Circuit Theory

808 Pages·2018·50.47 MB·English

by  A. Nagoor Kani

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CIRCUIT THEORY
About the Author
A. Nagoor Kani is a multifaceted personality with an efficient technical expertise and management
skills. He obtained his BE in EEE from Thiagarajar College of Engineering, Madurai, and
MS (Electronics and Control) through Distance Learning Program of BITS, Pilani.
He started his career as a self-employed industrialist (1986-1989) and then moved to teaching in
1989. He has worked as a lecturer in Dr MGR Engineering College (1989-1990) and as an Assistant
Professor in Satyabhama Engineering College (1990-1997). The author started his own coaching
centre for BE students, named as Institute of Electrical Engineering and was renamed as RBA
Tutorials in 2005. He started his own companies in 1997 and his currently running companies
are RBA Engineering (manufacturing of lab equipment and microprocessor trainer kits), RBA
Innovations (involved in developing projects for engineering students and industries), RBA Tutorials
(conducting coaching classes for engineering and GATE students) and RBA Publications (publishing
of engineering books). His optimistic and innovative ideas brought up RBA Group successfully.
He is an eminent writer and till now he has authored thirteen engineering books which are very
popular among engineering students. He is known by name through his books in all engineering
colleges in South India and some colleges in North India.
CIRCUIT THEORY
A. Nagoor Kani
Founder, RBA Educational Group
Chennai
McGraw Hill Education (India) Private Limited
CHENNAI
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Circuit Theory
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Dedicated to

Wife, Mrs. C. Gnanaparanjothi (B.Sc, M.L.)
Elder Son, N. Bharath Raj
Younger Son, N. Vikram Raj
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CONTENT
PREFACE.............................................................................................. xv

ACKNOWLEDGEMENT............................................................................ xvii

LIST OF SYMBOLS AND ABBREVIATIONS................................................. xix
CHAPTER 1 - BASIC CIRCUIT ANALYSIS.................................................. 1.1
1.1 Introduction to Circuits and Networks........................................................................ 1. 1
1.1.1 Basic Phenomena ............................................................................................ 1. 1
1.1.2 Ideal Elements ................................................................................................. 1. 1
1.1.3 Electric Circuits ............................................................................................... 1. 1
1.1.4 Units ................................................................................................................. 1. 4
1.1.5 Definitions of Various Terms.......................................................................... 1. 5
1.1.6 Symbols used for Average, RMS and Maximum Values............................... 1. 7
1.1.7 Steady State Analysis and Transient Analysis.............................................. 1. 8
1.1.8 Assumptions in Circuit Theory....................................................................... 1. 8
1.2 Basic Concepts of Circuits and Networks ................................................................. 1. 9
1.2.1 Basic Elements of Circuits............................................................................. 1. 9
1.2.2 Nodes, Branches and Closed Path ................................................................. 1. 10
1.2.3 Series, Parallel, Star and Delta Connections................................................. 1. 12
1.2.4 Open Circuit and Short Circuit....................................................................... 1. 15
1.2.5 Sign Conventions ............................................................................................ 1. 16
1.2.6 Voltage and Current Sources.......................................................................... 1. 17
1.2.7 Ideal and Practical Sources............................................................................. 1. 17
1.2.8 DC Source Transformation............................................................................. 1. 18
1.2.9 Power and Energy............................................................................................ 1. 19
1.3 Network Terminology................................................................................................... 1. 20
1.3.1 Graph of a Network ......................................................................................... 1. 20
1.3.2 Trees, Link, Twig and Cotree ......................................................................... 1. 21
1.3.3 Network Variables ........................................................................................... 1. 23
1.3.4 Solution of Network Variables ...................................................................... 1. 23
viii
1.4 Ohm’s and Kirchhoff’s Laws ........................................................................................ 1. 24
1.4.1 Ohm’s Law........................................................................................................ 1. 24
1.4.2 Kirchhoff’s Current Law (KCL)....................................................................... 1. 25
1.4.3 Kirchhoff’s Voltage Law (KVL)....................................................................... 1. 25
1.5 Resistive Elements....................................................................................................... 1. 26
1.5.1 Resistance....................................................................................................... 1. 26

1.5.2 Resistance Connected to DC Source............................................................. 1. 26

1.5.3 Resistance in Series........................................................................................ 1. 27
1.5.4 Resistance in Parallel...................................................................................... 1. 28
1.5.5 Analysis of Resistors in Series-Parallel Circuits .......................................... 1. 28
1.5.6 Single Loop Circuit.......................................................................................... 1. 31
1.5.7 Single Node Pair Circuit................................................................................. 1. 31

1.6 Mesh Current Method of Analysis for DC and AC Circuits...................................... 1. 41

1.6.1 Mesh Analysis of Resistive Circuits Excited by DC Sources....................... 1. 41
1.6.2 Mesh Analysis of Circuits Excited by Both Voltage
and Current Sources ....................................................................................... 1. 67
1.6.3 Supermesh Analysis....................................................................................... 1. 67
1.6.4 Mesh Analysis of Circuits Excited by AC Sources
(Mesh Analysis of Reactive Circuits)............................................................. 1. 73
1.6.5 Mesh Analysis of Circuits Excited by Independent
and Dependent Sources.................................................................................. 1. 80
1.7 Node Voltage Method of Analysis for DC and AC Circuits....................................... 1. 91
1.7.1 Node Analysis of Resistive Circuits Excited by DC Sources........................ 1. 92
1.7.2 Node Analysis of Circuits Excited by Both
Voltage and Current Sources.......................................................................... 1. 109
1.7.3 Supernode Analysis........................................................................................ 1. 110
1.7.4 Node Analysis of Circuits Excited by AC Sources
(Node Analysis of Reactive Circuits).............................................................. 1. 124
1.7.5 Node Analysis of Circuits Excited by Independent
and Dependent Sources.................................................................................. 1. 128
1.8 Summary of Important Concepts................................................................................ 1. 135
1.9 Short-answer Questions.............................................................................................. 1. 140
1.10 Exercises....................................................................................................................... 1. 150
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CHAPTER 2 - NETWORK REDUCTION AND THEOREMS FOR
AC AND DC CIRCUITS....................................................... 2. 1

2.1 Network Reduction....................................................................................................... 2. 1
2.1.1 Resistances in Series and Parallel.................................................................. 2. 1
2.1.2 Voltage Sources in Series and Parallel.......................................................... 2. 3

2.1.3 Current Sources in Series and Parallel.......................................................... 2. 6

2.1.4 Inductances in Series and Parallel................................................................. 2. 8
2.1.5 Capacitances in Series and Parallel............................................................... 2. 11
2.1.6 Impedances in Series and Parallel................................................................. 2. 14

2.1.7 Reactances in Series and Parallel.................................................................. 2. 16

2.1.8 Conductances in Series and Parallel............................................................. 2. 17

2.1.9 Admittances in Series and Parallel................................................................ 2. 19

2.1.10 Susceptances in Series and Parallel.............................................................. 2. 22

2.1.11 Generalised Concept of Reducing Series/Parallel-connected Parameters.... 2. 22
2.2 Voltage and Current Division...................................................................................... 2. 25

2.2.1 Voltage Division in Series-connected Resistances....................................... 2. 25

2.2.2 Voltage Division in Series-connected Impedances....................................... 2. 26

2.2.3 Current Division in Parallel-connected Resistances..................................... 2. 26

2.2.4 Current Division in Parallel-connected Impedances..................................... 2. 27
2.3 Source Transformation................................................................................................ 2. 28

2.4 Star-Delta Conversion.................................................................................................. 2. 29
2.4.1 Resistances in Star and Delta ........................................................................ 2. 29
2.4.2 Impedances in Star and Delta........................................................................ 2. 31

2.5 Solved Problems in Network Reduction.................................................................... 2. 32

2.6 Network Theorems....................................................................................................... 2. 49
2.6.1 Thevenin’s and Norton’s Theorems................................................................ 2. 49
2.6.2 Superposition Theorem.................................................................................. 2. 76

2.6.3 Maximum Power Transfer Theorem.............................................................. 2. 99

2.6.4 Reciprocity Theorem....................................................................................... 2. 126

2.6.5 Reciprocity Theorem Applied to Mesh Basis Circuit.................................... 2. 126
2.6.6 Reciprocity Theorem Applied to Node Basis Circuit.................................... 2. 127

2.6.7 Millman’s Theorem.......................................................................................... 2. 137
2.7 Summary of Important Concepts................................................................................ 2. 141
2.8 Short-answer Questions.............................................................................................. 2. 144

2.9 Exercises....................................................................................................................... 2. 159
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CHAPTER 3 - TRANSIENT RESPONSE ANALYSIS...................................... 3.1
3.1 L and C Elements and Transient Response............................................................... 3. 1
3.1.1 Natural and Forced Response........................................................................ 3. 1

3.1.2 First and Second Order Circuits.................................................................... 3. 2

3.2 Transient Analysis Using Laplace Transform........................................................... 3. 3
3.2.1 Some Standard Voltage Functions................................................................ 3. 3

3.2.2 s-Domain Representation of R, L, C Parameters .......................................... 3. 5
3.2.3 Solving Initial and Final Conditions Using Laplace Transform.................. 3. 9
3.3 Transient Response of RL Circuit.............................................................................. 3. 10
3.3.1 Natural or Source-Free Response of RL Circuit............................................ 3. 10
3.3.2 Step Response of RL Circuit
(Response of RL Circuit Excited by DC Supply)........................................... 3. 11
3.3.3 RL Transient With Initial Current I .............................................................. 3. 16
0
3.4 Transient Response of RC Circuit............................................................................. 3. 19

3.4.1 Natural or Source-Free Response of RC Circuit ........................................... 3. 19
3.4.2 Step Response of RC Circuit
(Response of RC Circuit Excited by DC Supply).......................................... 3. 21

3.4.3 RC Transient With Initial Voltage V ............................................................ 3. 25
0
3.5 Transient Response of RLC Circuit........................................................................... 3. 29
3.5.1 Natural or Source-Free Response of RLC Circuit......................................... 3. 29
3.5.2 Step Response of RLC Circuit
(Response of RLC Circuit Excited by DC Supply)........................................ 3. 29
3.5.3 s-Domain Current and Voltage Equation of RLC Circuit............................. 3. 36

3.5.4 Initial Conditions in RLC Circuit................................................................... 3. 37

3.5.5 Final Conditions in RLC Circuit..................................................................... 3. 39
3.6 Transient Response of Circuits Excited by Sinusoidal Source................................ 3. 41
3.6.1 RL Circuit Excited by Sinusoidal Source ...................................................... 3. 41
3.6.2 RC Circuit Excited by Sinusoidal Source...................................................... 3. 43

3.6.3 RLC Circuit Excited by Sinusoidal Source.................................................... 3. 45
3.7 Solved Problems in RL Transient............................................................................... 3. 47

3.8 Solved Problems in RC Transient............................................................................... 3. 63
3.9 Solved Problems in RLC Transient............................................................................ 3. 84

3.10 Summary of Important Concepts............................................................................... 3. 94

3.11 Short-answer Questions.............................................................................................. 3. 97
3.12 Exercises...................................................................................................................... 3. 100