Heaven’s Light is Our Guide
Rajshahi University of Engineering & Technology
Course Title: Circuit and System-I Sessional
Course Code: 1102
Lab Report-05
Date of Experiment: 08.11.2023
Date of Submission: 15.11.2023
Submitted By:
Submitted To:
Name: Gulam Gilani Hasan
Md. Abu Hanif Pramanik
Roll: 2210056
Lecturer,
Department of Electrical and
Computer Engineering, RUET
Registration: 1110
Session: 2022-2023
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5.1 Experiment No: 05
5.2 Experiment Name: Verification of Mesh and Nodal analysis.
5.3 Objectives:To understand the concepts and applications of mesh and nodal analysis
methods for solving linear circuits.
5.4 Theory:
Mesh and nodal analysis are two methods of solving linear circuits by applying Kirchhoff’s
laws. Kirchhoff’s voltage law (KVL) states that the sum of all voltages in a closed loop is
zero. Kirchhoff’s current law (KCL) states that the sum of all currents entering a node is
equal to the sum of all currents leaving that node.
Mesh analysis is a technique that uses KVL to find the unknown currents in the mesh loops
of a circuit. A mesh loop is a closed path that does not contain any other closed paths within
it. To apply mesh analysis, the following steps are followed:
i.
ii.
iii.
iv.
Identify all the mesh loops in the circuit and assign a mesh current to each loop. The
direction of the mesh current can be arbitrary, but it is usually chosen to be clockwise.
Write a KVL equation for each mesh loop, expressing the voltage drops and rises in
terms of the mesh currents. If there are any dependent sources in the circuit, express
them in terms of the mesh currents as well.
Solve the system of equations for the mesh currents using any method of linear
algebra, such as substitution, elimination, or matrix inversion.
Use the mesh currents to find any other quantities of interest, such as branch currents,
voltages, or power.
Nodal analysis is a technique that uses KCL to find the unknown voltages at the nodes of a
circuit. A node is a point where two or more branches of a circuit meet. To apply nodal
analysis, the following steps are followed:
i.
Identify all the nodes in the circuit and assign a node voltage to each node. One of the
nodes is chosen as the reference node and assigned a voltage of zero. The node
voltages are measured with respect to the reference node.
ii. Write a KCL equation for each node, except the reference node, expressing the
currents entering and leaving the node in terms of the node voltages. If there are any
dependent sources in the circuit, express them in terms of the node voltages as well.
iii. Solve the system of equations for the node voltages using any method of linear
algebra, such as substitution, elimination, or matrix inversion.
iv.
Use the node voltages to find any other quantities of interest, such as branch currents,
voltages, or power.
5.5 Required Apparatus:
1. Ammeter (2 pieces;0-10A)
2. Voltmeter (1 piece;0-600V)
3. Resistance (3 pieces; 100Ω,100Ω,100Ω)
4. DC Voltage Source (100V)
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5. Connecting wires
5.6 Circuit Diagram:
Figure 5.1: Circuit Diagram for mesh analysis
Figure 5.2 Circuit Diagram For Nodal analysis
5.7 Data Table:
Table 1: Mesh Analysis
SL
No.
1
Supply
Voltage
,Vs (V)
50
Mesh Current
Theoretical
Current,I1
(A)
0.33
Error,
e=
{I1Theo~I1Meas)
/I1Theo}×
100%
Measured
Current,
I1(A)
0.3
Mesh Current
Theoretical
Current, I2
(A)
0.167
9.09%
Error,e=
{I1Theo~I1Meas)/I1
Theo}×
100%
Measured
Current, I2
(B)
0.14
16.17%
Table 2: Nodal Analysis
SL
No.
Supply Nodal Voltage
Voltage
,
Vs
(V)
Theoretical
Voltage,V1
1
50
18.75
Measured
Voltage,
V1
16.5
Error,
e=
{V1Theo~V1Me
as)/V1Theo}×
100%
Nodal Voltage
Theoretical
Voltage,
V2
6.25
12%
3
Measured
Voltage,V
2
6.5
Error,e=
{V1Theo~V1Meas)
/V1Theo}×
100%
4%
5.7 Calculations:
For mesh analysis,
Error,e (for I1)={(I1Theo~I1Meas)/I1Theo}×100%=9.09%
Error, e(for I2)= {(I1Theo~I1Meas)/I1Theo}×100%=16.17%
Eavg (for mesh)=(9.09+16.17)/2=12.63%
For Nodal analysis,
Error, e (for v1)= {V1Theo~V1Meas)/V1Theo}×100%=12%
Error, e (for v1)= {V1Theo~V1Meas)/V1Theo}×100%=4%
Eavg (for Nodal analysis) = (12+4)%/2=8%
5.9 Result:
The calculated and measured mesh current are close to each other as the average error is
12.63%. Also the calculated and the measured nodal voltage are close to each other as the
average error is 8%.
5.10 Discussion:
The results show that the calculated and measured values are close to each other, with only
minor discrepancies due to measurement errors and rounding errors. This confirms that KVL
and KCL are valid and can be used to analyze electrical circuits using mesh analysis and
nodal analysis. The experiment also demonstrates the equivalence of the two methods, as
they yield the same values for the branch currents and voltages.
5.11 Precautions:
❖ Before connecting the circuit, check the values and ratings of the resistors, voltage
sources, and current sources, and make sure they match the given specifications.
❖ Use a breadboard or a printed circuit board to connect the circuit components, and
avoid loose or overlapping wires that may cause short circuits or unwanted
connections.
❖ Use a multimeter or an ammeter to measure the mesh currents, and a multimeter or a
voltmeter to measure the node voltages. Make sure to set the appropriate range and
polarity for the measurements, and connect the probes correctly to the circuit.
❖ Compare the calculated and measured values of the mesh currents and node voltages,
and analyze the sources of errors and discrepancies. Possible sources of errors include
measurement errors, rounding errors, component tolerances, and parasitic effects.
❖ Follow the safety rules and guidelines for working with electrical circuits, such as
wearing protective gloves and goggles, avoiding contact with live wires, and turning
off the power supply when not in use.
5.11 References:
Alexander C.K.; Matthew N.O.S., Fundamentals of Electric Circuits 2014, 5e, McGrew Hill
Education (india) Private Ltd, New Delhi, India.
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