ElEctrical circuit analysis

Delhi-1100922015

K. MAHADEVANProfessor

Electrical and Electronics EngineeringPSNA College of Engineering and Technology

Dindigul, Tamil Nadu

C. CHITRAProfessor

Electronics and Communication EngineeringPSNA College of Engineering and Technology

Dindigul, Tamil Nadu

ELECTRICAL CIRCUIT ANALYSISK. Mahadevan and C. Chitra

© 2015 by PHI Learning Private Limited, Delhi. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher.

ISBN-978-81-203-5047-2

The export rights of this book are vested solely with the publisher.

Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, Patparganj Industrial Estate, Delhi-110092 and Printed by Mohan Makhijani at Rekha Printers Private Limited, New Delhi-110020.

Dedicated to Our Parents

Preface xiAcknowledgements xiii

1. Introduction to DC Circuits 1–501.1 International System of Units 11.2 Network Terminology 21.3 Lumped Circuit Versus Distributed Circuit 41.4 Quantity of Electricity 41.5 Charge 41.6 Current 51.7 Electric Potential 51.8 Circuit Elements 5

1.8.1 Resistance 51.8.2 Inductance 61.8.3 Capacitance 6

1.9 Ohm’s Law 71.10 SpecificResistance (Resistivity) 81.11 Conductance andConductivity 91.12 Open-Circuit and Short-Circuit 101.13 Variation of Resistance with Temperature 101.14 Electrical Power 121.15 Electrical Energy 121.16 Energy Sources 12

1.16.1 Independent Sources 131.16.2 Dependent Sources 14

1.17 Resistances in Series 141.18 Resistances in Parallel 151.19 Star–Delta Transformation 25

1.19.1 Delta–Star Transformation 251.19.2 Star–Delta Transformation 27

v

Contents

vi Contents

1.20 ConversionofSources 34Short Questions with Answers 38Unsolved Problems 44

2. Kirchhoff’s Laws 51–922.1 Introduction 512.2 Kirchhoff’sCurrentLaw (KCL) 512.3 Kirchhoff’sVoltageLaw (KVL) 522.4 CurrentDivision inParallelResistors 592.5 VoltageDivision inSeriesResistors 612.6 Mesh Analysis 632.7 Nodal Analysis 76Short Questions with Answers 87Unsolved Problems 88

3. Fundamentals of AC Circuits 93–1163.1 Introduction 933.2 Generation of Alternating E.M.F. 933.3 Terminology 963.4 Average andRootMeanSquareValues 97

3.4.1 AverageValue 973.4.2 AverageValueofSinusoidalCurrent 983.4.3 RootMeanSquare (RMS)ValueorEffectiveValue 983.4.4 RMS Value of Sinusoidal Current 99

3.5 Form Factor and Peak Factor 993.5.1 Form Factor 993.5.2 Peak Factor 100

3.6 In-Phase, Out-of-Phase and Phase Difference 1063.7 Phasor Representation 1073.8 Phasor Algebra and Operator j 108Short Questions with Answers 112Unsolved Problems 114

4. Single-Phase AC Circuits 117–1444.1 Analysis of AC Circuits 117

4.1.1 AC Circuit Containing Resistance Only 1174.1.2 AC Circuit Containing Inductance Only 1194.1.3 AC Circuit Containing Capacitance Only 1224.1.4 RL Series Circuit 1254.1.5 RC Series Circuit 1264.1.6 RLC Series Circuit 127

4.2 Impedance 1284.2.1 Impedances in Series 1284.2.2 Impedances in Parallel 129

4.3 Power and Power Factor in AC Circuits 1304.4 Parallel Circuits 131

Contents vii

4.5 Admittance 1314.5.1 Admittances in Series 1324.5.2 Admittances in Parallel 133

Short Questions with Answers 140Unsolved Problems 143

5. AC Network Analysis 145–1565.1 Introduction 1455.2 Mesh Analysis for AC Circuits 1455.3 Nodal Analysis for AC Circuits 149Unsolved Problems 154

6. Network Theorems 157–2416.1 Introduction 1576.2 Superposition Theorem 1576.3 Thevenin’sTheorem 1676.4 Norton’s Theorem 1806.5 Reciprocity Theorem 1956.6 Maximum Power Transfer Theorem 2036.7 Millman’s Theorem 2156.8 Substitution Theorem 2196.9 Compensation Theorem 2246.10 Tellegen’s Theorem 228Short Questions with Answers 232Unsolved Problems 234

7. Three-Phase Circuits 242–2747.1 Introduction 2427.2 Generation of Three-phase E.M.F. 2427.3 AdvantagesofThree-phaseSystem 2437.4 Interconnection of Three Phases 244

7.4.1 Balanced Y-Connection 2447.4.2 Balanced D Connection 246

7.5 Unbalanced Loads 2527.5.1 Unbalanced D-Connected Load 2527.5.2 UnbalancedY-ConnectedLoad (Three-phase,Three-wireSystem) 2547.5.3 Solution of Three-phase, Three-wire, Y-Connected Load by Millman’s Method 2587.5.4 UnbalancedY-ConnectedLoad (Three-phase,Four-wireSystem) 261

7.6 Measurement of Power and Power Factor 2637.6.1 Three-wattmeter Method 2637.6.2 Two-wattmeter Method 2647.6.3 Power Factor Calculation 2667.6.4 Effect of Power Factor on Wattmeter Readings 2677.6.5 ReactivePowerwithTwo-wattmeterMethod 2687.6.6 One-wattmeter Method 2697.6.7 ReactivePowerwithOne-wattmeterMethod 269

Short Questions with Answers 272Unsolved Problems 273

viii Contents

8. Magnetic Circuits 275–3008.1 Introduction 2758.2 Magnetic Circuit 2758.3 Terminology 2768.4 Composite Magnetic Circuit 279

8.4.1 Determination of Ampere-Turns 2808.5 Parallel Magnetic Circuit 2808.6 Leakage Flux and Fringing 2818.7 Magnetisation (B–HCurve) 2868.8 Electromagnetic Induction 2888.9 Faraday’s Laws of Electromagnetic Induction 2898.10 Direction of Induced E.M.F. and Current 291

8.10.1 Lenz’s Law 2918.10.2 Fleming’s Right-Hand Rule 291

8.11 Induced E.M.F. 2928.11.1 Dynamically Induced E.M.F. 2928.11.2 Statically Induced E.M.F. 293

Short Questions with Answers 294Unsolved Problems 297

9. Coupled Circuits 301–3389.1 Introduction 3019.2 Self-inductance 3019.3 Mutual Inductance 3029.4 Coefficient ofCoupling 3039.5 DotConvention 3059.6 Analysis of Coupled Circuits 3069.7 InductiveCoupling inSeries 307

9.7.1 Series Aiding 3079.7.2 Series Opposing 308

9.8 InductiveCoupling inParallel 3099.8.1 Parallel Aiding 3099.8.2 Parallel Opposing 310

9.9 Transformer 3229.10 Ideal Transformer 3249.11 Tuned Circuits 325

9.11.1 Single-tuned Circuits 3269.11.2 Double-tuned Circuits 329

Short Questions with Answers 334Unsolved Problems 336

10. Resonance 339–36710.1 Series Resonance 339

10.1.1 Effects of Series Resonance 34010.1.2 ReactanceCurves 340

Contents ix

10.1.3 Variationof ImpedancewithFrequency 34110.1.4 ResonanceCurve 34110.1.5 Bandwidth of Series RLC Circuit 34210.1.6 Quality Factor of Series RLC Circuit 34510.1.7 VoltageMagnification inSeriesResonance 346

10.2 Parallel Resonance 35010.2.1 SusceptanceCurves 35210.2.2 Variationof Impedance andCurrentwithFrequency 35310.2.3 Bandwidth of Parallel RLC Circuit 35410.2.4 Quality Factor of Parallel RLC Circuit 356

Short Questions with Answers 363Unsolved Problems 366

11. DC Transients 368–47011.1 Introduction 36811.2 Free Response and Forced Response 36811.3 Initial Conditions 369

11.3.1 Initial Conditions for Resistor 36911.3.2 Initial Conditions for Inductor 36911.3.3 Initial Conditions for Capacitor 369

11.4 RL Transients 37011.4.1 Current Rise in RL SeriesCircuit (byClassicalMethod) 37011.4.2 Current Rise in RL SeriesCircuit (byLaplaceTransformationMethod) 37311.4.3 Current Decay in RL SeriesCircuit (byClassicalMethod) 37511.4.4 Current Decay in RL SeriesCircuit (byLaplaceTransformationMethod) 377

11.5 RC Transients 37811.5.1 Charging in RC SeriesCircuit (byClassicalMethod) 37811.5.2 Charging in RC SeriesCircuit (byLaplaceTransformationMethod) 38111.5.3 Discharging in RC SeriesCircuit (byClassicalMethod) 38211.5.4 Discharging in RC SeriesCircuit (byLaplaceTransformationMethod) 384

11.6 RLC Transients 38511.6.1 Response by Classical Method 38511.6.2 Response by Laplace Transformation Method 388

Short Questions with Answers 462Unsolved Problems 463

12. AC Transients 471–52212.1 RL Transients with Sinusoidal Excitation 471

12.1.1 Response by Classical Method 47112.1.2 Response by Laplace Transformation Method 475

12.2 RC Transients with Sinusoidal Excitation 47812.2.1 Response by Classical Method 47812.2.2 Response by Laplace Transformation Method 482

12.3 RLC Transients with Sinusoidal Excitation 48712.3.1 Response by Classical Method 48712.3.2 Response by Laplace Transformation Method 489

Short Questions with Answers 520Unsolved Problems 520

Electrical Circuit Analysis

Publisher : PHI Learning ISBN : 9788120350472 Author : K. Mahadevan

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