Fundamentals of Electrical Engineering

THIRD EDITION

Rajendra Prasad Former Professor and Head Department of Electrical Engineering National Institute of Technology Patna

Delhi-110092 2014 FUNDAMENTALS OF ELECTRICAL ENGINEERING, Third Edition Rajendra Prasad

© 2014 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-978-81-203-4895-0

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

Ninth Printing (Third Edition)    January, 2014

Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, Patparganj Industrial Estate, Delhi-110092 and Printed by Rajkamal Electric Press, Plot No. 2, Phase IV, HSIDC, Kundli-131028, Sonepat, Haryana. To My beloved granddaughters Aishwarya, Ananya and Aarna and my beloved grandson Ayaan

Contents

Preface xi Preface to the Second Edition xiii Preface to the First Edition xv

1. Fundamentals of Electrical Energy 1–60 1.1 Introduction 1 1.2 Electrical Current and Voltage 3 1.3 Electrical Power and Energy 6 1.4 Electrical Circuit Elements 7 1.4.1 Resistor 7 1.4.2 Capacitor 11 1.4.3 Inductor 20 1.5 Sources of Electrical Energy 28 1.5.1 Independent Sources 28 1.5.2 Dependent Sources 29 1.6 Kirchhoff’s Laws 30 Review Questions 32 Solved Problems 32 Exercises 56

2. Circuit Analysis: Resistive Network 61–130 2.1 Electrical Circuit and Network 61 2.2 Applications of Kirchhoff’s Laws 62 2.3 Source Equivalence and Conversion 67 2.4 Nodal Analysis 69 2.5 Mesh Analysis 73 2.6 Node and Loop Equations with Controlled Sources 74 2.7 Principle of Superposition 77 2.8 Thevenin’s Theorem and Norton’s Theorem 81 2.9 Network Simplification 84 2.10 Maximum Power Transfer 89 Review Questions 90 Solved Problems 91 Exercises 125 v vi Contents

3. Circuit Analysis: Time Varying Excitation 131–234 3.1 Network Responses 131 3.2 Responses to Exponential Excitations 132 3.3 Responses to Sinusoidal Excitation 138 3.4 R.M.S. Values, Power and Reactive Power 145 3.5 Phasor Method of AC Circuit Analysis 150 3.6 Resonance 155 3.7 Mesh and Nodal Analysis 161 3.8 Thevenin’s and Norton’s Theorems 165 3.9 Maximum Power Condition 168 3.10 Volt-Ampere Method 172 3.11 Fourier Series 176 3.12 Response to Periodic Functions 184 Review Questions 187 Solved Problems 187 Exercises 228 4. Electrostatics 235–312 4.1 Electric Charge and Laws of Electrostatics 235 4.2 Electric Field and Lines of Force 239 4.3 Electrostatic Induction 241 4.4 Electric Field Intensity 241 4.5 A Charge Particle in an Electric Field 248 4.6 Electric Flux and Electric Flux Density 252 4.7 Gauss’s Law and Its Applications 253 4.8 Electrical Potential and Energy 257 4.9 Dielectric Materials and Their Properties 272 4.10 Poisson’s Equation and Laplace’s Equation 277 4.11 Capacitor 280 4.12 Insulation Resistance of a Cable 286 4.13 Energy Stored in a Capacitor 287 Review Questions 289 Solved Problems 290 Exercises 310 5. and Electromechanical Energy Conversion 313–370 5.1 Electromagnetism 313 5.2 Effect of Magnetic Field on Current Carrying Conductor 318 5.3 Magnetic Circuit 323 5.4 Magnetizing Curves 330 5.5 Characteristics of Magnetic Materials 334 5.6 Electromagnetic Induction 337 5.7 Excitation to Magnetic Circuits 340 5.8 Hysteresis and Eddy Current Losses 342 Contents vii

5.9 Energy Stored in Magnetic Circuits 344 5.10 Mutual Inductance and 345 5.11 Electromechanical Energy Conversion 348 Review Questions 350 Solved Problems 351 Exercises 368

6. Measuring Instruments 371–434 6.1 Measurement of Current and Voltage 371 6.2 Moving Iron Ammeter and Voltmeter 374 6.3 Permanent Moving Coil Ammeter and Voltmeter 381 6.4 Dynamometer Type Moving Coil Ammeter and Voltmeter 384 6.5 Thermal Ammeter and Voltmeter 389 6.6 Rectifier Ammeter and Voltmeter 394 6.7 Extension of Range of Ammeter and Voltmeter 395 6.8 Measurement of Power 399 6.9 Measurement of Energy 406 6.10 Measurement of Resistance 411 6.11 Megger 414 6.12 Multimeter 415 Review Questions 415 Solved Problems 416 Exercises 432

7. Transformer 435–480 7.1 Practical Transformer 435 7.2 Phasor Diagram and Equivalent Circuit 438 7.3 Voltage Regulation 442 7.4 Losses and Efficiency of a Transformer 444 7.5 Open-circuit and Short-circuit Tests 447 7.6 Three-phase Transformer 451 7.7 Auto-transformer 456 7.8 458 7.9 Pulse Transformer 461 Review Questions 462 Solved Problems 463 Exercises 478

8. Machines 481–573 8.1 Principle 481 8.2 Action 482 8.3 Winding 483 8.4 EMF Equation 491 8.5 Armature Reaction 493 viii Contents

8.6 Commutation 496 8.7 Direct Current Generators 499 8.8 Direct Current Motors 506 8.9 Characteristics of DC Motors 509 8.10 Starting of DC Motors 513 8.11 Speed Control of DC Motors 517 8.12 Braking of DC Motors 524 8.13 Losses and Efficiency of DC Machines 531 8.14 Dynamics of DC Machines 539 Review Questions 544 Solved Problems 545 Exercises 571 9. Synchronous Machines 574–642 9.1 Introduction 574 9.2 Windings 576 9.3 Flux and M.M.F. Wave 584 9.4 Steady State Equivalent Circuit 591 9.5 Determination of Armature Reaction and Leakage Reactance 595 9.6 Two Reaction Theory 597 9.7 Power Output 601 9.8 Voltage Regulation 606 9.9 Synchronizing and Parallel Operation 608 9.10 612 9.11 Starting of Synchronous Motor 617 9.12 Synchronous Condensers 618 Review Questions 623 Solved Problems 624 Exercises 640 10. Three Phase 643–708 10.1 Principle of Operation 643 10.2 Equivalent Circuit and Phasor Diagram 646 10.3 Types of Three Phase Induction Motors 649 10.4 Output Characteristics 650 10.5 Different Modes of Operation 657 10.6 Performance and Testing 658 10.7 Current Locus () 666 10.8 Starting of Induction Motors 672 10.9 Braking of Induction Motors 680 10.10 Speed Control of Induction Motors 683 10.11 Cogging and Crawling 691 Review Questions 692 Solved Problems 693 Exercises 707 Contents ix

11. Special Purpose Electrical Machines 709–769 11.1 Single Phase Induction Motors 709 11.1.1 Principle of Operation 709 11.1.2 Equivalent Circuit 710 11.1.3 Determination of Parameters 712 11.1.4 Starting 716 11.2 Single Phase AC Series Motors 719 11.3 721 11.4 Rotary Converter 724 11.5 726 11.6 Schrage Motor 728 11.7 729 11.8 Single Phase Synchronous Motors 733 11.8.1 733 11.8.2 Hysteresis Motor 735 11.9 Stepper Motors 736 11.10 Special DC Machines 742 11.11.1 Permanent Magnet dc Motor 742 11.11.2 Brushless dc Motors 744 11.11 and 745 11.12 Tachogenerator 748 11.13 749 11.14 754 Review Questions 758 Solved Problems 758 Exercises 768

12. Analysis of Three Phase Circuits 770–824 12.1 Introduction 770 12.2 Three Phase Voltage, Current and Power 772 12.3 Relationship between Line and Phase Voltages and Currents 774 12.4 Analysis of Balance Three Phase Circuits 777 12.5 Analysis of Unbalance Three Phase Circuits 781 12.6 Measurement of Power in Three Phase Circuits 793 Review Questions 798 Solved Problems 798 Exercises 823

13. Dynamic Response of Network 825–891 13.1 Introduction 825 13.2 Response of RC Circuit 827 13.3 Response of RL Circuit 834 13.4 Response of RLC Circuit 840 Fundamentals Of Electrical Engineering

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