AMERICAN INTERNATIONAL UNIVERSITY–BANGLADESH (AIUB)

INTRODUCTION TO ELECTRICAL CIRCUITS LAB

Spring 2024-25

Section: P

Group: 02

Experiment No. 10: Study of ‘Nodal Analysis’ in R-L-C combination circuit in AC

Submitted to: MD. MAHMUDUL HASAN

Name ID Contribution Remarks

1. EMAMUL KABIR OVI 22-49664-3 20%
2. AL SHAMS MD. ROHAN 22-49684-3 20%
3. TOUSIF TARIK 23-53577-3 20%
4. SHAFAYAT JAMIL 23-55457-3 20%
5. SAMIRA ALAM DIA 24-57605-2 20%

Date of Performance: 21.04.2025

Date of Submission: 24.05.2025

Comments/Marks:
 Contribution

Serial ID NAME Contribution Percentage

Procedure,
1. 22-49664-3 1. EMAMUL KABIR OVI Result, 20%
Discussion
Abstract,
2. 22-49684-3 2. AL SHAMS MD. ROHAN 20%
Result,
Calculation,
3. 23-53577-3 3. TOUSIF TARIK 20%
Abstract,
Data Table,
4. 23-55457-3 4. SHAFAYAT JAMIL 20%
Simulation
Theory,
5. 24-57605-2 5. SAMIRA ALAM DIA 20%
Apparatus

Total: 100%
Title of the Experiment: response. To facilitate analysis, a detailed Data
Study of ‘Nodal Analysis’ in R-L-C Table 1 is completed, allowing for a meticulous
combination circuit in AC examination of any deviation or error between
Abstract: theoretical predictions and practical measurements.
Fig 1 depicts the circuit diagram, serving as a
The purpose of this experiment is to develop visual aid in understanding the nodal analysis
an understand the method of determining setup and enhancing the overall clarity of the
voltage and current using ‘Nodal Analysis’
in a R-L-C AC circuit. The circuits
containing R, L and C components and is to
be able to analyze the outputs of R-L-C
series-parallel combination circuit to obtain
practical value as well as simulated or
theoretical results. Moreover, the
determination of phase relationship between experiment.
V and I in an R- L-C combination circuit and
Figure 1: Circuit diagram for Nodal Analysis
to draw the complete vector diagram will be
done to understand the method of using Apparatus:
Nodal analysis.
1. Oscilloscope.
Theory:
2. Function generator.

Nodal analysis, a fundamental technique for 3. Resistor: 100 Ω (5)

solving electrical networks, involves
mathematically calculating voltage 4. Inductor: 6.3 mH
distribution across circuit nodes. This
experiment applies nodal analysis to AC 5. Capacitor: 4.7uF and 10 uF
circuits, emphasizing practical
6. Connecting wire.
measurements alongside theoretical and
simulated values. The AC node-voltage 7. Bread board
method, analogous to its DC counterpart,
relies on Kirchhoff's current law and Experimental Procedure and Data:
simultaneous solution of equations for each
node. In this study, we theoretically 1. We assembled the circuit as indicated in
calculate node voltages (VA, VB, VC) for a Figure 1. Connected the oscilloscope's
specific circuit (Figure 1) with given channel 1 to the function generator and the
parameters (C1 = 10 µF, C2 = 4.7 µF, R1 = oscilloscope's channel 2 to the R2.
R2 = R3 = R4 = 100 Ω, L1 = 6.3 mH, f = 1
KHz, V1 = 10 VPk with 0º phase shift). 2. We’ve set the input signal's amplitude to
Practical measurements of node voltages are 10V peak and the frequency to 1 kHz.
obtained using an oscilloscope and Chosen a sinusoidal waveform.
expressed in phasor form, capturing both
3. We measured the value of VA and IVA-B .
magnitude and angle information. This
approach ensures a comprehensive 4. Then we determined phase relationship
understanding of the circuit's behavior under between supply voltage V and node voltage
real-world conditions. The calculated data is at VA.
then leveraged to determine branch currents,
providing deeper insights into the circuit's 5. We connected the oscilloscope's channel 2
 to the R3.

6. After that we determined the phase

relationship between the waves.

7. We calculated the VC and I vB-C

values.

8. We determined phase relationship

between Supply voltage V and node
voltage at VC .

9. We determined I V A-C, I V A-G

and I V C-G.

10. Then we compared all the current

found with the theoretical value and
find the %Error.

Data Table:

Practical Value

Supply
Frequency IV B – A IV B – C IV A – C IV A – G IV C – G
Voltage
f
P–P
(kHz)
(V)
Mag. Phase Mag. Phase Mag. Phase Mag. Phase θ Mag. IV C – Phase θ
IV B – IV B – IV A – IV A – G G
θ θ θ (o) (mA) (o)
A C C (mA)
(mA) (o) (mA) (o)
(mA) (o)

1 7.071 33.48 45.1 34.1 44.8 6.16 45.3 34.94 45 34.87 18o
1
The table shows the measured current Calculation :
magnitudes and phase angles at various
points in the circuit when a 7.071 V peak
sinusoidal signal at 1 kHz is applied. It
illustrates how current varies through
different branches, with significant phase
shifts due to reactive components like
capacitors and inductors affecting the
overall behavior of the AC circuit.
Simulation:

DISCUSSION:
The application of Nodal Analysis in this experiment
has provided valuable insights into the behavior of
complex electrical circuits. By analyzing the circuit
step by step, the experimenters were able to observe
how individual nodes contribute to the overall circuit
response, emphasizing the principle of linearity. The
results demonstrate that Nodal Analysis is a powerful
tool for predicting voltages and currents at different
points within the circuit accurately. One significant
Figure 4: Transient Diagram of the Circuit
advantage of Nodal Analysis is its ability to simplify
complex circuits, making them more comprehensible
The simulation shows the AC response of and facilitating real-world applications. The experiment
the circuit.The transient graph indicates reinforced the importance of understanding the concept
how each current varies over time with of Nodal Analysis in various branches of engineering,
different amplitudes and phase shifts due underscoring its practical utility in solving intricate
to the presence of capacitive and electrical problems. Despite its effectiveness, it's
inductive components. important to note that Nodal Analysis has limitations,
such as the need for linear circuit conditions and
idealized components, which may not always hold true
in practical scenarios.

CONCLUSION:
The study of Nodal Analysis has enhanced our
understanding of complex electrical circuits. By
analyzing individual nodes separately, the
experimenters gained insight into the overall
system
response. This experiment confirmed the
accuracy of Nodal Analysis in predicting circuit
behavior,
a crucial aspect in electrical engineering for
designing and

COMPARATIVE ANALYSIS:

In this section, theoretical predictions based on

Nodal Analysis are meticulously compared with
practical measurements obtained from the Reference:
oscilloscope. The comparative analysis
reveals instances of accurate validation 1. Robert L. Boylestad, “Introductory
and notable discrepancies. The impact of
Circuit Analysis”, Prentice Hall, 12th
circuit complexity becomes evident,
Edition, New York, 2010, ISBN
highlighting the effectiveness of Nodal
Analysis in simpler circuits while 9780137146666.
showcasing challenges in more intricate
configurations. Despite limitations and
potential deviations from theoretical
assumptions, the hands-on experience
offers valuable insights into the practical
utility of Nodal Analysis, suggesting
avenues for refinement and further
research.

LIMITATIONS AND FUTURE

ENDEAVORS :

Nodal Analysis, while a powerful tool

for analyzing linear circuits, faces
limitations in real-world applications.
These limitations include applicability
to linear circuits only, reliance on
idealized conditions, potential
complexity in practical engineering
contexts, and the potential for
timeconsuming computations in large
circuits. Despite these challenges, the
Nodal Analysis method remains
valuable. Future endeavors aim to
enhance its applicability by exploring
extensions to nonlinear circuits, a
significant advancement. High-
powered computer simulations offer
practical solutions for handling
complex computations, and
integrating Nodal Analysis with other
analysis techniques could lead to more
comprehensive methods. Additionally,
the development of educational tools
aiding visualization and application is
crucial. Ongoing research and
technological progress hold the
promise of overcoming these
limitations, as advancements in
nonlinear circuit analysis and
computational tools continue.