ELECTRICAL CIRCUIT ANALYSIS

(20A02301T)

LECTURE NOTES

II -B.TechI-Semester

Prepared by
Dr. A.Hema Sekhar, M.Tech., Ph.D
Professor & HOD
Department of Electrical and Electronics Engineering

VEMU INSTITUTE OF TECHNOLOGY

(Approved By AICTE, New Delhi and Affiliated to JNTUA, Ananthapuramu)

Accredited By NAAC, NBA( EEE, ECE & CSE)& ISO: 9001-2015 Certified Institution

Near Pakala, P.Kothakota, Chittoor- Tirupathi Highway

Chittoor, Andhra Pradesh-517 112

Web Site: www.vemu.org

 JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY ANANTAPUR
(Established by Govt. of A.P., ACT No.30 of 2008)
ANANTHAPURAMU – 515 002 (A.P) INDIA

ELECTRICAL AND ELECTRONICS ENGINEERING

Course Code ELECTRICAL CIRCUIT ANALYSIS LTPC

20A02301T 3003

UNIT - I Locus Diagrams & Resonance 8 Hrs

Series R-L, R-C, R-L-C and Parallel Combination with Variation of Various Parameters -
Resonance-Series, Parallel Circuits, Frequency Response, Concept of Bandwidth and Q Factor.

UNIT - II Two Port Networks 9 Hrs

Two Port Network Parameters – Impedance – Admittance - Transmission and Hybrid Parameters
and their Relations - Concept of Transformed Network - Two Port Network Parameters Using
Transformed Variables.

UNIT - III Transient Analysis 12 Hrs

D.C Transient Analysis: Transient Response of R-L, R-C, R-L-C Series Circuits for D.C Excitation
- Initial Conditions in network - Initial Conditions in elements - Solution Method Using Differential
Equation and Laplace Transforms - Response of R-L & R-C Networks to Pulse Excitation.

A.C Transient Analysis: Transient Response of R-L, R-C, R-L-C Series Circuits for Sinusoidal
Excitations - Solution Method Using Differential Equations and Laplace Transforms.

UNIT - IV Fourier Transforms 10 Hrs

Fourier Theorem - Trigonometric Form and Exponential Form of Fourier series – Conditions of
Symmetry - Line Spectra and Phase Angle Spectra - Analysis of Electrical Circuits to Non
Sinusoidal Periodic Waveforms. Fourier Integrals and Fourier Transforms – Properties of Fourier
Transforms and Application to Electrical Circuits.

UNIT - V Filters 9 Hrs

Filters – Low Pass – High Pass, Band Pass and Band Stop– RC, RL filters– derived filters and
composite filters design – Attenuators – Principle of Equalizers – Series and Shunt Equalizers – L
Type - T type and Bridged – T and Lattice Equalizers.

Textbooks:
1. William Hayt, Jack E. Kemmerly and Jamie Phillips, “Engineering Circuit Analysis”, Mc Graw
Hill, 9th Edition, 2019.
2. A. Chakrabarti, “Circuit Theory: Analysis & Synthesis”, Dhanpat Rai & Sons, 2008.
Reference Books:
1. M.E. Van Valkenberg, “Network Analysis”, 3rd Edition, Prentice Hall (India), 1980.
2. V. Del Toro, “Electrical Engineering Fundamentals”, Prentice Hall International, 2009.
3. Charles K. Alexander and Matthew. N. O. Sadiku, “Fundamentals of Electric Circuits” Mc Graw
Hill, 5th Edition, 2013.
4. MahamoodNahvi and Joseph Edminister, “Electric Circuits” Schaum’s Series, 6th Edition, 2013.
5. John Bird, Routledge, “Electrical Circuit Theory and Technology”, Taylor & Francis, 5th
Edition,
2014.
Online Learning Resources:
 VEU INSTITUTE OF TECHNOLOGY:P.KOTHAKOTA
Department of EEE
ECA
UNIT-1 LOCUS DAIGRAMS

1. Define resonance?
2. Define anti resonance?
3. Define bandwidth and quality factor?
4. Define quality factor and sensitivity of a series RLC circuit.(MAY 18)
5. Define cut off frequency. Obtain the expression of cut off frequency in series resonance?
6. Differentiate series and parallel resonance?
7. Write the relation between bandwidth, quality factor and cut off frequency?
8. For the circuit shown below, determine the value of capacitive reactance and impedance at
resonance.(DEC 16)

9. What is the current in the series R-L-C circuit at resonance? What is the reason
for that?(NOV 17)
10. Define Selectivity?
11. Define Locus Diagram?

ESSAY QUESTIONS:

1. (a) What is the relation between bandwidth and resonant frequency for series RLC Circuit?
(b) An inductance of 0.5H a resistance of 5 Ω and a capacitance of 8μF are in series across
a 220 V AC supply. Calculate the frequency at which the circuit resonates. Find the
current at resonance bandwidth, half power frequencies and the voltage across capacitance
of resonance. (MAY 18)

2. (a) Show that the resonant frequency ω0of an RLC series circuit is the geometric mean of
ω1andω2 , the lower and upper half power frequencies respectively.
(b) Given a series RLC circuit with R = 100 ohms, L = 0.5H and C = 40μF. Calculate the
resonant, lower and upper half – power frequencies.(MAY 2017)

3. A series circuit with R=10Ω, L=0.1H and C=50µF has an applied voltage V=50∟0° V with
a variable frequency. Find the resonant frequency & the value of frequency at which
maximum voltage occurs across the capacitor & inductor.(DEC 16)
4. Determine the quality factor of a coil for the series circuit consisting ofR=10Ω, L=0.1H and
C=10µF.(DEC 16)
5. In the following coupled circuit determine the current supplied by the source I.(JUNE 16)

6. A coil of impedance R + j XL is connected in series with a 50Ω resistor and a capacitor – j

XC ohms. The combination is connected across a 100 V variable frequency source. At a
frequency of 200 Hz, maximum current of 0.7 amps flows in the circuit and the voltage
 across the capacitor is 200 volts at this frequency. Find R, XL, XC and band width of the
circuit. (JUNE 16)
(b) An inductance of 0.5 H, a resistance of 5 Ω, and a capacitance of 8 μF are in series
across a 220 V AC supply. Calculate the frequency at which the circuit resonates. Find the
current at resonance, Band width, half power frequencies and the voltage across
capacitance at resonance.(NOV 17)
7. (a) Derive the expression for Q-factor in a series R-L-C circuit.
(b) The Q-factor of a RLC circuit is 5 at its resonance frequency of 1 kHz. Assuming the
power dissipation of 250 W when the current drawn is 1 A, find the circuit parameters.
Determine the BW of the circuit.(NOV 17)
8. Derive the Expression for Resonant Frequency for Series RLC Circuit?
9. Derive the Expression for Resonant Frequency for Parallel RLC Circuit?
10. What is the relation between bandwidth and resonant frequency for parallel RLC Circuit?
 UNIT-2 TWO PORT PARAMETERS

SHORT QUESTIONS:

1. Define two-port network?

2. Define Z-parameters?
3. Define Y-parameters?
4. Define h-parameters?(MAY 17, DEC 16)
5. Define transmission or ABCD or chain or general parameters?(NOV 17)
6. Write the symmetry condition for Z, Y, h and ABCD parameters?
7. Write the reciprocity condition for Z, Y, h and ABCD parameters?
8. Draw the parallel connection of 2 two-port networks?
9. Find the mutual impedance of the circuit shown below.(DEC 16)

10. What are called transmission parameters? Why are they called so?(DEC 16)
11. When 10 V is applied to a two port resistive network, on no load, the voltage at the open
circuit end is 8 V. When 1 amp load is connected, the voltage at the load end is 6 V. Find
the voltage at the load end for a load current of 2 amp. The supply voltage is same in all
the cases.

ESSAY QUESTIONS:
1. (b) Explain ABCD parameters in two port network.(MAY 18)
2. Find the h-parameters for the network shown in figure below.(MAY 18)

3. (a) Define and explain short circuit parameters by taking one example.

5. Derive the relation between transmission and impedance parameters.

6. Express the Z parameters of a two port network in terms of Y parameters.(DEC 16)

9. Find the Y and Z parameters of the following two port resistive network. Verify the relation
between them. .(JUNE 16)

10. (a) Derive the relation between impedance and admittance parameters.

11. (a) Derive the relation between hybrid and impedance parameters.
12. Express the Z parameters of a two port network in terms of h and ABCD parameters?
 13. Express the Y parameters of a two port network in terms of Z, h, ABCD parameters
14. Express the h parameters of a two port network in terms of Z,Y and ABCD parameters
15. Express the ABCD parameters of a two port network in terms of Y and ABCD parameters
16. Define and explain “h” parameters by taking one example
17. Define and explain ABCD parameters by taking one example
18. Find Z ,Y, h and ABCD parameters for the following problem

UNIT-3 TRANSIENT ANALYSIS

SHORT QUESTIONS:

1. Define transients?
2. Define time constant. What is the time constant for series RL and series RC circuit?
3. Define natural and forced responses?
4. Write the natural response equation of series RL and RCcircuit?
5. Write the forced response equation of series RL and RC circuit?
6. Write the transient response equation in series RLC circuit?
7. What is excitation?
8. Define time constant of RL circuit. (MAY 2018)
9. When an inductor is connected in a circuit, what is the status of inductor under steady
state condition? Draw the equivalent circuit?(MAY 2017)
10. When a capacitor is connected in a circuit, what is the status of capacitor under steady
state condition? Draw the equivalent circuit?(MAY 2017)
11. Write down the equation of current for an RC circuit when it is supplied by a DC
source.(DEC 16)
12. What is the time constant of an RC circuit excited by a DC source?(DEC 16)
13. A unit pulse of width 1 sec as shown is applied to an R – L series circuit with R=1Ω
and L = 1H. Sketch the current responsei(t) in the circuit.(JUNE 16)

14. A DC source of 1V is suddenly applied to a series R-L-C circuit with R=2Ω, L = 1H

and C = ½ F. Sketch the current response in the circuit.(JUNE 16)
15. When an inductor is connected in a circuit, what is the status of inductor under
transient state condition? Draw the equivalent circuit.(NOV 17)
16. When a capacitor is connected in a circuit, what is the status of capacitor under
transient state condition? Draw the equivalent circuit.(NOV 17)

ESSAY QUESTIONS:
1. Obtain the Current Expression for Transient Response of Series RL Circuit excited by DC
using Differential Evaluation Method?
2. Obtain the Current Expression for Transient Response of Series RL Circuit excited by DC
using Laplace Transform Method?
3. Obtain the Current Expression for Transient Response of Series RL Circuit excited by AC
using Differential Evaluation Method?
4. Obtain the Current Expression for Transient Response of Series RL Circuit excited by AC
using Laplace Transform Method?
5. Obtain the Current Expression for Transient Response of Series RC Circuit excited by DC
using Differential Evaluation Method?
6. Obtain the Current Expression for Transient Response of Series RC Circuit excited by DC
using Laplace Transform Method?
7. Obtain the Current Expression for Transient Response of Series RC Circuit excited by AC
using Differential Evaluation Method?
8. Obtain the Current Expression for Transient Response of Series RC Circuit excited by AC
using Laplace Transform Method?
9. Obtain the Current Expression for Transient Response of Series RLC Circuit excited by
DC using Differential Evaluation Method?
10. Obtain the Current Expression for Transient Response of Series RLC Circuit excited by
DC using Laplace Transform Method?
11. Obtain the Current Expression for Transient Response of Series RLC Circuit excited by
AC using Differential Evaluation Method?
12. Obtain the Current Expression for Transient Response of Series RLC Circuit excited by
AC using Laplace Transform Method?
13. A series RLC circuit with R = 300 ohms, L = 1H and C = 100μF has a constant voltage of
50 Vapplied to it at t = 0. Find the maximum current value. Assume zero initial
conditions.(MAY 2018)
14. In the circuit shown below, V = 10 V, R = 10 Ω, L = 1H and C = 10µF. The capacitor is
initially uncharged. The switch is closed at t = 0. Determine
And also derive the formulae used. (MAY 2017)

15. In the circuit shown below, L= 1H, R = 6 Ω and C = 0.2F. The capacitor is initially
charged to 24 V and the switch is closed at t = 0. Determine the expression for i(t) and the
value of current at one second after the switch is closed. And also derive the formulae
used.

16. The following network is in steady state with S open. At t = 0, S is closed. Find Vc(t) for
t>0.(JUNE 16)

17. In the following network, the switch S is open and steady state is reached. At t = 0, S is
closed. Find iL(t) for t>0.(JUNE 16)
 18. The switch in the circuit shown below is moved from position (1) to (2) at t = 0. Find the
expression for VC and VR for t > 0. And also derive the formulae used.

19. For the network shown in figure below, determine the expression for i(t). The switch is
closed at t = 0. Take V = 1 V, R = 2 Ω, L = 1H and C = 0.5F. And also derive the formulae
used.

20. In the circuit shown in the figure, switch is at position 1 and steady state is reached. At t=0, switch
is moved to position 2. Find the expression for current?

UNIT-4 FOURIER TRANSFORMS

2 Marks Questions

SHORT QUESTIONS:
1. Write the any two properties of Fourier transform
2. Write the exponential form of Fourier series
3. Write the Trigonometric form of Fourier series
4. Write the condition for odd and even symmetry
5. Define fourier transforms?
6. Define fourier series?
7. Write the different forms of fourier series?

SHORT QUESTIONS:
1. Obtain the Fourier Series for the waveform shown in figure below.
2. Obtain the Fourier Series for the waveform shown in figure below.

3. Obtain a Fourier series for the periodic function f(x) defined as:
f (x)= −k, when –π < x < 0
+k, when 0 < x < π
The function is periodic outside of this range with period 2π

4. Determine the Fourier series to represent the function f (x)=2x in the range −π to +π

5. Derive the fourier series for both sine and cosine function?
6. Derive the fourier transforms for both sine and cosine function?
7. Find the relation between trigonometry and exponential fourier series?
8. Find the fourier transform of
a) Unit step function
b) Ramp function
9. Find the fourier series of two sided signal of eAt?
10. Explain the Properties of Fourier Transforms?
11.

12. Obtain the expressions for Trigonometric Form and Exponential For of Fourier Series?
13. Develop Fourier series for the following signal?
 UNIT-5 FILTERS

1. Define filter?
2. Define constant-K type filter?
3. Define Neper.(MAY 18)
4. Deduce the relation between Neper and Decibel?
5. Define propagation constant, Attenuation constant and phase constant?
6. Write the pass band and stop band conditions for a filter?
7. Write the characteristic equations of T and Π network?
8. Write the applications of different types of filter.(MAY 18)
9. Draw constant-k low pass filter (proto type).(MAY 17)
10. Draw constant-k high pass filter (proto type).(NOV 17)
11. Draw the frequency response characteristics of a band pass filter and indicate the
important frequencies in it.

ESSAY TYPE QUESTIONS

1. Design a constant-K low pass filter, both t and π sections having a cut-off frequency of 2
kHz to operate with a terminated load resistance of 500 Ω. (MAY 18)
2. A T-section low pass filter has an inductance of 30mH in each of the series arms and a
shunt arm capacitance of 0.25 . Calculate the cut off frequency, characteristic impedance,
ratio of input, output voltages and phase shift at: (i) 1 kHz. (ii) 5 kHz.(MAY 17)
3. Analyze constant K low pass filters.(DEC 16)
4. Analyze constant K High pass filters
5. Analyze constant Band pass filters
6. A prototype high pass filter has a cut off frequency of 8 kHz and a nominal impedance of 600
Ω.Calculate the values of inductance and capacitance used in the filter.(NOV 17)
7. Design a prototype band pass filter with cut off frequencies 1.5 kHz and 5 kHz and a
design impedance of 500 Ω.(NOV 17)
8. A low pass section filter consists of an inductance of 25mH in the series arm and two capacitors of
0.2μF in the shunt arms. Calculate the cut off frequency, design impedance,attenuation at 5 kHz
and phase shift at 2 kHz. Also find the characteristic impedance at 2 kHz.(MAY 17)
9. Analyze m Derived low pass filters
10. Analyze m Derived High pass filters
11. Analyze Composite filters?
12.

13.