yes, how?
(b). Using Norton’s Theorem, calculate current flowing through 15Ω load resistor in the circuit
below. All resistance values are in ohms.

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EE Department Linear Circuit Analysis

PRACTICAL WORK BOOK

Complied By: Checked By:

CEME (NUST), Rawalpindi 1

DEPARTMENT OF ELECTRICAL ENGINEERING

S.NO. TITLE OF EXPERIMENT Page No.

01 Introduction: Basic Concepts and Lab Equipment. 04

02 Experimental Verification of OHM’s Law. 20

03 Verification of Current & Voltage Divider Rule. 25

04 Experimental Verification of Nodal Analysis. 30

05 Experimental Verification of Mesh Analysis. 35

06 Experimental Verification of Superposition Theorem. 40

07 Study of Star and Delta Connections of Resistances. 44

Experimental Verification of Star-Delta Transformation.

08 Experimental Verification of Thevenin’s Theorem. 48

09 Study of Maximum Power Transfer Theorem & its 52

10 Verification of Reciprocity Theorem. 57

11 Implementation of Inverting Amplifier & Non-Inverting 61

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12 Implementation of Unity Gain Follower & Summing 66

13 Transient Analysis & Time Constant Determination for an 72

14 Experimental Verification of Norton’s Theorem. 80

LABORATORY WORK ESSENTIALS

● Resistances –fixed (Ω) 50 x 2,80 x 2, 100 x 2, 120 x 2,390 x 2,430 x 2, 1k x 6,

● Resistances –variable (Ω) 1k x 2, 2k x 2, 5k x 2, 10k x 2

● Digital Multi Meter

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we can think of a breadboard as a board that can be divided in 2 functional areas:

Bench Top Power Supply:

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voltage, there’s a good chance the scope will be damaged.

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Probe Selection and Setup

Connect the Probe and Turn the Scope On

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Testing the Probe

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Compensating an Attenuated Probe

Probing, Triggering, and Scaling Tips

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Measure Twice, Cut Once

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Measuring the ringing of a square wave with cursors.

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PROCEDURE & OBSERVATIONS:

I (mA) V (volts) I (mA) V (volts) I (mA) V (volts)

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Procedure Part II: Combinations of Resistors