Instrumentation Engineering. Network Theory. Comprehensive Theory with Solved Examples and Practice Questions

Transcription

1 Instrumentation Engineering Network Theory Comprehensive Theory with Solved Examples and Practice Questions

2 MADE EASY Publications Corporate Office: 44-A/4, Kalu Sarai (Near Hauz Khas Metro Station), New Delhi Contact: , Visit us at: Network Theory Copyright, by MADE EASY Publications. All rights are reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted in any form or by any means (electronic, mechanical, photo-copying, recording or otherwise), without the prior written permission of the above mentioned publisher of this book. First Edition: 2015 Second Edition: 2016 (Revised and Updated) All rights reserved by MADE EASY PUBLICATIONS. No part of this book may be reproduced or utilized in any form without the written permission from the publisher.

3 Preface This book was motivated by the desire to further the evolution of a concise book on Network Theory. Keeping in focus the importance of this subject in GATE and ESE, we have done a proper study and thereafter developed the content of the book accordingly. This edition has an expanded discussion of all relevant topics in the subject. Initially, we compiled the perceptions of our students on their problems in GATE and ESE while dealing with the questions from this subject. We identified their various problems like- lack of fundamentals of the subject, difficulty in solving simple questions, shortage of a complete study package, etc. These strengthened our determination to present a complete edition of Network Theory textbook. The book addresses all the requirements of the students, i.e. comprehensive coverage of theory, fundamental concepts, objective type problems and conventional problems, articulated in a lucid language. The concise presentation will help the readers grasp the concepts with clarity and apply them with ease to solve problems quickly. The book not only covers the entire syllabus of GATE and ESE, but also addresses the need of many other competitive examinations. Topics like KVL, KCL, Mesh and Nodal Analysis, Circuit Theorems, Capacitor, Inductor, First Order RL, RC Circuits, AC Power Analysis, Magnetically Coupled Circuits, Resonance and Two Port Networks etc. are given full coverage in line with of our research on their importance in competitive examinations. We have put in our sincere efforts to present elaborate solutions for various problems, different problem solving methodology, some useful quick techniques to save time while attempting MCQs without compromising the accuracy of answers. A summary of important points to remember is added at the end of each topic. For the convenience of the readers, points to remember are specifically highlighted in the form of a note- both in theory as well as solved examples. At the end of each chapter, sets of practice question are given with their keys, that will allow the readers to evaluate their understanding of the topics and sharpen their problem solving skills. Our team has made their best efforts to remove all possible errors of any kind. Nonetheless, we would highly appreciate and acknowledge if you find and share with us any printing, calculation and conceptual error. It is impossible to thank all the individuals who helped us, but we would like to sincerely thank all the authors, editors and reviewers for putting in their efforts to publish this book. With Best Wishes B. Singh CMD, MADE EASY

4 Contents Network Theory Chapter 1 Basic and Electric Circuits Introduction Charge Current Voltage Power Energy Circuit Elements Sources... 8 Student Assignments...11 Chapter 2 Basic Laws Introduction Ohm s Law and Resistance Nodes, Paths, Loops and Branches Kirchhoff s Current Law (KCL) Kirchhoff s Voltage Law (KVL) Series Resistances and Voltage Division Parallel Resistances and Current Division Source Transformation Sources in Series or Parallel Wye-Delta Transformations Network Manipulations for Easy Analysis...25 Student Assignments...32 Chapter 3 Basic Nodal and Mesh Analysis Introduction Nodal Analysis Nodal Analysis with Voltage Source Mesh Analysis Mesh Analysis with Current Sources Comparison Between Nodal Analysis and Mesh Analysis...44 Student Assignments...49 Chapter 4 Circuit Theorems Introduction Linearity and Superposition Source Transformation Thevenin s Theorem Norton s Theorem Maximum Power Transfer...59 Student Assignments...69 Chapter 5 Capacitors and Inductors Introduction Voltage, Current and Energy Relationship of a Capacitor Capacitance Combinations Inductors Voltage, Current and Energy Relationship of an Inductor Inductor Combinations...78 Student Assignments...83 Chapter 6 First Order RL and RC Circuits Introduction Definition of the Laplace Transform Circuit Elements in the s-domain Source-Free or Zero-Input Response Step Response of First Order Circuit...99 Student Assignments (iv)

5 Chapter 7 Second Order RLC Circuits Introduction Finding Initial and Final Values The Source-Free Series RLC Circuit Source-Free Parallel RLC Circuit Step By Step Approach of Solving Second Order Circuits Step Response of Series RLC Circuit Step Response of Parallel RLC Circuit Circuit Analysis in the s-domain Student Assignments Chapter 8 Sinusoidal Steady-State Analysis Introduction Sinusoids Phasors Phasor Relationship for Circuit Elements Impedance and Admittance Kirchhoff s Laws in the Frequency Domain Impedance Combinations Circuit Analysis in Phasor Domain Phasor Diagrams Student Assignments Chapter 9 AC Power Analysis Introduction Instantaneous Power Average Power Effective Values of Current and Voltage Average Value of Periodic Waveform Apparent Power and Complex Power Student Assignments Chapter 10 Magnetically Coupled Circuits Introduction Self Inductance Mutual Inductance The Ideal Transformer Student Assignments Chapter 11 Frequency Response & Resonance Introduction Transfer Functions Resonant Circuit Student Assignments Chapter 12 Two Port Network Introduction Z-parameters Y-parameters h-parameters or Hybrid Parameters g-parameters or Inverse Hybrid Parameters Transmission Parameters (ABCD) Inverse Transmission Parameters Inter Relations in Network Parameters Interconnection of Two-port Networks Network Components Barletts Bisection Theorem Open Circuited and Chapter 13 Short Circuited Impedances Student Assignments Network Topology Introduction Network Graph Tree and Co-Tree Incidence Matrix Tie-Set Cut-Set Duality Student Assignments (v)

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26