Circuit Analysis I with MATLAB® Applications Steven T. Karris G=[35/50 −j*3/50; −1/5 1/10+j*1/10]; I=[1 0]'; V=G\I; Ix=5*V(2,1)/4; % Multiply Vc by 5 and divide by 4 to get current Ix magIx=abs(Ix); theta=angle(Ix)*180/pi; % Convert current Ix to polar form fprintf(' \n'); disp(' Ix = ' ); disp(Ix);... fprintf('magIx = %4.2f A \t', magIx); fprintf('theta = %4.2f deg \t', theta);... fprintf(' \n'); fprintf(' \n'); Ix = 2.1176-1.7546i magIx = 2.75 A theta = -39.64 deg Orchard Publications, Fremont, California www.orchardpublications.com Students and working professionals will find Circuit Analysis I with MATLAB® Applications to be a con- Circuit Analysis I cise and easy-to-learn text. It provides complete, clear, and detailed explanations of the principal elec- with MATLAB® Applications trical engineering concepts, and these are illustrated with numerous practical examples. This text includes the following chapters and appendices: • Basic Concepts and Definitions • Analysis of Simple Circuits • Nodal and Mesh Equations - Circuit Theorems • Introduction to Operational Amplifiers • Inductance and Capacitance • Sinusoidal Circuit Analysis • Phasor Circuit Analysis • Average and RMS Values, Complex Power, and Instruments • Natural Response • Forced and Total Response in RL and RC Circuits • Introduction to MATLAB • Review of Complex Numbers • Matrices and Determinants Each chapter contains numerous practical applications supplemented with detailed instructions for using MATLAB to obtain quick and accurate answers. Steven T. Karris is the president and founder of Orchard Publications. He earned a bachelors degree in electrical engineering at Christian Brothers University, Memphis, Tennessee, a mas- ters degree in electrical engineering at Florida Institute of Technology, Melbourne, Florida, and has done post-master work at the latter. He is a registered professional engineer in California and Florida. He has over 30 years of professional engineering experience in industry. In addi- tion, he has over 25 years of teaching experience that he acquired at several educational insti- tutions as an adjunct professor. He is currently with UC Berkeley Extension. Orchard Publications Visit us on the Internet www.orchardpublications.com or email us: [email protected] ISBN 0-9744239-3-9 $39.95 Circuit Analysis I with MATLAB® Applications Steven T. Karris Orchard Publications www.orchardpublications.com Circuit Analysis I with MATLAB® Applications Copyright © 2004 Orchard Publications. All rights reserved. Printed in Canada. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. Direct all inquiries to Orchard Publications, 39510 Paseo Padre Parkway, Fremont, California 94538, U.S.A. URL: http://www.orchardpublications.com Product and corporate names are trademarks or registered trademarks of the MathWorks®, Inc., and Microsoft® Corporation. They are used only for identification and explanation, without intent to infringe. Library of Congress Cataloging-in-Publication Data Library of Congress Control Number 2004093171 ISBN 0-9744239-3-9 Disclaimer The author has made every effort to make this text as complete and accurate as possible, but no warranty is implied. The author and publisher shall have neither liability nor responsibility to any person or entity with respect to any loss or damages arising from the information contained in this text. This book was created electronically using Adobe Framemaker®. Preface This text is an introduction to the basic principles of electrical engineering. It is the outgrowth of lecture notes prepared by this author while teaching for the electrical engineering and computer engineering departments at San José State University, DeAnza college, and the College of San Mateo, all in California. Many of the examples and problems are based on the author’s industrial experience. It can be used as a primary text or supplementary text. It is also ideal for self-study. This book is intended for students of college grade, both community colleges and universities. It presumes knowledge of first year differential and integral calculus and physics. While some knowledge of differential equations would be helpful, it is not absolutely necessary. Chapters 9 and 10 include step-by-step procedures for the solutions of simple differential equations used in the derivation of the natural and forces responses. Appendices B and C provide a thorough review of complex numbers and matrices respectively. There are several textbooks on the subject that have been used for years. The material of this book is not new, and this author claims no originality of its content. This book was written to fit the needs of the average student. Moreover, it is not restricted to computer oriented circuit analysis. While it is true that there is a great demand for electrical and computer engineers, especially in the internet field, the demand also exists for power engineers to work in electric utility companies, and facility engineers to work in the industrial areas. Circuit analysis is comprised of numerous topics. It would be impractical to include all related topics in a single text. This book, Circuit Analysis I with MATLAB® Applications, contains the standard subject matter of electrical engineering. Accordingly, it is intended as a first course in circuits and the material can be covered in one semester or two quarters. A sequel, Circuit Analysis II with MATLAB® Applications, is intended for use in a subsequent semester or two subsequent quarters. It is not necessary that the reader has previous knowledge of MATLAB®. The material of this text can be learned without MATLAB. However, this author highly recommends that the reader studies this material in conjunction with the inexpensive MATLAB Student Version package that is available at most college and university bookstores. Appendix A of this text provides a practical introduction to MATLAB. As shown on the front cover, a system of equations with complex coefficients can be solved with MATLAB very accurately and rapidly. MATLAB will be invaluable in later studies such as the design of analog and digital filters. In addition to several problems provided at the end of each chapter, this text includes multiple-choice questions to test and enhance the reader’s knowledge of this subject. Moreover, answers to these questions and detailed solutions of all problems are provided at the end of each chapter. The rationale Circuit Analysis I with MATLAB Applications Orchard Publications Preface is to encourage the reader to solve all problems and check his effort for correct solutions and appropriate steps in obtaining the correct solution. And since this text was written to serve as a self-study or supplementary textbook, it provides the reader with a resource to test his knowledge. The author has accumulated many additional problems for homework assignment and these are available to those instructors who adopt this text either as primary or supplementary text, and prefer to assign problems without the solutions. He also has accumulated many sample exams. Like any other new book, this text may contain some grammar and typographical errors. Accordingly, all feedback for errors, advice and comments will be most welcomed and greatly appreciated. Orchard Publications Fremont, California Circuit Analysis I with MATLAB Applications Orchard Publications Contents Chapter 1 Basic Concepts and Definitions The Coulomb...................................................................................................................................................1-1 Electric Current and Ampere........................................................................................................................1-1 Two Terminal Devices...................................................................................................................................1-4 Voltage (Potential Difference) ......................................................................................................................1-5 Power and Energy...........................................................................................................................................1-8 Active and Passive Devices ........................................................................................................................ 1-12 Circuits and Networks................................................................................................................................. 1-12 Active and Passive Networks..................................................................................................................... 1-12 Necessary Conditions for Current Flow .................................................................................................. 1-12 International System of Units .................................................................................................................... 1-13 Sources of Energy........................................................................................................................................ 1-17 Summary........................................................................................................................................................ 1-18 Exercises.......................................................................................................................................................