American International University- Bangladesh (AIUB)

Faculty of Engineering (EEE)

Introduction to Electrical
Course Name: Course Code: COE 2102
Circuits (IEC) Lab
Semester: Spring 2022-23 Sec: [J] All
Faculty: Dr. A. A. Mohammad Monzur-Ul- Group: 06
Akhir

Task: Perform Open End Lab following given instructions.

Experiment title: Applying KVL and KCL on an R-L-C circuit and analyzing the behavior of the circuit.

Student Name: Meheraj Hasan Student ID: 22-49363-3

Group Members ID Name

1. 22-49363-3 Meheraj Hasan
2. 22-47506-2 Mst. Shoumun Linnas Jim
3. 22-47370-2 MD. Sakibul Hoque
4. 22-48252-2 Atik Shahrier Rakir
5. 22-47378-2 Jaber Bhuiyan

CO4: Implement electrical circuit (including DC, AC source, load and measuring equipment) in a group from the given
schematics circuits and adapt with electrical measuring devices considering standards for professional engineering.
(P.e.2.P4), K6-P1,P4,P5

Objectives Unsatisfactory (0-1) Good (2-3) Excellent (4-5) Marks

Setup of experiment, Cannot setup experiment without Can setup some of the portions of Can setup the whole
Take proper support experiment without support experiment
Cannot take measurements
Performance (10)

measurements Can take measurements but without support

inaccurately Can take organized and
accurate
measurements
Identify experiment Cannot identify goals Can identify some goals but Can identify necessary and
goals, Summarize Cannot summarize or compare findings unable to draw adequate sufficient goals
findings and to expected results hypothesis
compare actual to Summarize finding in an Summarize finding in a
expected results incomplete way complete way
Cannot answer any question related to Can answer some of the Can answer most or all the
Observation 1 the questions questions
Report (10)

experimental setup
Unexpected experimental outcome Somewhat unexpected Accurate data collected from
Observation 2 between calculated data experiment the hardware
and experimented data outcome

Comments Assessed by (Name, Sign, and Date) Total (out of 10):

Marking Rubrics (to be filled by Faculty)

 American International University- Bangladesh
Department of Electrical and Electronic Engineering
COE 2102: Introduction to Electrical Circuits (IEC) Laboratory
Title: Construct an R-L-C circuit with a series-parallel combination and apply KCL and KVL in AC and analyze the
behavior of the circuit through data obtained during Laboratory work.
Objective
Validate RLC circuit and verification of KCL and KVL in AC circuits. Justify AC analysis technique that should be
applied in this experiment,
Equipment
• Use at least 4 resistors, 2 inductor, 1 capacitor and an AC source,
• Breadboard and Multimeter.
• A PC or Laptop.
Tasks
(i) Design a RLC AC circuit.
(ii) Apply an AC analysis theorem for extracting measuring data to validate KCL and KVL.
(iii) Compare experimental data and simulation data that can be obtained for any circuit simulation tool, e.g.,
Multisim, PSPICE.
OEL Report
Your OEL report should include the following sections:
a) Objective
This is the main problem statement. It provides the overall direction for laboratory investigation and must be
addressed in the conclusion.
b) Equipment
• A list of all laboratory equipment/tools used for the experiment.
• A detailed and labeled diagram to illustrate the setup of the experiment, either drawn using some diagramming
application or from the design software itself.
• List of all the different components used.

c) Procedure
• Brief description of the theory behind the conflicting performance requirements, limitations, and
reasoning behind design choices.
• Step-by-step procedure carefully explained in a numbered sequence.
• Alternate design options should be explored through parameter sweeps and justification for the selection should
be provided later in the results section.
Procedure should be detailed and contain the explanation of usual jargons to ensure that the readers can
understand how the experiment should be performed and replicate the results by following the same process.
d) Results and Data analysis
• Show all the data obtained in the experiment in the tabular format.
• Analysis of data using appropriate graphs if needed.

e) Conclusions
• Comment on how much objective mentioned in the problem statement is achieved.
• Identify any questionable data or limitation in results and explain the possible source of any errors.
TiTle: Construct an R-L-C circuit with a series-parallel combination and apply KCL and KVL
in AC and analyze the behavior of the circuit through data obtained during Laboratory work.

ObjecTive: Validation of RLC circuit and verification of KCL and KVL in AC circuits. Justifying
AC analysis technique that applied in this experiment.

inTrOducTiOn: An RLC circuit is an electrical circuit consisting of a resistor, an inductor,

and a capacitor, connected in series. The RLC part of the name is due to those letters being
the usual electrical symbols for resistance, inductance and capacitance respectively. Series
RLC circuits are classed as second-order circuits because they contain two energy storage
elements, an inductance and a capacitance.

TheOry and MeThOdOlOgy:

Three basic passive components- R, L and C have very different phase relationships to each
other when connected to a sinusoidal AC supply. In case of a resistor the voltage waveforms
are "in-phase" with the current. In case of pure inductor, the voltage waveform "leads" the
current by 90o whereas in case of pure capacitor, the voltage waveform "lags" the current by
90o . This phase difference depends upon the reactive value of the components being used.
Reactance is zero if the element is resistive, positive if the element is inductive and negative
if the element is capacitive. Instead of analyzing each passive element separately, we can
combine all three together into a series RLC circuit. The analysis of a series RLC circuit is the
same as that for the dual series RL and RC circuits we studied in the last experiment, except
this time we need to take account the magnitudes of both inductive reactance and
capacitive reactance to find the overall circuit reactance.

Figure: RLC Series Circuit

relevanT equaTiOns:
Inductive reactance, XL = 2пfL Capacitive reactance, XC = 1/2п𝑓𝐶
Net reactance, X = XL - XC
Total impedance, Z = √(𝑅2 + 𝑋2)
Current, I = 𝑉/𝑍
Resistive voltage drop, VR = I*R
Reactive voltage drops = VL – VC, where VL = I*XL and VC = I*XC
Total voltage drop = √{𝑉R2 + (𝑉𝐿 − 𝑉𝐶)}

vecTOr diagraM:

equipMenT:
1. 4 Resistor
2. 2 Indicator
3. 1 Capacitor
4. 1 AC source
5. Multimeter

circuiT diagraM:
prOcedure:
1 At first we have collect required equipment and components, including at least 4 resistors,
2 inductors, 1 capacitor, an AC source, breadboard, and multimeter.
2 Then we measured the value of resistance. Now we constructed the circuit as shown in
fig1. 3.Then we Set the amplitude of the voltage input 5V.
4. We Set the frequency of the signal generator 1 kHz. Then we Measured the value of V R1,
VR2, VR3, VR4, VL1, VL2, VLC.
5. We Measured value of IR1, IR2, IR3, IR4, IL1, IL2, ILC.
6. We Verified KVL and KCL using the experimental data.
Simulation:
KVl:

KCl:
 daTa Table:

FOr Kvl:

Measured Value Simulation Value

f E VR1 VR2 VR3 VR4 VR1 VR2 VR3 VR4

(KHz) (V) (V) (mV) (V) (V) (V) (mV) (V) (V)

1 5 1.16 687.25 2.2 2.5 1.1742 696.95 2.5 2.601

FOr Kcl:

Measured Value Simulation Value

f E IR1 IR2 IR3 IR4 IR1 IR2 IR3 IR4

(KHz) (V) (mA) (mA) (mA) (uA) (mA) (mA) (mA) (uA)

1 5 1.02 1.02 0.98 22.8 1.162 1.162 1.136 26.164

 Calculation and Result:

f = 1KHz = 1000Hz
R1 + R2 = (0.6 + 1.5 ) Ω =2.1 Ω

XL2 = 2 x 3.1416 x 103 x 1 x6.3 x 10−3 = 39.58Ω = 39.58𝑥10−3 k Ω

XL1 = 2 x 3.1416 x 103 x 1 x 100 x 10−3 = 682.32 Ω = 682.32 𝑥10−3 k Ω
𝟏 1
𝑿𝒄𝟏 = 𝟐∗𝟑.𝟏𝟒𝟏𝟔∗𝒇∗𝒄𝟏= 2𝑥3.1416𝑥10−3 𝑥10−6 = 159.154 Ω = 159.154 𝑥10−3 kΩ

𝒁𝟏 = (R1 + R2 )+ jXL2

=2.1+ 𝑗 39.58𝑥10−3 k Ω

𝒁𝟐 =R3+ jXL1

=2.2+j 628.32𝑥10−3 k Ω

𝒁𝟑 =R4 -jXc1

=99.4-j159.154 𝑥10−3 𝑘 Ω

Here 𝑍2 ||𝑍3,

𝒁𝑻 = 𝑍1 +(𝑍2 ||𝑍3 )

𝑍2 x 𝑍3
= 𝑍1+
𝑍2 + 𝑍3

(2.2 + j 628.32𝑥10−3 ) x (99.4 − j 159.154 𝑥10−3 )

= 2.1 + j 39.58𝑥10−3 +
(2.2 + j 628.32𝑥10−3 ) + (99.4 − j 159.154 𝑥10−3 )
−3
= (2.1+ 𝑗 39.58𝑥10 𝑘 Ω) + (2.15916 + j 0.61𝑘 Ω)
=4.25+ 𝑗 0.65 𝑘 Ω
𝐸 5
𝑰𝑻 = 𝑍 = 4.45−𝑗0.65 𝑘 Ω= 1.1486-j0.1766 = 1.16mA <-8.744
𝑇

Due to series connection ,

𝑰𝒁𝟏 = 1.16mA <-8.744

By using CDR, for𝑍2 ||𝑍3

 (𝑍2 ||𝑍3 ) 2.15916+j 0.61
𝑰𝒁𝟐 = x 𝐼𝑇 = 2.2+j 628.32𝑥10−3 x 1.1486- j 0.1766 =1.1258+j 0.176=1.13mA <- 8.09
𝑍2

(𝑍2 ||𝑍3 ) 2.15916+j 0.61

𝑰𝒁𝟑 = x 𝐼𝑇 =99.4 − j 159.154 𝑥10−3x1.1486- j 0.1766 = 0.26-j 3.36=0.026 mA<7.36
𝑍3

KCL:

𝑰𝑻 = 𝐼𝑍1 =𝐼𝑍2 + 𝐼𝑍3 = 1.13mA <-8.09+0.026mA <7.36 =1.154mA <-8.89

1.30−1.26
Error = X 100=2.06%
1.26

Now,
(𝑍2 ||𝑍3)

(𝑍2 ||𝑍3 ) = 2.159 +j 0.6 𝑘 Ω

𝑍2 ||𝑍3 2.159+j 0.61

𝑉(𝑍2 ||𝑍3 ) = = ×5
𝑍𝑇 4.25+ j 0.65
=2.5 - j0.1945 V
= 2.518 V <-4.43

Due to parallel branches=2.52V<-4.43

VZ2= 2.52 V VZ3= 2.52 V

𝑍2 and 𝑍3 have same voltage,

𝑍 2.1+j 39.58×10−3
𝑉( 𝑍1 ) = 𝑍1 X E = ×5
𝑇 4.25+ j 0.65
=2.42 - j0.32 V
=2.442 V<-7.63

KVL:
E = 5V < 0
Now ,
𝑉 (Z2 || Z3 )+ 𝑉 z1
= 2.52 V <-4.43 + 2.442 V <-97.63= 4.97V < -5.99
E= 𝑉(Z2 || Z3 )+ 𝑉 z1 = 4.97V ≅ 5

5−4.97
Error = X 100=1.18%
4.97
In this experement , sum of the entering current and leaving current of the same junction
is equal and some supply voltage is equal to the sum of voltage drop of the circute but
there is 1.18% error in KVL and 2.06 % error in KCL.

Discussion :
• So far, we have achieved the validation of RLC circuit and validation of KVL and KCL.
We have implemented the equation in series parallel circuit in breadboard. After
measuring voltage and current across each resistor we got our desired value. These final
values were verified through simulated values. In this way, we practically justified both
the laws through the series parallel circuit. We also justified the AC circuit analysis
technique by applying it in the experiment.
• We have identified error percentage by comparing the value between experimental data
and calculation. Which can be caused by measurement inaccuracies, improper
connections. Additionally, human errors such as incorrect wiring or misreading values
can also. Contribute to the error percentage. The error percentage in these experiments
reflects the deviation of the experimental results from the expected theoretical values on
the experiment.

Conclusion: We would like to point out that the experiment has been completed
successfully over several circuits and KVL and KCL is verified in the RLC series circuit.
We have gained practical experience and improve our understandings and learn how to
calculate KVL and KCL in AC circuit. The experiment 1.18% error in KVL and 2.06 %
error in KCL measurement.