ECA 1 Lab Manual

ECE Department Electric Circuit Analysis-
COMSATS Institute of Information Technology
ELECTRIC CIRCUIT ANALYSIS-1

LABORATORY MANUAL
Department of Electrical Engineering

WAH Campus
ELECTRIC CIRCUIT ANALYSIS – 1
List of Experiments
a) Course Software: Electrical Circuits Simulation using Multisim

Lab 01 Electronics Workbench.
b) Resistance Calculation from Color Codes and Verification through
measurement with Multi-meter.
Lab 02 Equivalent Resistance of Series, Parallel and Series-Parallel circuits.
Lab 03 To verify Kirchoff‟s Voltage Law.
Lab 04 Mesh Analysis.
Lab 05 To verify Kirchoff‟s Current Law.
Lab 06 Nodal Analysis.
Lab 07 To verify Millman‟s Theorem.
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Lab 08 To verify Thevenin‟s Theorem.
Lab 09 To verify Norton‟s Theorem.
Lab 10 To verify Superposition Theorem.
Lab 11 To verify Maximum Power Transfer Theorem.
Lab 12 To verify Reciprocity Theorem.
Lab 13 To verify Compensation Theorem.
Lab 14 To verify Tellegen‟s Theorem.
Lab 15 Calculation of Total Impedance in RL and RC Circuits using Multisim.
Lab 16 Circuit Analysis of RLC series circuit.
Lab 17 Circuit Analysis of RLC parallel circuit.
Basic Electrical Safety Practices
The Institute requires everyone who uses electrical equipment to understand these safety
precautions to comply with the Electrical Safety-Related Work Practices standard and
COMSAT's electrical safety policies. The following safe work practices can prevent electrical
shock. Contact your supervisor for additional safety training if your working involves repairing,
installing or working on energized parts.
Never Work Alone: If you are working with energized circuits or equipment over 50 volts peak,
make sure that at least one other person can see you and hear you.
Voltage Rules: If you intend to work on a project using power sources over 50 volts peak, you
must secure permission and receive specific training from your Instructor, Lab Engineer or Lab
Assistant before any work on the project begins.
Never hurry: Work deliberately and carefully. Connect to the power source LAST.
If you are working with a lab kit that has internal power supplies: Turn the main power
switch OFF before you begin work on the circuits. Wait a few seconds for power supply
capacitors to discharge. These steps will also help prevent damage to circuits.
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If you are working with a circuit that will be connected to an external power supply: Turn
the power switch of the external supply OFF before you begin work on the circuit.
Check circuit power supply voltages: For proper value and for type (DC, AC, frequency)
before energizing the circuit.
Do not run wires: Over moving or rotating equipment, or on the floor, or string them across
walkways from bench-to-bench.
Remove conductive watch bands or chains, finger rings, wrist watches, etc., and do not use
metallic pencils, metal or metal edge rulers, etc. when working with exposed circuits.
When breaking an inductive circuit: Open the switch with your left hand and turn your face
away to avoid danger from any arc which may occur across the switch terminals.
When using large electrolytic capacitors: Be sure to wait long enough (approximately five time
constants) for the capacitors to discharge before working on the circuit.
All conducting surfaces intended to be at ground potential should be connected together.
Only use DRY hands and tools and stand on a DRY surface: When using electrical
equipment, plugging in an electric cord, etc.
Unplug cords from electrical outlets: By pulling on the plug instead of pulling on the cord.
Never put conductive metal objects into energized equipment.
Always pick up and carry portable equipment by the handle and/or base: Carrying
equipment by the cord damages the cord's insulation.
Use extension cords temporarily: The cord should be appropriately rated for the job.
Don't overload extension cords: multi-outlet strips and wall outlets.
Heed the warning signs, barricades and/or guards: That are posted when equipment or wiring
is being repaired or installed or if electrical components are exposed.
Re-route electrical cords or extension cords: So they aren't run across the floor, under rugs or
through doorways, etc. Stepping on, pinching or rolling over a cord will break down the
insulation and will create shock and fire hazards.
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Never remove the grounding post from a 3 prong plug: So you can plug it into a 2 prong, wall
outlet or extension cord.
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Lab Report
A lab Report contains objective, circuit diagram, simulations, results, observations, calculations,
discussion and results. It should be very brief and to the point. Last submission date is the very
next week of the lab performed. It must contain the name, registration number, class section,
performed lab date and submission date. All the lab reports should be in the same format. For
more information contact your instructor.
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Experiment No. 01:
a) Course Software: Electrical Circuits Simulation using Multisim Electronics Workbench.
b) Resistance Calculation from Color Codes and Verification through measurement with
Multi-meter.
a) Course Software: Electrical Circuits Simulation using Multisim Electronics Workbench
Simulation is a mathematical way of emulating the behavior of a circuit. With simulation, you
can determine a circuit's performance without physically constructing the circuit or using actual
test instruments. Multisim is a complete system design tool that offers a very large component
database, schematic entry, full analog/digital SPICE simulation, etc. It also offers a single easy to
use graphical interface for all design needs.
Introduction
Go to Start Programs Multisim and click on Multisim. This will open the main window as
shown in Figure 1. In Figure 1 important toolbars and menu are labeled. In addition to toolbars
shown in Figure 1, there may be other toolbars appearing on your screen concentrate on the
labeled items in Figure 1 at this time.
You can always open and close a toolbar from Main Menu. For example if you want to open or
close (select/unselect) the Design Toolbar, select View Toolbars Design. If any toolbar is not
appearing on your screen then use the above procedure to bring the toolbar. Most of the analysis
can be performed turning on-off the simulate switch. If the Simulation Switch shown in Figure 1
is not appearing on your screen then select View Show Simulate Switch in the Main Menu.
This will open the Simulation Switch.
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Figure 1: Main Window of Multisim Simulation software
We will now try to learn about Multisim simulation techniques by solving a simple example.
Example
Build the circuit shown in Figure 2 using Multisim Electronics Workbench.
Figure 2: Circuit for Multisim simulation.
STEP A: Placing the Components
1. Place a Battery (DC Source)
Bring a dc source in the Multisim workspace: Open the Multisim program if it is not open. In
the Component Toolbar, select Sources icon (refer to Figure 1 to find the Component Toolbar).
This will open another window with several types of dc sources and other components as shown
below in Figure 3. Click on "DC Voltage Source" in this new window.
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Figure 3: Selection of DC Voltage Source in Multisim
Now bring your cursor in the workspace area and notice the change in the shape of cursor to
Click at any point in the workspace. This will put the voltage source as
Change the value and name of voltage source: Double click on the voltage source placed in the
workspace, a new window with the name Battery will appear, as shown in Figure 4. Select
Value in the Battery menu. Change the value from 12 to 30. Keep the unit as Volts in this menu.
Now select Label in this menu and change the Reference ID to Vs. Click on OK.
Figure 4: Battery Window for setup of DC voltage source
2. Place a Resistor:
Bring a resistor in the Multisim workspace:

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In the Component toolbar, select Basic icon as shown. This will open another window with
several basic components as shown below in Figure 5.
Figure 5: Selection of Resistor in Multisim

Click on "Resistor", this will open the Browser-Basic window, as shown in Figure 6. Scroll
through the Component List, select 30kohm, and click OK. The cursor shape will change again.
Click in the workspace and this will put the resistor as
Tip To make your scroll through the Browser's Component List faster, simply type the first few
characters of the component's name. For example, type 30k to move directly to the 30kohm list.
Figure 6: Setup window for Resistor values
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Change the name of resistor: Double click on the resistor, a new window with the name
Resistor will open as shown in Figure 7. Select Label from the menu of this window. Change the
Reference ID to R1 (if it is not) and press OK. This will change the name to R1.
Figure 7: Battery Window for Label of Resistor
Add other resistor R2: Place resistor R2 of value 20k in the workspace through the same
procedure.
Rotate the resistor: Select resistor 'R2' and press Ctrl-R to rotate the resistor or select Edit 90
Clockwise from the Main Menu. This will make the resistor vertical. Labels and values of all the
components can be dragged individually. Drag the label 'R2' and value '20kohm' individually to
put them at a proper place.
3. Place Ground:
In the Component Toolbar, select Sources icon. Now click on Ground icon in the new window
as shown in Figure 8. Click in the workspace to put the Ground symbol as
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Figure 8: Selection of Ground in Multisim
STEP B: Connecting the Components
1. Arrange the components properly:

Arrange the components according to the circuit given in Figure 2. You can select and drag the
component to any place in the workspace. Select the components and drag them one by one to
proper places as shown in Figure 9.
Figure 9: Arranging the Components in proper order

2. Show Grid in the workspace:
You may show grid for ease of drawing the connections. Select View Grid Visible in the Main
Menu if it is not visible.
3. Connect DC Voltage Source "Vs" to "R1":

Bring the cursor close to upper pin of "Vs"; cursor shape will change to a plus sign. Click and
move a little upward. A wire appears, attached to the cursor. Click again at a small distance
above the "Vs" source. Notice that the line will change direction. Control the flow of the wire by
clicking on points as you drag. Each click fixes the wire to that point as shown in Figure 10. In
this way, when the cursor reaches the pin of R1 click again, this will connect "Vs" to "R1" in a
nice manner. Notice that a node number is automatically given.
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Figure 10: Manual connection of components
4. Connect "R1" to "R2":

In the same way connect R1 to R2 through the same procedure.
5. Making use of Junction to connect Ground:
In the similar manner connect ground with Vs and R2. Notice that a small black circle appears
just above the ground, this is called junction. When 2 or more components are connected at one
point, a junction is created. A junction can also be placed manually by pressing Ctrl+J or
selecting Edit Place Junction. This can be used to control the connection points manually.
Also notice the ground node is automatically given node number 0. Do not alter it. This
completes the connection and the complete circuit is shown in Figure 11.
Figure 11: Complete Circuit in Multisim

6. Wire paths can be modified using drag points:
Click on a wire. A number of drag points will appear on the wire as shown in Figure 12. Click
any of these and drag to modify the shape. You can also add or remove drag points to give you
even more control over the wire shape. To add or remove drag points, press CTRL and click on
the location where you want the drag point added or removed.
Figure 12: Drag points for connecting wire

STEP C: Placing Multimeter or Voltmeter in parallel to measure
voltage
1. To connect a Multimeter:
Select Toolbar Instruments. The Instrumentstoolbar will open as shown in Figure 13.
View
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Figure 13: Instruments Toolbar
Click on Multimeter icon. Now click in the workspace to place the Multimeter. Drag it and place
it near resistor R1 as shown in Figure 14. Make a connection from '+' terminal of Multimeter to
the left pin of R1 and from '-' terminal to right pin of R1. Note that reversal of + and - terminals
will give opposite readings.
Figure 14: Multimeter connection for voltage measurement

Set the Multimeter to measure DC voltage: Double click on Multimeter to open the properties
window shown in Figure 15. Select 'V' to measure voltage. Select the DC wave shape. (Notice
that the meter can also measure current 'A' and resistance ''. It can measure AC as well as DC
values. Leave the window open for viewing the measurements.
Figure 15: Multimeter properties window
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STEP D: Placing a Multimeter or Ammeter in series to measure current
1. Place a second Multimeter in the workspace as we did in Step C
Remove the connection between R1 and R2. Connect the '+' terminal of the Multimeter towards R 1
and the '-' terminal towards R2 as shown in Figure 16.
2. Set the Multimeter to measure current:
Double click on this multimeter and select 'A' in the multimeter properties window. Set the wave
shape to DC. If current flows from 3 to zero, the meter will read positive.
Figure 16: Multimeter connection for current measurement
STEP E: Simulate the circuit
1. Save the file

Select File Save.
2. Show the Simulate Switch, on the workspace. Select View Simulate Switch.
3. If the properties window is not open
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Double click the multimeters. Click to '1' position (ON) of the simulation switch to start
simulation. Results will appear in the properties window of Multimeter. Compare your result
with those in Figure 17 and show them to your instructor.
Figure 17: Simulation result
Exercise
Objectives:
1. Build the circuit of Figure 18 in Multisim Electronics Workbench.
2. Connect a voltmeter between nodes 'D' and 'E' and measure across 9 Ohm resistor.
3. Connect an ammeter for the measurement of „IE‟.
4. Place your Registration no. in place of „?‟.
5. Simulate and note down the results.
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Figure 18: A circuit for exercise

b) Resistance Calculation from Color Codes and Verification through measurement with
Multi-meter.
Apparatus:
• Multi-meter
• DC Supply
• Breadboard
• Assorted resistors
Objectives:
• Introduction to the course software.

• Resistance calculation through reading of color codes.
Pre-Lab:
The calculation from color codes is done according to the following rules:
Color Digit Multiplier Tolerance (%)
Black 0 100 (1)

Brown 1 101 1
Red 2 102 2
Orange 3 103
Yellow 4 104
Green 5 105 0.5
Blue 6 106 0.25
Violet 7 107 0.1
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Grey 8 108
White 9 109
Gold 0.1 10-1 5
Silver 0.01 10-2 10
None 20
The digit column gives the first two digits in the 4-band code and first 3 digits in the 5-bandcode.
Gold and silver appear in the 3rd digit place in the 5-band code. The multiplier column gives the
values, which have to be multiplied to the digit value attained above. The colors gold and silver
give the tolerances in the 4 band codes. The colors brown, red, green, blue, and violet are used as
tolerance codes on 5-band resistors only. All 5-band resistors use a colored tolerance band. The
blank (20%) Band is only used with the "4-band" code (3 colored bands + a blank "band").
Digit Multiplier
Tolerance
4-Band Code
Digit Multiplier
Tolerance
5-Band Code
Procedure:
• Calculate the resistance of the resistors available by using color codes.

• Switch the selector of multi-meter to resistance measurement.
• Select the minimum range and measure resistance by connecting both probes of meter to
the ends of resistor. Be sure, not to touch both ends of the resistor while the probes of
meter are connected to the resistor. This will make a resistive path through your body in
parallel with the resistor, thus affecting the correct reading.
• If the reading of the multi-meter is pegged, i.e. displays “1” on the left hand side of LCD
display, this means the resistance is greater than the selected range.
• Switch to the next available range and measure the resistance again.
• Repeat step 5 till a reading is available on the display.
• Check whether the calculated and measured values are comparable.  Repeat the
procedure for different resistors available.
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Verification:
S. No. Resistance Value () Difference ()

Calculated Measured
(Ohm) (Ohm)
1. 1k 1k 0
2. 2.2k 2.2k 0
3. 10k 10k 0
Exercise
Objective:
 To calculate the value of the resistors by color coding
 Submit your calculations as a Lab Report.
1. Complete the table by writing the name of the colors.
Resistor 1st Band 2nd Band 3rd Band 4th Band

Color Color Color Color
1@5% Black Brown Black Gold
100@5% Brown Black Brown Gold
1k@10% Brown Black Red Silver
2.2k@10% Red Red Red Silver
3.3k@10% Orange Orange Red Silver
4.6k@10% Yellow Blue Red Silver
10k@10% Brown Black Orange Silver
2. Write down the color code for the resistor of value equal to your registration number.
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Experiment No. 02: Equivalent Resistance of Series, Parallel and Series Parallel Circuits.
Apparatus:
• Resistors
• Multi-meter
• Jumper Wires
• Breadboard
• DC Supply
Objectives:
• Strengthening of concepts of
Series Parallel
and Seriesparallel
Equivalent resistances
• Circuit construction on breadboard
• Importance of “Viewpoint” while calculating equivalent resistance
Pre-Lab:
Two resistors are said to be in series if joining of the two forms a node. The total (often referred
to as “Equivalent Resistance”, abbreviated as Req) in this case is the simple sum of the individual
resistance. Current in series-connected elements is the same (a direct derivation from KCL).
Also, equivalent resistance is equal to the voltage applied across the combination divided by the
current flowing through it (R = V / I).
Two or more resistors are said to be in parallel, if joining them forms a node pair. The reciprocal
of equivalent resistance is the sum of reciprocals of the resistors connected in parallel. Voltage
across parallel-connected elements is the same. Also, equivalent resistance is equal to the voltage
applied across the combination divided by the current flowing through it (R = V / I).
For two resistors in parallel, the equivalent resistance is equal to the product of the two resistor
values divided by their sum.
Viewpoint is the pair of access points to the circuit, where the multi-meter probes are connected
to the circuit. All theoretical calculations have to be made keeping in view the selected set of
points.
Procedure:
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a) Series Circuit:
• Take three resistors and note their values after confirmation by color code and multimeter
measurements.
• Construct a series circuit of these resistors as shown below.
A B
R1 R2 R3
• Calculate the equivalent resistance using formula
• Check the resistance of the series combination by connecting the multimeter probes at
points A and B.
• Connect a measured voltage between points A and B and note the current flowing
through the circuit (For this the multimeter has to be connected in series with the circuit,
with selector pointed at mA and black probe plugged into mA socket of the meter). The
total resistance is calculated using the relationship R = V / I. The circuit diagram is
depicted below:
A B
R1 R2 R3
b) Parallel Circuit:
• Repeat step a) 1.
• Construct a parallel circuit of these resistors as shown below:
R3
• Calculate the equivalent resistance using formula
• Check the resistance of the A B parallel combination by
connecting the multimeter R2 probes at A and B.
• Connect a measured voltage between points A
and B and note the current flowing through
the circuit (For this the R1 multimeter has to be
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connected in series with this parallel circuit, with selector pointed at mA and black probe
plugged into mA socket of the meter). The total resistance is calculated using the
relationship R = V / I. The circuit diagram is depicted below:
R3
A B
R2
R1
c) Series Parallel Circuit:

• Repeat step a) 1.
• Construct a series parallel circuit of these resistors as shown below:
R1
R 2 R3
• Calculate the equivalent resistance using formula.

• Check the resistance of the series parallel combination by connecting the multimeter
probes at A and B.
through the circuit (For this the multimeter has to be connected in series with this series-
parallel circuit, with selector pointed at mA and black probe plugged into mA socket of
the meter). The total resistance is calculated using the relationship R = V / I. The circuit
diagram is depicted below:
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A A
R1
R2 R3
d) View point:
• Repeat step a) 1.  Construct a circuit of these resistors as shown below:
R2
R1 B
R3
• Calculate the resistance between points AB, BC and AC using theoretical concepts.
• Check the resistance of the circuit by connecting the multimeter probes at A and B, then
at B and C and then at A and C.
through the circuit (For this the multimeter has to be connected in series with the circuit,
with selector pointed at mA and black probe plugged into mA socket of the meter). The
total resistance is calculated using the relationship R = V / I. The different circuit
configurations are depicted below:
A
A
R2
R1 B
R3
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R2
R1 B
A
R3
A
A
R2
R1 B
R3
Measurements and Calculations
Individual resistance values:
Resistor symbol Value () Value to be used

in calculation ()
Color Code Multimeter
R1 1k 1k 1k
R2 2.2k 2.2k 2.2k
R3 10k 10k 10k
a) Series Circuit
S. Total Resistance Value () Applied Current Resistance

No. Calculated Measured with Voltage (I) value (V/I)
using formula multimeter (V) ()
Unit (Ohm) (Ohm) (v) (mA) (Ohm)
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1. 13.2k 13.2k 5 0.378 13.2k
b) Parallel Circuit

No. Calculated Measured with Voltage (I ) value (V/I)
using formula multimeter (V)
1. 643.275 643.275 5 7.772 643.275
c) Series-Parallel Circuit

No. Calculated Measured with Voltage (I ) value (V/I)
using formula multimeter (V)
1. 2.803k 2.803k 5 1.783 2.803k
d) View Point

No. Calculated Measured with Voltage (A) value (V/I)
using formula multimeter (V) ()
AB 1.833k 1.833k 5 2.727 1.833k
BC 2.424k 2.424k 5 2.062 2.424k
CD 924.242 924.242 5 5.41 924.242
Exercise
Objective:
 Use Multisim to find the required measurements and submit your simulations and
calculations as a Lab Report.
1. Find the equivalent resistance of the following circuits at different viewpoints „AB‟,
„CD‟,‟DE‟ and „CE‟.
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R(AB)=2.647Kohm
R(CD)=1.662Kohm
R(DE)=1.176Kohm
R(CE)=2.103Kohm
Experiment No. 03: To verify Kirchoff‟s Voltage Law.
Apparatus:
• Resistors
• Multi-meter
• Jumper Wires
• Breadboard
• DC Supply
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Objectives:
• Strengthening of concepts of Kirchoff‟s Voltage Law

• Identification of closed loops in a circuit
• Polarities of voltage drops or voltage rise
• Calculating unknown voltages using Kirchoff‟s Voltage Law
Pre-Lab:
Kirchoff‟s Voltage Law (commonly abbreviated as KVL) states that:

“The Algebraic Sum of voltages in a closed loop is zero.”
Equations developed using KVL can help find out an unknown voltage between any two points if
all other voltages in a loop are known.
In applying KVL, the referenced polarities of the voltages have to be taken into consideration, for
correct assignment of algebraic signs to these voltages. This is done giving an arbitrary direction
to the current in the loop and then indicating these voltage drops. The terminal, through which
the current enters a source, is marked negative and the terminal, through which it leaves, is
marked positive. For resistors, the terminal, through which current enters the resistor, is marked
positive and the terminal, through which the current leaves, is marked negative. This gives a
theoretical form of the equation for KVL.
In lab, the terminal at which the red probe is connected is termed positive and the terminal, at
which the black probe is connected, is termed negative.
Procedure:
a) Simple Series Circuit:

• Take three resistors and construct a series circuit as shown below.
1 2 3 4
• Identify points between which voltage can be measured.

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• In the given drawing, these are 1-2, 1-3, 1-4, 2-3, 2-4 and 3-4.
• The measured voltages are indicated as V12, V13, V14, V23, V24 and V34.
• The subscript of each voltage signifies that the first digit represents the point which is
assumed to be positive and the second point represents the point which is assumed
negative with respect to the first point.
• The voltages between all of these points will be measured with red probe connected to
first point in the subscript and black probe connected to second point.
• The voltages may also be measured by interchanging the probe position between any two
points.
• The voltages in this case are V21, V31, V41, V32, V42 and V43. It will be interesting to note
that V21 = -V12, V31 = -V13 and so on.
• For measurement of above voltages, follow step 6.
• Measure and note all these voltages.
• There can be many equations for KVL within this loop, these are: V 41 + V12 + V23 + V34 =
0
V41 + V12 + V24 = 0
V41 + V13 + V34 = 0 V41
+ V14 = 0
V42 + V23 + V34 = 0
V42 + V24 = 0
V43 + V34 = 0
V14 + V43 + V32 + V21 = 0
V14 + V43 + V31 = 0
V14 + V42 + V21 = 0
V14 + V41 = 0
V13 + V32 + V21 = 0
V13 + V31 = 0
V12 + V21 = 0
Verify these equations.
b) Multiple Loop Circuit:

• Take four resistors and construct a multiple mesh loop circuit as shown below:
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1 2 3
• Identify closed loops. In the given circuit, there are three closed loops namely 4-1-2-4, 4-
2-3-4 and 4-1-2-3-4.
• The voltages in the first loop (while traversing the loop from point 4 in the clockwise
direction, containing drops across all elements) are V41, V12, and V24. Measure and note
these values. Take the sum and verify KVL.
• The voltages in the second loop (while traversing the loop from point 4 in the clockwise
direction, containing drops across all elements) are V42, V23, and V34. Measure and note
these values. Take the sum and verify KVL.
• The voltages in the third loop (while traversing the loop from point 4 in the clockwise
direction, containing drops across all elements) are V41, V12, V23 and V34. Measure and
note these values. Take the sum and verify KVL.
c) Unknown Voltage Calculation:

• Take four resistors and construct a circuit as shown below:
2 3
• The purpose is to calculate the voltage V23 (= -V32).

• If we assume that an element of infinite resistance is connected between node 2 and 3,
then two loops will be formed namely, 1-3-2-1 (or 1-2-3-1) and 2-3-4-2 (or 2-4-3-2).
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• The voltages in the first loop shall be V 13, V32, V21 and KVL application will give us the
equation V13 + V32 + V21 = 0 from which V32 = -V13 - V21. Measure these voltages and
calculate V32 (= - V32). Measure V32 and verify your calculation.
• The voltages in the second loop shall be V23, V34, V42 and KVL application will give us the
equation V23 + V34 + V42 = 0 from which V23 = -V34 - V42. Measure these voltages and
calculate V23 (= - V32). Measure V23 and verify your calculation.
Measured Voltages:
V12= V13= V14= V21= V23= V24= V34=

V31= V41= V32= V42= V43=
Verification of equations:
V41 + V12 + V23 + V34 = + + + + =
V41 + V12 + V24 = + =
V41 + V13 + V34 = +

+ + + =
V41 + V14 = + =
+
V42 + V23 + V34 = =
+
V42 + V24 = + =
V43 + V34 = + =
=
V14 + V43 + V32 + V21 =
+
V14 + V43 + V31 =
+ + =
+ =
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V14 + V42 + V21 = +
V14 + V41 =
+
=
V13 + V32 + V21 =
+ + =
V13 + V31 = + =
V12 + V21 = + =
b) Multiple Loop Circuit:
Loop 1 (4-1-2-4)
V41= V12= V24=
V41 + V12 + V24= + + =
Loop 2 (4-2-3-4)
V42= V23= V34=
V42 + V23 + V34= + + =
Loop 3 (4-1-2-3-4)
V41= V12= V23= V34=
V41 + V12 + V23 + V34= + + + =
c) Unknown Voltage Calculation:
Loop 1 (1-3-2-1)
V13= V21=
=
+
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V32 = -V31 - V21 =
Measured V32 =
Loop 2 (2-3-4-2)
V34= V42=
=
+
V23 = -V34 – V42 =
Measured V23 =
Exercise
Objective:
1. Solve the following circuit using KVL. Put your registration number in place of B 1 and set B2
at registration number plus two volts. Use appropriate values of resistors. Find all the
unknowns.
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Experiment No. 04: Mesh Analysis
Apparatus:
• Resistors
• Multi-meter
• Jumper Wires
• Breadboard
• DC Supply
Objectives:
• Strengthening of concepts of Mesh Current Analysis Technique
Pre-Lab:
Mesh current method is a technique of circuit analysis which helps us calculate current, voltage
and power in any branch of a circuit.
The first step is the identification of meshes and assigning circulating currents to these meshes.
After this, mesh equations are developed using KVL and expressing voltage drops in terms of
Mesh currents. The process is elaborated in the figure shown below:
32
1
Normally, directions of mesh currents are assumed to be clockwise.

Notice that the mesh currents are the currents flowing in those branches of each mesh which are
not common to other meshes.
The solution of simultaneous equations developed using mesh current analysis gives the value of
mesh currents and these are then used to calculate the currents and voltage drops in all other
branches.
Procedure:
• Measure six resistors and construct a circuit as shown in pre-lab (point 3) above.
• Note down the values of the resistors and the applied voltage Vs.
• Measure the currents in those branches of each mesh which are not common to any other
mesh. These are the mesh currents I1 (which is the source current as well), I2 and I3.
• In the given circuit, these elements are R5, R6 and R1 respectively.
• As per rules of mesh current analysis, the currents in all other branches should be equal to
the difference of mesh currents depending upon commonality of those branches between
respective meshes.
• Measure all these currents with specific regard to the assumed direction.
• Calculate the values which should be present within these common branches.
• The measured and calculated values should tally which will verify the mesh current
analysis technique.
Measurements and Calculations:
R1 = kΩ R2 = kΩ
R3 = kΩ R4 = kΩ R5 =
kΩ R6 = kΩ
Vs = V
Mesh Measured Values Calculations
No. (mA) (mA)
1. I1 I1- I2 I1- I3 I1- I2 I1- I3
33
1
2. I2 I2- I1 I2- I3 I2- I1 I2- I3
3. I3 I3- I1 I3- I2 I3- I1 I3- I2
Exercise
Objective:
1. Solve the following circuit by Mesh Analysis. Use voltage equal to your registration number.
Find all unknowns as the branch currents and branch voltages.
Experiment No 05: To verify Kirchoff‟s Current Law.
Apparatus:
• Resistors
• Multi-meter
• Jumper Wires
• Breadboard
34
1
• DC Supply
Objectives:
• Strengthening of concepts of Kirchoff‟s Current Law

• Identification of nodes
• Current Directions though circuit element
• Calculating unknown current using Kirchoff‟s current Law
Pre-Lab:
Kirchoff‟s Current Law (abbreviated as KCL) states that:

“The Algebraic Sum of currents at any node is zero.”
Equations developed using KCL can help find out an unknown current at any node, provided all
other currents associated with that node are known.
In applying KCL, the referenced directions of currents have to be taken into consideration, for
correct assignment of algebraic signs to the currents. This is done giving an arbitrary sign (either
positive or negative) to currents coming into a node and assigning the currents leaving the same
node with an opposite sign.
The above means that we have to give reference directions to currents through all elements
connected at any node. This is done by noting the current by connecting the multimeter as an
ammeter in series with each element. The direction of current through each element is
understood to be from red probe to black probe. If the reading is positive, the actual and assumed
directions are the same. If the reading is negative, this means that the actual direction of flow of
current is opposite to that assumed by us.
Procedure:

• Take three resistors and construct a series circuit as shown below.
1 2 3 4
35
1
• Identify nodes and mark them. These are 1, 2, 3 and 4.

• The currents are I41, I12, I23 and I34.
• The first digit in the subscript of each current signifies the terminal from where the
current is flowing towards the terminal (signified by the second digit in subscript)
through one specific circuit element.
• The current in each element will be measured by connecting the multimeter as an
ammeter in series with that particular element, with red probe nearest to the first point in
the subscript and black probe nearest to the second point.
• There are a number of KCL equations at each node, these are: at node 1: -I 41 + I12 = 0
at node 2: -I12 + I23 = 0 at node 3: -I23 + I34 = 0 at node 4: -I34 + I41 = 0 
Measure the currents and verify these equations.
b) Multiple Mesh Circuit:

• Take four resistors and construct a multiple mesh circuit as shown below:
1 2 3
• Identify nodes. In the given circuit, there are 4 nodes, namely 1, 2, 3 and 4.
• The current in different branches are I41, I12, I24, I23 and I34.
• Measure and note these currents. Take the sum and verify KCL for each node.
c) Unknown Current Calculation:

• Take four resistors and construct a circuit as shown below:
36
1
2 3
• The purpose is to calculate the current I34.

• The currents associated with node 2 (or 3) are I12, I13, I24 and I34.
• The application of KCL at node 2 (or 3) will give us the equation:
-I12 - I13 + I24 + I34 = 0  I34 = I12 + I13 - I24. Take measurements and verify the results.
Measured Currents:
I41= I12= I23= I34=
-I41 + I12 = + =
-I12 + I23 = + =
-I23 + I34 = + =
-I34 + I41 = + =
37
1
b) Multiple Mesh Circuit:
Measured Currents:
I41= I12= I24= I23= I34=
-I41 + I12 = + =
-I12 + I24 + I23 = + + =
-I23 + I34 = + =
-I24 - I34 + I41 = - - + =
c) Unknown Current Calculation:
I12= I13= I24=
I34 = I12 + I13 - I24 = + - =
Measured I34 =
38
1
Exercise
Objective:
1. Solve the following circuit by KCL. Use voltages equal to your registration number. Find all
unknowns as the branch currents and branch voltages.
39
1
Experiment No. 06: Nodal Analysis
Apparatus:
• Resistors
• Multi-meter
• Jumper Wires
• Breadboard
• DC Supply
Objectives:
• Strengthening of concepts of Node Voltage Analysis Technique
Pre-Lab:
Node Voltage Analysis method is a technique of circuit analysis which helps us calculate
current, voltage and power in any branch of a circuit.
Circuits with lesser number of nodes with unknown voltages than the number of meshes are
easier to solve with the Node Voltage Analysis as compared to the Mesh Current Analysis
Technique.
• The first step is the identification of total nodes.
• Out of these nodes, principal or essential nodes are identified.
• Out of these, the ones with unknown voltages are designated with names
• One of these nodes is designated as a reference node. The voltages of other essential
nodes with unknown voltages are assigned relative to reference node.
• After this, node voltage equations are developed using KCL and expressing the currents at
each node in terms of voltages and resistances. The process is in the figure shown below:
40
1
I1
R1
I2 I4
A
B
R2 R4
I4/
Vs R3 R5
I3
I5
C
Normally, directions of currents are assumed to be away from the node.

The solution of simultaneous equations developed using KCL gives the value of node voltage and
these are then used to calculate the currents and voltage drops in all other branches.
Procedure:
• Measure five resistors and construct a circuit as shown in pre-lab (point 7) above. These
are R1, R2, R3, R4 and R5.
• Note down the values of the resistors and the applied voltage Vs.
• The identified essential nodes with unknown voltages are A, B and C.
• Node C is taken as a reference. This means node voltage equations are to be written for
only A and B.
• Measure voltages at A and B and note them down.
• Measure currents as indicated in the circuit diagram and note them down.
• Develop node voltage equations and expressing currents in the form of node voltages and
resistance.
• Solve these for unknown node voltages and compare with your results.
• Using the node voltages, calculate the currents in each resistor and compare with current
measurements.
Measurement and Calculations
R1 = kΩ R2 = kΩ
R3 = kΩ R4 = kΩ
41
1
R5 = kΩ VS = V
Node Measured Calculated
(V) (mA) (mA) (mA) (V) (mA) (mA) (mA)
A VA I2 I3 I4 VA I2 I3 I4
5.97 4.10 5.971 -1.867
B. VB I1 I5 I4/ VB I1 I5 I4/
10 4.92 3.054 1.867
Calculations:
KCL:
Node A: I2 + I3 + I4 = 0 

Node B: I1 + I 4/ + I5 = 0 
42
1

 Exercise
Objective:
2. Solve the following circuit by Nodal Analysis. Use voltages equal to your registration
number. Find all unknowns as the branch currents and branch voltages.
43
1
Experiment No. 07: To verify Millman‟s Theorem
Apparatus:
• Resistors
• Multi-meter
• Jumper Wires
• Breadboard
• DC Supply
Objectives:
• Strengthening of concepts of Millman‟s Theorem

• Source conversions
Pre-Lab:
Millman‟s Theorem is a tool for simplifying circuits with multiple sources.

It makes use of the fact that a voltage source can be converted to a current source and vice versa.
Consider the circuit shown below.
R1 R2
R3 VS2
V
S
1
If we are asked to calculate the voltage and current through R 3, we can do it in many ways, but
the application of Millman‟s Theorem will make the circuit very simple to solve.
44
1
If we convert, the voltage sources to equivalent current sources, then through conversion, the
circuit configuration will become as shown below.
VS1/
R1
R1 R3 R2 VS2/R2
Now, the two current sources

can be combined to make one current source in parallel with a single element. The resulting
circuit is shown below:
VS1/R1+VS2/R
2
1/(1/R1+1/R2) R3
This single current source, when converted to a voltage source will have the configuration as
shown below:
1/(1/R 1+1/R 2)
(VS1/R1+VS2/R2)(1/(1/R1+1/R2)) R 3
Now the circuit is a simple series circuit and current through and voltage across R 3 can be
calculated easily.
45
1
Procedure:
• Measure three resistors and construct a circuit as shown in pre-lab (point 3) above. These
are R1, R2 and R3.
• Note down the values of the resistors and the applied voltages VS1 and VS2.
• Measure the current though and voltage across R3 and note them down.
• Now construct a circuit as shown in pre-lab (point 7) above, with the values of the source
voltage and resistance adjusted to the calculated values of the single source and
resistance.
• Measure and note down the values of the current through and voltage across R 3 in this
circuit.
• The results should verify the legitimacy of the Millman‟s Theorem.
• Repeat the procedure for different values of R3.
R1 = kΩ R2 = kΩ
VS1 = V VS2 = V
Original Circuit Equivalent Circuit

Measurements Measurements
S. R3 across R 3 Equivalent Source across
No. R 3
Voltage Current Voltage Resistance Voltage Curren
t
(k) (V) (mA) (V) (k) (V) (mA)
1
Exercise
2
3
Objective:
46
1
1. Verify Millman‟s Theorem on following circuit. Use the voltages equal to your registration
number. Find voltage across R2.
47
1
Experiment No. 08: To verify Thevenin‟s Theorem.
Apparatus:
• Resistors (fixed and variable)

• Multi-meter
• Jumper Wires
• Breadboard
• DC Supply
Objectives:
• Strengthening of concepts of Thevenin theorem
Pre-Lab:
According to Thevenin theorem, any circuit while viewed from a specific pair of points can be
reduced to a simple series circuit with a voltage source V Th and a series resistance RTh connected
across that specific pair of points.
Both the original circuit and Thevenin's Equivalent Circuit are equivalent in terms of voltage and
current at the specific pair of points.
The voltage source value is the open circuit voltage across the pair of points and the series
resistance value is the resistance seen looking from the open circuited set of points and all
voltage and current sources in the original circuit replaced with their internal resistances.
The internal resistance of a voltage source is connected in series with it and that of a current
source is connected in parallel with it. This scheme is adopted to indicate the loss of voltage and
current with change in loading.
Ideally, the internal resistance of a voltage source is 0, i.e. it can maintain the same voltage across
its terminals regardless of the load being fed by it and that of a current source is , i.e. it can
maintain a constant current through its terminals regardless of the load being fed by it. Lab
equipments have these source values approaching ideal, therefore, we shall be using the ideal
approach while replacing sources with their internal impedances.
Procedure:
48
1
• Measure four resistors and construct a series circuit as shown below. A precaution for
minimizing the source resistance effect is to use a high value resistor which is connected
to positive battery terminal.
RL
• The specific set of points is 1 & 2, with respect to which, the circuit has to be
Thevenized.
• Measure and note V12 and I12 for different values of source voltage.
• Remove resistance RL from the circuit and measure V12 for different values of source
voltage (used in point 3 above) as shown below. This voltage is the Thevenin voltage VTh.
V 12
• Turn of source supply and place a short circuit across voltage source as shown below.
Measure resistance R12 which is the Thevenin resistance RTh.
R12
49
1
• Construct the Thevenin equivalent circuit and connect RL between points 1 & 2 as shown
below with source voltage adjusted to values of V Th (obtained in point 4 above). RTh value
will be obtained using a variable resistance.
RTh
RL
2
VTh
• Measure V12 and I12 and compare with the results obtained in 3 above.
S. Source Measurements in Thevenin Thevenin Measurements in

No. voltage Original Circuit Voltage Resistance Thevenin
(Volt) VTh RTh Equivalent Circuit
V12 I12 (Volt) (Ω) V12 I12
(Volt) (Amp.) (Volt) (Amp.)
1.
2.
3.
Exercise
Objective:
1. Use Thevenin‟s Theorem to solve following circuit. Use the voltages equal to your
registration number. Find voltage across Load Resistor.
50
1
51
1
Experiment No.09: To verify Norton‟s Theorem.
Apparatus:

• Multi-meter
• Jumper Wires
• Breadboard
• DC Supply
Objectives:
• Strengthening of concepts of Norton theorem

• Source Conversion
Pre-Lab:
According to Norton theorem, any circuit while viewed from a specific pair of points can be
reduced to a simple circuit with a current source with current I n and a parallel resistance Rn
connected across that specific pair of points.
Both the original circuit and Norton Equivalent Circuit are equivalent in terms of terminal
voltage and current at the specific pair of points.
The In value is the short circuit current through the pair of points and R n value is the resistance
seen looking from the open circuited set of points and all voltage and current sources in the
original circuit replaced with their internal resistances.
The internal resistance of a voltage source is connected in series with it and that of a current
source is connected in parallel with it. This scheme is adopted to indicate the loss of voltage and
current with change in loading.
Ideally, the internal resistance of a voltage source is 0, i.e. it can maintain the same voltage across
its terminals regardless of the load being fed by it and that of a current source is , i.e. it can
maintain a constant current through its terminals regardless of the load being fed by it. Lab
equipments have these source values approaching ideal, therefore, we shall be using the ideal
approach while replacing sources with their internal impedances.
Procedure:
52
1
• Measure four resistors and construct a circuit as shown below.

• The specific set of points is 1 & 2, with respect to which, the Norton equivalent circuit
has to be drawn.
RL
• Measure and note source voltage, V12 and I12 for different source voltages.
• Remove resistance RL and replace it with a short circuit and measure current through
terminals 1 and 2 for different values of source voltage (used in point 2 above) as shown
below. This current is the Norton current In.
In
• Turn off supply and place a short circuit across voltage source as shown below. Measure
the resistance which is Norton equivalent resistance Rn
Rn
• The Norton equivalent circuit is shown below:

53
1
1
In Rn L
2
R
• As a current source with a parallel resistance can be converted to an equivalent voltage

source in series with a source resistance, the same circuit can be redrawn as shown below:
Rn
RL
2
Vn = In x Rn
• Measure V12 and I12 in the circuit drawn in point 6 above and compare with the results
obtained in 2 above.
S. Source Measurements in Norton Equivalent Values Measurements in

No. voltage Original Circuit Norton Equivalent
Circuit
54
1
(Volt) V12 (V) I12 In Rn (kΩ) Vn = In x Rn V12 (V) I12 (mA)

(mA) (mA) (V)
1.
2.
3.
Exercise
Objective:
2. Use Nortons‟s Theorem to solve following circuit. Use the voltages equal to your registration
number. Find voltage across Load Resistor.
55
1
Experiment No. 10: To verify Superposition theorem.
Apparatus:
• Resistors
• Multi-meter
• Jumper Wires
• Breadboard
• DC Supply
Objectives:
• Strengthening of concepts of Superposition theorem

• Reference directions of currents
• Reference polarities of voltage drops
Pre-Lab:
Superposition theorem is related to circuits with multiple sources.It states that:

“The combined effect (voltage or current) in any circuit element in a multiple source circuit
is equal to the algebraic sum of individual effects of each source while others replaced with
their internal impedances”. Considering the circuit shown below:
1 2 3
R1 R3
I1 I3
R2
I2
The circuit has two sources and the total current through R1, R2 & R3 can be considered to be I1,
I2 & I3.
Then, superposition theorem, instructs us to take the effect of each source independently and sum
them up algebraically in order to get the overall effect.
56
1
The two circuits with assumed directions of current in each case are shown below:
1 2 3
R1 R3
I1' I3'
R2
I2'
1 2 3
R1 R3
I1'’ I3'’
R2
I2'’
It is worth noting that internal resistances of both sources have been considered to be zero, which
is practically not the case. However, this is quite an accurate approximation, as the electronic
circuit within the breadboard (providing DC voltage) normally has negligible output impedance.
As per assumed directions of currents through each element, the total currents can be calculated
using the following relationships,
I1 = I1‟ - I1‟‟ I2 = I2‟ + I2‟‟ I3 = I3‟‟ - I3‟
Similarly, voltage drops can be calculated using the following relationships:
V12 = V12‟ + V12‟‟ V24 = V24‟ + V24‟‟ V32 = V32‟ + V32‟‟
Procedure:
• Construct a circuit as shown in point 3 (pre-lab) above. Take one source voltage from
variable supply and the other voltage from fixed supply of breadboard. Note these two, so
that in case of these being disturbed, the same can be readjusted to the original value.
• Measure and note the values of currents and voltages in each branch by connecting the
multimeter in an appropriate manner across each element, with specific reference to
assumed polarity and direction of flow of current.
57
1
• Turn by turn; take the effect of each source by replacing the other with a short circuit and
disconnecting it. Repeat step 2 for each source until individual effects of all the sources
have been taken into account.
• Take algebraic sum of voltages and currents at each branch and verify superposition
theorem.
Measurements and Calculation:
Measured values:
I1‟= I2‟= I3‟=
V12‟= V24‟= V32‟=
I1‟‟= I2‟‟=
I3‟‟= V12‟‟= V24‟‟=
V32‟‟=
I1 = I1‟ - I1‟‟ = - =
I2 = I2‟ + I2‟‟ = + =
I3 = I3‟‟ - I3‟ = - =
V12 = V12‟ + V12‟‟= + =
V24 = V24‟ + V24‟‟= + =
V32 = V32‟ + V32‟‟= + =
Measured Values:
I1 = I2 = I3 =
V12 = V24 = V32 =

Exercise
Objective:
58
1
1. Verify the Superposition Theorem on the following circuit. Use the voltages equal to your
registration number. Find voltage across Load Resistor.
59
1
Experiment No. 11: To verify Maximum Power Transfer Theorem.
Apparatus:

• Multi-meter
• Jumper Wires
• Breadboard
• DC Supply
Objectives:
• Strengthening of concepts of Maximum Power Transfer Theorem
Pre-Lab:
It has been found out that any network can be reduced to a Thevenin or a Norton Equivalent
Circuit with respect to any two points of interest.
The Thevenin Equivalent Circuit consists of a voltage source in series with the Thevenin
resistance.
The Norton Equivalent Circuit consists of a current source in parallel with a Norton resistance.
According to Maximum Power Transfer Theorem, any circuit will be able to provide maximum
power to a load resistance provided the value of the load resistance is equal to the Thevenin or
Norton resistance.
For all other values of load resistance the power dissipation will be less than the maximum power
dissipated.
Procedure:
• Measure four resistors and construct a circuit as shown below.
R1 R3
• Maximum Power Transfer Theorem
tells us that if we connect a resistance
R2
60
2
1
RL between points 1 & 2, maximum power will be transferred from the network to the
load resistance if RL.= Thevenin or Norton resistance.
• We shall use Thevenin equivalent circuit during this practical.
• Set the source voltage at the breadboard to a maximum value (i.e. 15 volts)
• Measure voltage between points 1 & 2 and note it down. This is the Thevenin voltage
VTh.
• Measure the Thevenin equivalent resistance RTh and note it down.
• Construct the Thevenin equivalent circuit by setting the supply voltage to V Th and the
variable resistance at the breadboard equal to the Thevenin resistance R Th and connect a
variable resistance between points 1 & 2. The circuit configuration is shown below:
RTh
RL
2
VTh
• Measure V12 in the Thevenin equivalent circuit for different values of RL (i.e. 0.8 RTh, 0.9
RTh, RTh, 1.1 RTh, and 1.2 RTh).
• Calculate the power delivered using formula PL = V 12 2 / RL  It will be verified that
maximum power is delivered at RL = RTh.
R1 = kΩ R2 = kΩ
R3 = kΩ RTh = kΩ
Vsource = V VTh = V
61
EE Department Electric Circuit Analysis-1
S. Load Resistance V12 (V) PL = V122 / RL

No. RL (mW)
x RTh Value
(kΩ)
1. 0.8
2. 0.9
3. 1.0
4. 1.1
5. 1.2
Exercise
Objective:
1. Use Maximum power Transfer Theorem on the following circuit. Use the voltages equal to
your registration number. Find the value of Load Resistor and the respective maximum
power.
62
Experiment No. 12: To verify Reciprocity Theorem.
Apparatus:
• Power Supply
• Resistances
• Multimeter
• Breadboard
• Jumper wires
Objectives:
• To analyze a circuit using Reciprocity Theorem.
Pre-Lab:
“Reciprocity Theorem” can be stated as in any bilateral linear network if a source of emf E in
any branch produces a current I in any other branch then the same emf E acting in the second
branch will produce the same current I in the first branch.
Unilateral circuits means a circuit consists of unilateral elements which allows the current flow in
only one direction. Examples diode, it allows current only in forward bios mode but not in
reverse bias mode while bilateral circuits means a circuit consists of bilateral elements which
allows the current flow in both the directions. Examples resistor, inductor, capacitor the allow
current in both the directions means if we interchange the terminals of these elements they will
allow the current flow.
Procedure:
63
• Make the connection according to the circuit diagram.

• Measure the value of current by ammeter.
• Interchange the position of the ammeter and the voltage source.
• Now again measure the value of current.
• Verify that I = I‟. Repeat thrice.
Sr. No. Source I I‟ Difference

Voltage (mA) (mA)
(Volts)
01
02
03
64
Exercise
Objective:
1. Verify reciprocity theorem for the following circuit. Set the value of Voltage source
magnitude equal to your registration number in the first circuit.
65
Experiment No. 13: To verify Compensation Theorem.
Apparatus:
• Power Supply
• Resistances
• Multimeter
• Breadboard
• Jumper wires
Objectives:
• To analyze a circuit using Compensation Theorem.
Pre-Lab:
The “Compensation Theorem” states that any element in the linear, bilateral network, may be
replaced by a voltage source of magnitude equal to the current passing through the element
multiplied by the value of the element, provided the currents and voltages in other parts of the
circuit remain unchanged.
This theorem is useful in finding the changes in current or voltage when the value of resistance is
changed in the circuit.
Procedure:

• Measure the value of current I by ammeter.
• Calculate the voltage source V‟=IR4 and replace R4 by new voltage source.
• Now again measure the value of current I‟.
• Verify that I = I‟. Repeat thrice for different values of voltage sources.
Sr. No. Source Voltage I Compensated I‟ Difference

(Volts) (mA) Source (mA) (I-I‟)
Voltage
66
V=IR4
(Volts)
01
02
03
67
Exercise
Objective:
1. Verify compensation theorem for the following circuit by inserting a voltage source at the
position of resistance R2. Put your registration number in place of „?‟.
68
Experiment No. 14: To verify Tellegen‟s Theorem
Apparatus:
• Power Supply
• Resistances
• Multimeter
• Breadboard
• Jumper wires
Objectives:
• To analyze a circuit using Tellegen‟s Theorem.
Pre-Lab:
“Tellegen‟s Theorem” states that in any electrical network which satisfies Kirchhoff‟s laws ,
the summation of instantaneous power in all the branches is equal to zero.
Tellegen‟s theorem is applicable to a wide range of electrical networks; the only requirement for
the validation of the Tellegen‟s theorem in any circuit is that it satisfies the Kirchhoff‟s Current
Law and Kirchhoff‟s Voltage Law.
Procedure:

• Set the voltage source at an appropriate voltage.
• Measure the value of all the currents by ammeter.
• Calculate power of each branch.
• Sum all the powers.
• The result should be equal to zero.
Sr. Source Currents Powers Sum
69
No. P= VI P= VI P= VI P= VI P= VI
Voltage
(Watts) (Watts) (Watts) (Watts) (Watts)
I I1 I2 I3 I4
V
(mA) (mA) (mA) (mA) (mA)
(Volts)
01
02
03
70
Exercise
Objective:
1. Verify Tellegen‟s theorem for the following circuit. Set the value of Voltage source
magnitude equal to your registration number in the first circuit.
Experiment No. 15: Calculation of Total Impedance in RL and RC Circuits using Multisim.
Apparatus:
• Multisim software on PC
Objectives:
• Reactance calculation and measurement for Inductors and Capacitors

• Impedance calculation and measurement for RL and RC circuits
• Phasor Concepts
Pre-Lab:
71
• In AC analysis, the concepts of reactance and impedance are fundamental.

• The opposition posed by an inductor or a capacitor to the flow of current is known as
reactance. The unit of measurement is  (like resistance).
• Reactance of inductor is known as inductive reactance and that of a capacitor is known as
capacitive reactance.
• Inductive reactance is given by the relation XL =  L
Where  = 2  f (in radians/sec) and L = inductance (in henries)
• Capacitive reactance is given by the relation XC = 1 / ( C)
Where C = capacitance (in Farads)
• In phasor form the inductive reactance is written with an angle of +90 or j XL and
capacitive reactance with an angle of -90 or – j XC.
• The combined opposition of a circuit containing R, L and C elements is known as
impedance denoted by Z and measured in .
• The general form of impedance is Z = R + j X (Where X can be inductive (positive) or
capacitive (negative)) In polar form Z = Z
Where Z = (R2 + X2),  = Tan-1 (X/R), R = Z Cos  & X = Z Sin 
This means that impedance is a vector quantity and can be represented by a triangle
depicted below:
X
X
• Ohm‟s Law is applicable on circuits with complex impedance just like on simple resistive
circuits i.e. Current is represented by the relation
I = V  / Z  = V/Z ( - )  Z = V /
I  KVL application yields the following relationship:
V = VR + j VX = I R + j I X
This means that source, resistance and reactance voltages also form a triangle identical to
the impedance triangle.
72
Procedure:
Series RL Circuit:
• Take an inductor and a resistor and construct a circuit as shown below.
XL
AC
• Set a suitable value of frequency of ac source. The voltage output (Vs) and the frequency
(f) of the source are to be noted down.
• Measure total current (I) through the circuit and note it down.
• Measure voltage across resistor (VR) and inductor (VL) and note them down.
• Calculate impedance using relationship Z = Vs / I & angle  = Tan-1(VL/VR)
• Calculate inductive reactance using relationship XL = VL / I.
• Calculate resistance using relationship R = VR / I.
• Calculate inductance (L) using relationship XL =  L  L = XL /  = XL / 2f
Series RC Circuit:
• Take a capacitor and a resistor and construct a circuit as shown below:

73
XC
AC
• A function generator has to be used as a source, with a suitable range of frequency

selected. The voltage output (Vs) and the frequency (f) of the source are to be noted down.
• Measure total current (I) through the circuit using the multimeter and note it down. 
Measure voltages across resistor (VR) and capacitor (VC) and note them down. 
Calculate impedance using relationship Z = Vs / I & angle  = Tan-1(VC/VR) 
Calculate capacitive reactance using relationship XC = VC / I.
• Calculate resistance magnitude using relationship R = VR / I.
• Calculate capacitance (C) using relationship XC=1/CC=1/XC=1/2fXC
Series RL Circuit:
f= kHz R= k


74
 Measurement Calculations
 s
 S.
 No. R 
 I
VS VR VL Z VS XL VL Tan- L VL/I
 VR
/I /I /I 2f
1(V L /V R)
(mA) (k) (mH)
(k) (k)
(V) (V) (V) 
1.
2.
3.
Series RC Circuit:
f= kHz R= k


 Measurements Calculations

I 
 S.
 VS VR VC Z R XC Tan- C
No.
 VS/I VR/I VC/I 1(V C R/V ) I/VC2f
(mA
(k) (k) (k)  (F)
(V) ) (V) (V)
1.
2.
3.
75
Exercise
Objective:
• submit your simulations and calculations as a Lab Report.
76
Experiment No. 16: Circuit Analysis of RLC series circuit.
Apparatus:
• Power Supply
• Function Generator
• Resistances
• Capacitors
• Inductors
• Multimeter
Objectives:
• To study the behavior of RLC series circuit.

• To calculate source voltage, phase angle, resistance, inductive reactance, capacitive
reactance, Total impedance, inductance and capacitance in an RLC series circuit.
• To study the resonant frequency phenomenon.
Pre-Lab:
Thus far we have seen that the three basic passive components, R, L and C have very different
phase relationships to each other when connected to a sinusoidal AC supply. In a pure ohmic
resistor the voltage waveforms are “in-phase” with the current. In a pure inductance the voltage
waveform “leads” the current by 90o. In a pure capacitance the voltage waveform “lags” the
current by 90o.
This Phase Difference, Φ depends upon the reactive value of the components being used and
hopefully by now we know that reactance, ( X ) is zero if the circuit element is resistive, positive
if the circuit element is inductive and negative if it is capacitive thus giving their resulting
impedances as:
Circuit Element Resistance, (R) Reactance, (X) Impedance, (Z)

R 0
Resistor
0 ωL
Inductor
0
Capacitor
77
Series RLC circuits are classed as second-order circuits because they contain two energy storage
elements, an inductance L and a capacitance C. Consider the RLC circuit below.
The series RLC circuit above has a single loop with the instantaneous current flowing through the
loop being the same for each circuit element. Since the inductive and capacitive reactance‟s are a
function of frequency, the sinusoidal response of a series RLC circuit will vary with the applied
frequency, ( ƒ ). Therefore the individual voltage drops across each circuit element of R, L
and Celement will be “out-of-phase” with each other as defined by:
• i(t) = Imax sin(ωt)
• The instantaneous voltage across a pure resistor, VR is “in-phase” with the current.
• The instantaneous voltage across a pure inductor, VL “leads” the current by 90o 
The instantaneous voltage across a pure capacitor, VC “lags” the current by 90o 
Therefore, VL and VC are 180o “out-of-phase” and in opposition to each other.
Then the amplitude of the source voltage across all three components in a series RLC circuit is
made up of the three individual component voltages, VR, VL and VC with the current common to
all three components. The vector diagrams will therefore have the current vector as their
reference with the three voltage vectors being plotted with respect to this reference as shown
below.
78
This means then that we cannot simply add together V R, VL and VC to find the supply
voltage, VS across all three components as all three voltage vectors point in different directions
with regards to the current vector. Therefore we will have to find the supply voltage, V S as the
Phasor Sum of the three component voltages combined together vectorially.
Kirchoff‟s voltage law ( KVL ) for both loop and nodal circuits states that around any closed
loop the sum of voltage drops around the loop equals the sum of the EMF‟s. Then applying this
law to the these three voltages will give us the amplitude of the source voltage, VS as,
KVL: VS - VR - VL – VC = 0
VS - IR - L - =0
VS = IR + L +
The phasor diagram for a series RLC circuit is produced by combining together the three
individual phasors above and adding these voltages vectorially. Since the current flowing
through the circuit is common to all three circuit elements we can use this as the reference vector
with the three voltage vectors drawn relative to this at their corresponding angles.
The resulting vector VS is obtained by adding together two of the vectors, VL and VC and then
adding this sum to the remaining vector VR. The resulting angle obtained between VS and i will be
the circuits phase angle as shown below.
79
We can see from the phasor diagram on the right hand side above that the voltage vectors
produce a rectangular triangle, comprising of hypotenuse V S, horizontal axis VR and vertical axis
VL – VC Hope fully you will notice then, that this forms our old favourite the Voltage Triangle
and we can therefore use Pythagoras‟s theorem on this voltage triangle to
mathematically obtain the value of VS as shown.
VS =
Please note that when using the above equation, the final reactive voltage must always be positive
in value, that is the smallest voltage must always be taken away from the largest voltage we
cannot have a negative voltage added to VR so it is correct to have VL – VC or VC – VL. The
smallest value from the largest otherwise the calculation of VS will be incorrect.
We know from above that the current has the same amplitude and phase in all the components of
a series RLC circuit. Then the voltage across each component can also be described
mathematically according to the current flowing through, and the voltage across each element as.
VR = iR sin( ) = i . R VL =
iXL sin( ) = i . jwL VC
= iXC sin( )= i. By substituting
these values into Pythagoras‟s equation above for the voltage triangle:
80
Vs
=
Since Vs = I.Z where Z =
So we can see that the amplitude of the source voltage is proportional to the amplitude of the
current flowing through the circuit. This proportionality constant is called the Impedance of the
circuit which ultimately depends upon the resistance and the inductive and capacitive
reactance‟s.
Then in the series RLC circuit above, it can be seen that the opposition to current flow is made up
of three components, XL, XC and R with the reactance, XT of any series RLC circuit being defined
as:XT = XL – XC or XT = XC – XL with the total impedance of the circuit being thought of as the
voltage source required to drive a current through it. As the three vector voltages are out-of-phase
with each other, XL, XC and R must also be “out-of-phase” with each other with the relationship
between R, XL and XC being the vector sum of these three components thereby giving us
the circuits overall impedance, Z. These circuit impedance‟s can be drawn and represented
by an Impedance Triangle as shown below:
The impedance Z of a series RLC circuit depends upon the angular frequency, ω as
do XL and XC If the capacitive reactance is greater than the inductive reactance, XC > XL then the
overall circuit reactance is capacitive giving a leading phase angle. Likewise, if the inductive
reactance is greater than the capacitive reactance, XL > XC then the overall circuit reactance is
inductive giving the series circuit a lagging phase angle. If the two reactance‟s are the same and
XL = XC then the angular frequency at which this occurs is called the resonant frequency and
produces the effect of resonance which we will look at in more detail in another tutorial.Then the
magnitude of the current depends upon the frequency applied to the series RLC circuit. When
impedance, Z is at its maximum, the current is a minimum and likewise, when Z is at its
minimum, the current is at maximum.
The phase angle, θ between the source voltage, VS and the current, i is the same as for the angle
between Z and R in the impedance triangle. This phase angle may be positive or negative in value
81
depending on whether the source voltage leads or lags the circuit current and can be calculated
mathematically from the ohmic values of the voltage triangle as:
= , =
, =
And similarly from impedance triangle,
= , = , =
In order to find the resonance frequency we will use the following relationship,
fR =
Procedure:
• Connect the resistance, inductance and capacitance in series as shown in the circuit.
• Set the source frequency from function generator at an appropriate frequency say 1kHz.
• Measure the voltages VR, VL, VC and the series current I.
• Calculate source voltage, phase angle, resistance, inductive reactance, capacitive reactance,
Total impedance, inductance and capacitance in an RLC series circuit.
• Calculate the resonance frequency fR.
• Repeat the measurements and calculations by setting the voltage source frequency at the
resonance frequency fR.
• Note down the readings in the tables.
Measurements:
Voltage Source I VR (Volts) VL (Volts) Vc (Volts)

Frequency (mA)
(kHz)
Calculations:
82
„f‟ = R= = Z= L= C=
=
(kHz) ( )
VS = ( ) (
(Volts) (Degree) ( )
) (Ohms) (mH)
( )
( )
( )
Measurements at Resonance frequency:
Voltage Source I VR (Volts) VL (Volts) Vc (Volts)

Frequency (mA)
(kHz)
Calculations at Resonance frequency:
„f‟ = R= = = Z= L= C=
(kHz) (Ohms) ( )
VS = ( )
( ) ( ) (mH)
(Volts)
( )
(Degree) ( ) ( )
Exercise
Objective:
83
1. A series RLC circuit containing a resistance of 12Ω, an inductance of 0.15H and a capacitor
of 100uF are connected in series across a 100V, 50Hz supply. Calculate the total circuit
impedance, the circuits current, power factor and draw the voltage phasor diagram.
84
Experiment No. 17: Circuit Analysis of RLC parallel circuit.
Apparatus:
• Power Supply
• Function Generator
• Resistances
• Capacitors
• Inductors
• Multimeter
Objectives:
• To study the behavior of RLC parallel circuit.

• To calculate source voltage, phase angle, resistance, inductive reactance, capacitive
reactance, Total impedance, inductance and capacitance in an RLC parallel circuit.
• To study the resonant frequency phenomenon.
Pre-Lab:
The Parallel RLC Circuit is the exact opposite to the series circuit we looked at in the previous
tutorial although some of the previous concepts and equations still apply. However, the analysis
of parallel RLC circuits can be a little more mathematically difficult than for series RLC circuits
so in this tutorial about parallel RLC circuits only pure components are assumed in this tutorial to
keep things simple.
This time instead of the current being common to the circuit components, the applied voltage is
now common to all so we need to find the individual branch currents through each element. The
total impedance, Z of a parallel RLC circuit is calculated using the current of the circuit similar to
that for a DC parallel circuit, the difference this time is that admittance is used instead of
impedance. Consider the parallel RLC circuit below.
85
Since the voltage across the circuit is common to all three circuit elements, the current through
each branch can be found using Kirchoff‟s Current Law, (KCL). Kirchoff‟s current law or
junction law states that “the total current entering a junction or node is exactly equal to the
current leaving that node”, so the currents entering and leaving node “A” above are given as:
KCL: IS-IR-IL-IC = 0
IS
IS(t) =
Taking the derivative, dividing through the above equation by C and rearranging gives us the
following Second-order equation for the circuit current. It becomes a second-order equation
because there are two reactive elements in the circuit, the inductor and the capacitor. The
opposition to current flow in this type of AC circuit is made up of three components: X L XC and R
and the combination of these three gives the circuit impedance, Z. We know from above that the
voltage has the same amplitude and phase in all the components of a parallel RLC circuit. Then
the impedance across each component can also be described mathematically according to the
current flowing through, and the voltage across each element as.
In the above parallel RLC circuit, we can see that the supply voltage, V S is common to all three
components whilst the supply current IS consists of three parts. The current flowing through the
resistor, IR, the current flowing through the inductor, IL and the current through the capacitor, IC.
But the current flowing through each branch and therefore each component will be different to
each other and to the supply current, I S. The total current drawn from the supply will not be the
mathematical sum of the three individual branch currents but their vector sum.
86
Like the series RLC circuit, we can solve this circuit using the phasor or vector method but this
time the vector diagram will have the voltage as its reference with the three current vectors
plotted with respect to the voltage. The phasor diagram for a parallel RLC circuit is produced by
combining together the three individual phasors for each component and adding the currents
vectorially.
Since the voltage across the circuit is common to all three circuit elements we can use this as the
reference vector with the three current vectors drawn relative to this at their corresponding
angles. The resulting vector IS is obtained by adding together two of the vectors, I L and IC and then
adding this sum to the remaining vector I R. The resulting angle obtained between
V and IS will be the circuits phase angle as shown below.
We can see from the phasor diagram on the right hand side above that the current vectors produce
a rectangular triangle, comprising of hypotenuse I S, horizontal axis IR and vertical axis IL – IC
Hopefully you will notice then, that this forms a Current Triangle and we can therefore use
Pythagoras‟s theorem on this current triangle to mathematically obtain the magnitude of the
branch currents along the x-axis and y-axis and then determine the total current I S of these
components as shown. From current triangle we can find the relations,
87
Where R= , and
So,
Z=
This phase angle may be positive or negative in value depending on whether the source voltage
leads or lags the circuit current and can be calculated mathematically from the ohmic values of
the current triangle as:
= , = , =
And similarly from impedance triangle,
= , = , =
In order to find the resonance frequency we will use the following relationship,
fR =
Procedure:
• Connect the resistance, inductance and capacitance in series as shown in the circuit.
• Set the source frequency from function generator at an appropriate frequency say 1kHz.
• Measure the currents IR, IL, IC and the parallel source voltage V.
• Calculate source voltage, phase angle, resistance, inductive reactance, capacitive reactance,
Total impedance, inductance and capacitance in an RLC series circuit.
• Calculate the resonance frequency fR.
• Repeat the measurements and calculations by setting the voltage source frequency at the
resonance frequency fR.
• Note down the readings in the tables.
Measurements:
88
Voltage Source V IR IL Ic
Frequency
(Volts) (mA) (mA) (mA)
(kHz)
Calculations:
„f‟ IS = = R= Z= L= C=
= =
(kHz) (Degree)
(mA) () (mH)
()
( )
( ) () ( )
( )
( )
Measurements at Resonance frequency
Voltage Source V IR IL Ic
Frequency
(Volts) (mA) (mA) (mA)
(kHz)
Calculations at Resonance frequency
„f‟ IS = = R= Z= L= C=
= =
89
(Degree) ( )
(kHz)
()
(mA) () (mH)
( ) () ( )
( )
( )
Exercise
Objective:
1. A 1kΩ resistor, a 142mH coil and a 160uF capacitor are all connected in parallel across a
240V, 60Hz supply. Calculate the impedance of the parallel RLC circuit and the current
drawn from the supply.
2. A 50Ω resistor, a 20mH coil and a 5uF capacitor are all connected in parallel across a
50V, 100Hz supply. Calculate the total current drawn from the supply, the current for
each branch, the total impedance of the circuit and the phase angle. Also construct the
current and admittance triangles representing the circuit.
90
91
EE Departmen Electric Circuit Analysis-1
t
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ECE Department Electric Circuit Analysis-

COMSATS Institute of Information Technology

ELECTRIC CIRCUIT ANALYSIS-1

Department of Electrical Engineering

ELECTRIC CIRCUIT ANALYSIS – 1

a) Course Software: Electrical Circuits Simulation using Multisim

Lab 02 Equivalent Resistance of Series, Parallel and Series-Parallel circuits.

Lab 03 To verify Kirchoff‟s Voltage Law.

Lab 04 Mesh Analysis.

Lab 05 To verify Kirchoff‟s Current Law.

Lab 06 Nodal Analysis.

Lab 07 To verify Millman‟s Theorem.

Lab 09 To verify Norton‟s Theorem.

Lab 10 To verify Superposition Theorem.

Lab 11 To verify Maximum Power Transfer Theorem.

Lab 12 To verify Reciprocity Theorem.

Lab 13 To verify Compensation Theorem.

Lab 14 To verify Tellegen‟s Theorem.

Lab 15 Calculation of Total Impedance in RL and RC Circuits using Multisim.

Lab 16 Circuit Analysis of RLC series circuit.

Lab 17 Circuit Analysis of RLC parallel circuit.

Basic Electrical Safety Practices

All conducting surfaces intended to be at ground potential should be connected together.

Don't overload extension cords: multi-outlet strips and wall outlets.

a) Course Software: Electrical Circuits Simulation using Multisim Electronics Workbench

Figure 1: Main Window of Multisim Simulation software

Build the circuit shown in Figure 2 using Multisim Electronics Workbench.

Figure 2: Circuit for Multisim simulation.

STEP A: Placing the Components

1. Place a Battery (DC Source)

Figure 3: Selection of DC Voltage Source in Multisim

Figure 4: Battery Window for setup of DC voltage source

Bring a resistor in the Multisim workspace:

Figure 5: Selection of Resistor in Multisim

Figure 6: Setup window for Resistor values

Figure 7: Battery Window for Label of Resistor

Figure 8: Selection of Ground in Multisim

STEP B: Connecting the Components

1. Arrange the components properly:

Figure 9: Arranging the Components in proper order

3. Connect DC Voltage Source "Vs" to "R1":

4. Connect "R1" to "R2":

5. Making use of Junction to connect Ground:

Figure 11: Complete Circuit in Multisim

Figure 12: Drag points for connecting wire

Figure 13: Instruments Toolbar

Figure 14: Multimeter connection for voltage measurement

Figure 15: Multimeter properties window

1. Place a second Multimeter in the workspace as we did in Step C

2. Set the Multimeter to measure current:

Figure 16: Multimeter connection for current measurement

STEP E: Simulate the circuit

1. Save the file

3. If the properties window is not open

Figure 17: Simulation result

Figure 18: A circuit for exercise

• Introduction to the course software.

Black 0 100 (1)

• Calculate the resistance of the resistors available by using color codes.