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- 1. BASIC ENGINEERING CI RCU IT ANALYSIS
- 2. SENIOR ACQU ISITIONS EDITOR PROJECT EDITOR SENIOR PRODUCTION EDITOR EXECUTIVE MARKETING MANAGER SEN IOR DESIGNER SENIOR ILLUSTRATION EDITOR SENIOR PHOTO EDITOR MEDIA EDITOR EDITORIAL ASSISTANT INTERIOR DES IGN COVER DESIGN BICENTENNIAL LOGO DES IGN COVER PHOTOS Catherine Fields Shultz Gladys $010 William A. Murray Christopher Rucl Kevin Murphy Anna Melhorn Lisa Gee Lauren Sapira Carolyn Weisman Nomey Field David Levy Richard J. P"cilico TOI) left. courtesy of Lockheed Martin: top eel/fer. courtesy of PPM Energy: tol) rig/II. courtesy of Hyund:.i Motor M:muf:K:turing Alabama LLC: haltom/eft. courtesy of Ihe National Oceanic and Atmospheric }dlllinistralion/Dcparlrncnt of COllllllerce: bottom cell/cr. courtesy of NASAIJPL-C:llicch: /)0110111 righl. courtesy of the National Oceanic and Atmospheric Administt:ltion/DcpartlllCI11of Commerce This book was SCI in 10/12 Times Roman by Prepare. Inc. and printed and bound by R.R. Donnelley. Inc. The cover was printed by R.R. Donnelky. Inc. This book is prinled on acid free paper. 00 Copyrigln © 2008 10hn WiJcy & Sons. Inc. All rights reserved. No pun of Ihis publication may be reproduced. stored in a retrieval system. or transmiued in any fonn or by ~my means, electronic, mechanical. photocopying. recording. scanning or otherwise. except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act. without either the prior written permission of the Publisher. or authorization through payment of the appropriate per-copy fcc to the Copyright Cleamnce Cenler, Inc.. 222 Rosewood Drivc. Danvcrs. MA 01923, Web site: www,Copyright.colll. Requests to the Publisher for permission should be addressed to the Penll i ssion~ Depanmenl. 10hn Wiley & Sons. Inc.. 11 I River Street. Hoboken, NJ 07030-5774. (20 I) 748·60 II, l':Ix (20 I) 748·6008. Web sile; www.wilcy.comlgo!permissions. To order books or for customer service please call 1-800-CALL WILEY (225-5945). Library of Co" gre,'.· C(lW/Ogillg-ill-PlIhIiClllioll Data: Irwin, 1. David Basic engineering circuit analysiS/1. David Irwin. R. Mark Nelms.-9th ed. p. cm. Includes bibliographical references and index. ISBN 978·0-470-12869-5 (cloth) I. Electric circuit analysis. I. Nelms, R. M. II. litle. TK454.17S 2()()7 62l.3 19'2-<1c22 Printell in th~ United State:-- of America 10 9 8 7 6 5 4 3 2007040689
- 3. To my loving family: Edie Geri, Bruno, Andrew and Ryan John, Julie, John David and Abi Laura To my parents: Robert and Elizabeth Nelms
- 4. BRIEF CONTENTS CHAPTER 1 Basic Concepts 1 CHAPTER 2 Resistive Circuits 23 CHAPTER 3 Nodal and Loop Analysis Techniques 95 CHAPTER 4 Operational Amplifiers 149 CHAPTER 5 Additional Analysis Techniques 183 CHAPTER 6 Capacitors 248 CHAPTER 7 First- and Second-Order Transient Circuits 291 CHAPTER 8 AC Steady-State Analysis 375 CHAPTER 9 Steady-State Power Analysis 455 CHAPTER 10 Magnetically Coupled Networks 507 CHAPTER 11 Polyphase Circuits 553 CHAPTER 12 Variable-Frequency Network Performance 587 CHAPTER 13 The Laplace Transform 677 CHAPTER 14 Application of the Laplace Transform to Circuit Analysis 705 CHAPTER 15 Fourier Analysis Techniques 758 CHAPTER 16 Two-Port Networks 809
- 5. Preface CHAPTER 1 BASIC CONCEPTS J.I System of Units 2 1.2 Basic Quantities 2 1.3 Circuit Elements 8 Summary 16 Problems 16 CHAPTER 2 RESISTIVE CIRCUITS 2.1 Ohm's Law 24 2.2 Kirchhoff's Laws 28 2.3 Single·Loop Circuits 37 2.4 Single-Node-Pair Circuits 43 2.5 Series and Parallel Resistor Combinations 48 2.6 Circuits with Series-Parallel Combinations of Resistors 53 2.7 Wye ~ Della Transfonmuions 57 2.8 Circuits with Dependent Sources 60 2.9 Resistor Technologies for Electronic Manufacturing 64 2.10 Application Examples 67 2.11 Design Examples 71 Summary 76 Problems 77 xv 1 23 CONTENTS CHAPTER 3 NODAL AND LOOP ANALYSIS TECHNIQUES 95 3.1 Nodal Analysis 96 3.2 Loop Analysis 11 5 3.3 Application Example 131 3.4 Design Example 133 Summary 133 Problems 134 CHAPTER 4 OPERATIONAL AMPLIFIERS 149 4.1 Introduction 150 4.2 Op-Amp Models 150 4.3 Fundamental Op-Amp Circuits 156 4.4 Comparators 164 4.5 Application Examples 165 4.6 Design Examples 169 Summary 172 Problems 172 CHAPTER 5 ADDITIONAL ANALYSIS TECHNIQUES S.I Introduction 184 5.2 Superposition 186 5.3 Thevenin's and Norton 's Theorems 19 1
- 6. xii CON TENT S 5.4 Maximum Power Transfer 208 5.5 dc SPICE Analysis Using Schemalic Capture 2 12 5.6 Application Example 224 5.7 Design Examples 225 Summary 23 1 Problems 231 CHAPTER 6 CAPACITANCE AND INDUCTANCE 6.1 Capacitors 249 6.2 Inductors 255 6.3 Capacitor and Inductor Combinations 264 6.4 RC Operational Amplifier Circuits 271 6.5 Application Examples 274 6.6 Design Examples 278 Summary 280 Problems 280 CHAPTER 7--------------- FIRST- AND SECOND-ORDER TRANSIENT CIRCUITS 7.1 Introduction 292 7.2 First-Order Circuits 293 7.3 Second-Order Circuits 3 14 7.4 Transient PSPICE Analysis Using Schematic Capture 328 7.5 Application Examples 337 7.6 Design Examples 348 Summary 356 Problems 356 CHAPTER 8 AC STEADY-STATE ANALYSIS 8.1 Sinusoids 376 291 375 8.2 Sinusoidal and Complex Forcing Functions 379 8.3 Phasors 383 8.4 Phasor Relationshi ps for Circui t Elements 385 8.S Impedance and Admittance 389 8.6 Phasor Diagrams 396 8.7 Basic Analysis Using Kirchhoff's Laws 399 8.8 Analysis Techniques 40 I 8.9 AC PSPICE Analysis Using Schematic Capture 4 16 8.10 Application Examples 429 8.11 Design Examples 43 1 Summary 434 Problems 435 CHAPTER 9 STEADY-STATE POWER ANALYSIS 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 Instantaneous Power 456 Average Power 457 Maximum Average Power Transfer 462 Effective or rms Values 466 The Power Factor 469 Complex Power 47 1 Power Factor Correction 476 Single-Phase Three-Wire Circuits 479 Safety Considerations 482 Application Examples 490 Design Example 494 Summary 496 Problems 496 455 CHAPTER 10'-------------- MAGNETICALLY COUPLED NETWORKS 10.1 Mutuallnductanee 508 10.2 Energy Analysis 5 18 10.3 The Ideal Transformer 521 10.4 Safety Considerations 529 10.5 Application Examples 530 10.6 Design Examples 535 Summary 539 Problems 540 CHAPTER 11 POLYPHASE CIRCUITS ILl Three-Phase Circuits 554 11.2 Three-Phase Connections 559 11.3 SoufcelLoad Connections 560 50 7 553
- 7. 11.4 Power Relat ionships 568 11.5 Power Factor Correction 572 11.6 Application Examples 573 11.7 Design Examples 576 Summary 580 Problems 58 1 CHAPTER 12 VARIABLE-FREQUENCY NETWORK PERFORMANCE 12.1 Variable Frequency-Response Analysis 12.2 Sinusoidal Frequency Analysis 596 12.3 Resonant Circuits 608 12.4 Scaling 629 12.5 Filter Networks 63 1 12.6 Application Examples 655 12.7 Design Examples 659 Summary 665 Problems 666 CHAPTER 13 THE LAPLACE TRANSFORM 13.1 Definition 678 588 13.2 Two Important Singularity Functions 679 13.3 Transfortn Pairs 681 13.4 Properties of the Transform 683 13.5 Performing the Inverse Transform 686 13.6 Convolution Integral 692 13.7 Initial-Value and Final-Value Theorems 696 13.8 Application Example 697 Summary 699 Problems 699 CHAPTER 14 APPLICATION OF THE LAPLACE TRANSFORM TO CIRCUIT ANALYSIS 14.1 Laplace Circuit Solutions 706 14.2 Circuit Element Models 707 705 CONTEN TS xiii 14.3 Analysis Tcchniques 709 14.4 Transfer Function 72 1 14.S Pole-Zero PlotlBode Plot Connection 732 14.6 Steady-State Response 735 14.7 Application Example 737 14.8 Design Examples 739 Summary 746 Problems 746 CHAPTER 15 FOURIER ANALYSIS TECHNIQUES 15.1 Fourier Series 759 IS.2 Fourier Transform 781 IS.3 Application Examples 788 IS.4 Design Examples 795 Summary 80 1 Problems 802 7SB CHAPTER 1~()~----------------------- TWO-PORT NETWORKS 80 9 16.1 Admittance Parameters 810 16.2 Impedance Parameters 8 13 16.3 Hybrid Parameters 8 15 16.4 Transmission Parameters 8 17 16.S Parameter Conversions 8 18 16.6 Interconnection of Two~ Port s 8 19 16.7 Application Examples 822 16.8 Design Example 826 Summary 828 Problems 828 APPENDIX COMPLEX NUMBERS INDEX
- 8. Circuit analysis is not only fundamental 10 the enti re breadth of electrical and computer engineering- the concepts studied here extend far beyond those boundaries. For this reason it remains the starting point for many future engineers who wish to work in this field. The text and all the supplementary materials associated with it will aid you in reaching this goal. We strongly recommend while you are here to read the Preface closely and view all the resources available to you as a learner. And one last piece of advice, learning requires practice and repetition. take every opportunity to work one more problem or study one more hour than you planned. In the end. you·1I be thankful you did. The Ninth Edition has been prepared based on a careful examination of feedback received from instructors and students. The revisions and changes made should appeal to a wide vari- ety of instructors. We are aware of significant changes taking place in the way this material is being taught and learned. Consequently, the authors and the publisher have created a for- midable array of traditional and non-traditional learning resources to meet the needs of students and teachers of modern circuit analysis. • A new four-color design is employed to enhance and clarify both text and illustrations. This sharply improves the pedagogical presentation, particularly with complex illustra- tions. For example, see Figure 2.5 on page 29. • New chapter previews provide moti vation for studying the material in the chapter. See page 758 for a chapter preview sample. Learning goals for each chapter have been updated and appear as pan of the new Chapter openers. • End-of-chapter homework problems have been substantially revised and augmented. There are now over 1200 problems in the Ninth Edition! Multiple-choice Fundamentals of Engineering (FE) Exam problems now appear at the end of each chapter. • Practical applications have been added for nearly every topic in the text. Since these are items sllldenlS will naturally encounter on a regular basis, they serve 10 answer ques- tions such as, "Why is this important?" or " How am I going to use what I learn from this course?" For a typical example application, see page 338. • Problem-Solving Videos have been created showing students step-by-step how to solve selected Learning Assessment problems within each chapter and supplemental PREFACE To the Student To the Instructor Highlights of the Ninth Edition
- 9. xvi PREFACE Organization Text Pedagogy end-of-chapter problems. The problem-solving videos (PSVs) are now also available for the Apple iPod. Look for the iPod icon ii for the application of this unique feature. • The end-of-chapter problems noted with the 0 denote problems that are included in OUf WileyPLUS course for this title. In some cases, these problems are presented as algo- rithmic problems which offer differcllI variables for the problem allowing each student to work a similar problem ensuring for individualized work, also some problems have been developed into guided online (GO) problems with tutorials for students, as well as multi- part problems allowing the student (0 show their work at various steps of the problem. • The ~ icon next to end-of-chapter problems denotes those that are more challenging problems and engage the student to apply multiple concepts to solve the problem. • Problem-Solving Strategies have been retained in the Ninth Edition. They are utili zed as a guide for the solutions contained in the PSVs. • A new chapter on diodes has been created for the Ninth Edition. This chapter was developed in response to requests for a supplemental chapter on this topic. Whi le not included as part of the printed text, it is available through WileyPLUS. This text is suitable for a one·semester, a two·semester, or a three·quarter course sequence. The first seven chapters are concerned with the anal ysis of dc circuits. An introduction to operational amplifiers is presented in Chapter 4. This chapter may be omiued without any loss of continuity; a few examples and homework problems in later chapters must be skipped. Chapters 8-12 are focused on the analysis of ac circuits beginning with the analysis of single- frequency circuits (single·phase and three·phase) and ending with variable·frequency circuit operation. Calculation of power in single·phase and three-phase ae circuits is also presented. The important topics of the Laplace transform, Fourier transform, and two·port networks are covered in Chapters 13- 16. The organization of the text provides instructors maximum flexibility in designing their courses. One instructor may choose to cover the first seven chapters in a single semester, while another may omit Chapter 4 and cover Chapters 1-3 and 5-8. Other instruclOrs have chosen to cover Chapters 1-3, 5-{;, and sections 7. 1and 7.2 and then cover Chapters 8 and 9. The remai ni ng chapters can be covered in a second semester course. The pedagogy of this text is rich and varied. It includes print and media and much thought has been put into integrating its use. To gain the most from this pedagogy, please review the following elements commonly available in most chapters of this book. Learning Goals are provided at the outset of each chapter. This tabular list tells the reader what is important and what will be gained from studying the material in the chapter. Examples are the mainstay of any circuit analysis text and numerous examples have always been a trademark of this textbook. These examples provide a more graduated level of pres· entation with simple, medium, and challengi ng examples, Besides regular examples, numer- ous Design Examples and Application Examples are found throughout the texl. See for example, page 348. Hints can often be fo und in the page margins. They faci litate understanding and serve as reminders of key issues. See for example, page 6. Learning Assessments are a crilicalleaming tool in this text. These exercises test the cumu- lative concepts to that point in a given section or sections. Both a problem and the answer are provided. The student who masters these is ready to move forward. See for example, page 7.
- 10. Problem-Solving Strategies are step-by-step problem-solving techniques that many stu- dents find particularly useful. They answer the frequently asked question, "where do I begin?" Nearly every chapter has one or more of these strategies. which are a kind of sum- mation on problem-solving for concepts presented. See for example. page 115. The Problems have been greatly revised for the Ninth Edition, This edition has hundreds of new problems of varying depth and level. Any instructor will find numerous problems appro- priate for any level class. There are over 1200 problems in the Ninth Edition! Included with the Problems are FE Exam Problems for each chapter. If you plan on taking the FE Exam, these problems closely match problems you will typically fi nd on the FE Exam. Circuit Simulation and Analysis Software are a fundamental part of engineering circuit design today. Simulation software such as PSpice®, Multisim®, and MATLAB® allow engi- neers to design and simulate circuits quickly and efficiently. The use of PSPICE and MATLAB has been integrated throughout the text and the presentation has been lauded as exceptional by past users. These examples are color coded for easy location. After much disclission and consideration, we have continued use of PSPICE 9.1 with the Ninth Edition. Although other versions are available, we believe the schematic interface with version 9. 1 is simple enough for students to quickly begin solving circuits using a simulation (00 1. A self-extracting archive for PSPICE 9. 1 may be downloaded from WileyPLUS or http://www,eng.auburn.edu/ece/download/9 Ipspstu.exe. New to this edition is NI Multisim with simulated circuit exercises from the text. NI Multisim allows you to design and simulate circuits easily with its intuitive schematic capture and interactive simulation environment. The Muhisim software is uniquely available to you for download with this edition. Simulated circuit examples and exercises from different chapters are also available on the book's companion web site. While PSpice is referenced with screen shots in the textbook, either software program may be employed to simulate the circuit simu- lation exercises. Use the tool you are comfortable with. If you choose Multisim, we recommend viewing the following Multisim resources. Visit www.ni.com/info and enter IRWIN • Multisim Circuit Files - 50 Multisim circuit files provide an interactive solution for improving student learning and comprehension • SPICE Thtorials - information on SPICE simulation, OrCAD pSPICE simulation, SPICE modeling, and other concepts in circuit simulation • Multisim Educator Edition Eyaluation Download - 30-day evaluations of NI Multisim, NI Ultiboard, and the NI Multisim MCU Module A rich collection of interactive Multisim circuit files may also be downloaded from the textbook companion page. Try them on your own. This circuit set offers a distinctive and helpful way for explori ng examples and exercises from the text. PREFACE xvii The supplements list is extensive and provides instructors and students with a wealth of Supplements traditional and modern resources to match different learning needs. THE INSTRUCTOR'S OR STUDENT'S COMPANION SITES AT WILEY (WILEYPLUS) The Student Study Guide contains detailed examples that track the chapter presentation for aiding and checking the student's understanding of the problem-solving process. Many of these involve use of software programs like Excel, MATLAB, PSpice, and Multisim. The Problem-Solving Companion is freely available for download as a PDF file from the WileyPLUS site. This companion contains over 70 additional problems with detailed solu- tions, and a walk through of the entire problem-solving process.
- 11. xviii PREFACE Acknowledg- ments Problem-SolvingVideos are conlinued in Ihe Nimh Edilion. A novelty with Ihis edilion is Iheir availability for use on the Apple iPod. Throughout the text i icons indicate when a video should be viewed. The videos provide step-by-step solutions to learning extensions and supplemental end-of-chapter problems. Videos for learning assessments will follow directly after a chapter feat ure called Problem-Solving Strategy. Icons with end-oF-chapter problems indicate that a video solution is avai lable for a similar problem-not the actual end-or-chapter problem. Students who use these videos have found them to be very helpful. The Solutions Manual for the Nimh Edilion has been complelely redone. checked, and double-checked for accuracy. Allhaugh it is handwritten to avoid typesetting errors, it is the 111051 accurate solutions manual ever created for this textbook. Qualified instructors who adopt the lext for classroom use can download it off' Wiley's Instructor's Companion Site. PowerPoint Lecture Slides are an especially valuable supplementary aid for so me instruc- tors. While 1110st publishers make only figures available, these slides are true lecture tools that summarize the key learning points fo r each chapter and are easily editable in PowerPoinl. The slides are available for download from Wiley's Instruclor's Companion Sile for qualified adoplers. Over the two decades (25 years) that this text has been in existence, we estimate more than one thousand instructors have used our book in teaching circuit analysis to hundreds of thou- sands of students. As authors there is no greater reward than having your work used by so many. We are grateful for the confidence shown in our text and for the numerous evaluations and suggestions from professors and their students over the years. This feedback has helped us continuollsly improve the presentation. For this Ni nth Edition, we especially thank Ji m Rowland from the University of Kansas for his guidance on the pedagogical use of color throughout the text and Aleck Leedy with Tuskegee University for assistance in the prepara- tion of the FE Exam problems and the solutions manual. We were fortunate 10 have an outstanding group of reviewers for this edition. They are: Charles F. Bunli ng, Oklahoma State University Manha Sloan, Michigan Technological University Thomas M. Sullivan. Carnegie Mellon University Dr. Prasad Enjeli, Texas A&M UniversilY Muhammad A. Khaliq, Minnesota State University Hongbi n Li, Slevens Instilute of Technology The preparalion of Ihis book and the malerials Ihal supporl il have been handled wilh both en thusiasm and great care. The combined wisdom and leadershi p of Catherine Shultz, our Senior Editor. has resulted in a tremendous team effort lhat has addressed every aspect of the presentation. This team included the following individuals: Executive Marketing Manager, Christopher Ruel Senior Production Editor, William Murray Senior Designer, Kevi n Murphy Senior 1I1ustralion Editor, Anna Melhorn Projeci Editor, Gladys SOlO Media Editor, Lauren Sapira Editorial Assistant. Carolyn Weisman Each member of this team played a vital role in preparing the package that is the Ninth Edition of Basic Engineerillg Circuit Analysis. We are most appreciative of their many contributions.
- 12. As in the past, we arc most pleased to acknowledge the support that has been provided by numerous individuals to earlier editions of this book. Our Auburn colleagues who have helped are: Thomas A. Baginski Travis Blalock Henry Cobb Bill Dillard Zhi Ding Kevin Driscoll E. R. Graf L. L. Grigsby Charles A. Gross David C. Hill M. A. Honnell R. C. Jaeger Keith Jones Betty Kelley Ray Kirby Matthew Langford Aleck Leedy George Lindsey Jo Ann Loden James L. Lowry David Mack Paulo R. Marino M. S. Morse Sung-Won Park John Purr Monty Rickles C. L Rogers Tom Shumpert Les Simonton James Trivltayakhull1 Susan Williamson Jacinda Woodward Many of our friends throughout the United States, some of whom are now retired, have also made numerous suggestions for improving the book: David Anderson, University of Iowa Jorge Aravena, Louisiana State University Les Axelrod, lIIinois Institute of Technology Richard Baker, UCLA John Choma. University of Southern C;:tlifornia David Conner, University of Alabama at Birmingham James L. Dodd, Mississippi State University Kevin Donahue, University of Kentucky John Durkin, University of Akron Earl D. Eyman. University of Iowa Arvin Grabel, Northeastern University Paul Gray. University of Wisconsin-Platteville Ashok Goel, Michigan Technological University Walter Green, University of Tennessee Paul Greiling, UCLA Mohammad Habli, Uni versity of New Orleans John Hadjilogiou, Florida Institute of Technology Yasser Hegazy, University of Waterloo Keith Holbert, Arizona State University Aileen Honka, The MOSIS Service- USC Inf. Sciences Institute Ralph Kinney, LSU Marty Kaliski, Cal Poly, San Luis Obispo Robert Krueger, University of Wisconsin K. S. P. Kumar, University of Minnesota Jung Young Lee, UC Berkeley student Aleck Leedy, Tuskegee University James Luster, Snow College Erik Luther, National Instruments Ian McCausland, University of Toronto Arthur C. Moeller, Marquette University PREFA C E xix
- 13. xx PRE FA CE Darryl Morrell. Arizona Slate Universily M. Paul Murray, Mississippi State University Burks Oakley II, University of Illinois al Champaign-Urbana John O'Malley, University of Florida William R. Parkhurst, Wichila Siale Universily Peylon Peebles, Universily of Florida Clifford Pollock, Cornell UniversilY George Prans. Manhanan College Mark Rabalais. Louisiana State University Tom Robbins, National Instruments Armando Rodriguez. Arizona State University James Rowland, University of Kansas Robert N. Sackelt, Normandale Community College Richard Sanford, Clarkson University Peddapullaiah Sannuti, Rutgers University Ronald Schulz. Cleveland Slale University M. E. Shafeei, Penn Stale University at Harrisburg SCOIt F. Smilh, Boise Siale University Karen M. St. Germaine, University of Nebraska Janusz Strazyk, Ohio University Gene Sluffle, Idaho Siale UniversilY Saad Tabel, Florida Stale UniversilY Val Tareski, North Dakola Siale University Thomas Thomas, University of South Alabama Leonard J. Tung, Florida A&M UniversityfFlorida Siale Universily Darrell Vines. Texas Tech University Carl Wells, Washington State University Selh Wolpert, University of Maine Finally. Dave Irwin wishes to express his deep appreciation to his wife, Edie, who has been mosl supportive of our efforts in this book. Mark Nelms would like to Ihank his parents, Robert and Elizabeth, for their support and encouragement. J. David Irwin and R. Mark Nelms
- 14. CHAPTER BASIC CONCEPTS Review the 51 system of units and standard prefixes • Know the definitions of basic electrical quantities: voltage, current, and power • Know the symbols for and definitions of independent and dependent sources • Be able to calculate the power absorbed by a circuit element using the passive sign convention Courtesy NA5A/JPL-Caltech r-~ LEeTRle CIRCUITS ARE OUT OF THIS WORLD! In January 2007. the Mars Rovers- Opportunity and Spirit-began their fourth Cameras, antennae. and a computer receive energy from the electrical system. In order to analyze and design electrical systems for the rovers or futu re exploratory robots. we must year of exploring Mars. Solar panels on the roverscollect have a firm understanding of basic electrical concepts such as energy to power the electrical systems. Batteries are utilized to voltage. current. and power. The basic introduction provided in store energy so that the rovers can operate at night. The rovers this chapter wi( lay the foundation for our study of engineering are propelled and steered by electric motors on the six wheels. circuit analYSis. <<< 1
- 15. 2 CHAPTE R 1 BASI C CONCEPTS 1.1 System of Units Figure 1,1 •••~ Standard 51 prefixes, 1.2 Basic Quantities I, = 2 A @ (al 12 = - 3 A ~(bl . ..:..Figure 1,2 l Conventional current flow: (a) positive current flow; (b) negative current flow. The system of units we employ is the international system of units, the Syslcme international des Unites, which is normally referred to as the SI standard system. This system, which is composed of the basic units meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), and candela (cd), is defined in all modern physics texts and therefore will not be defined here, However, we will discuss the units in some detail as we encounter them in our subsequent analyses. The standard prefixes that are employed in SI are shown in Fig. 1.1. Note the decimal rela- tionshi p between these prefi xes. These standard prefi xes are employed throughout O llf slUdy of electric circuits. Circuillcchnoiogy has changed drastically over the years. For example, in the early 1960s the space on a circuit board occupied by the base of a single vacuum tube was about the size of a quaner (25-cel11 coin). Today that same space could be occupied by an Intel Penlium integrated circuit chip containing 50 million transistors. These chi ps are the engine for a host of electron ic equipment. 10- 12 10-9 10-6 10- 3 10' 10' 10' 1012 I I I I I I I I pico (pI nano (n) micro (II.) milli (m) kilo (kl mega (MI giga (GI lera (TI Before we begin our analysis of electric circuits, we must define terms that we will employ. However, in th is chapter and throughout the book our definitions and explanations will be as simple as possible to foster an understanding of the use of the material. No attempt will be made to give complete definitions of many of the quantities because such defi nitions are not only unnecessary at this level but are often confusing. Although 1110st of us have an intuitive concept of what is meant by <l circuit. we will simply refer to an elee1ric circlli1 as an inter- connection of electrical components, each of which we will describe with a mathematical model. The most elementary quantity in an analysis of electric circuits is the electric charge. Our interest in electric charge is centered around its motion, since charge in motion results in an energy transfer. Of p<1I1icular interest to us are those situations in which the motion is confined to a definite closed path. An e lectric c ircuit is essentiall y a pipeline that facilitates the transfer of charge from one point to another. The lime rate of change of charge constitutes an electric current. Mathematically. the relationship is expressed as i(l) dq(l) or '1(1) = ,Li(X) tit 1.1 dl where i und q represent current and charge, respectively (lowercase letters represent time dependency, and capital leiters are reserved for constant quaJ1lities). The basic unit of current is the ampere (A), and I ampere is I coulomb per second. Although we know that current flow in metallic conductors results from electron motion. the conventional cun·ent flow, which is universally adopted, represents the movement of positive charges. It is important that the reader think of cllrrent tlow as the movement of positive charge regardless of the physical phenomcna that take place. The symbolism that will be lIsed to represent currcnt flow is shown in Fig. J.2. I[ = 2 A in Fig. 1.2a indicates that at any point in the wire shown, 2 C of charge pass from left to right each second. I']. = - 3 A in Fig. 1.2b indicates that at any point in the wire shown, 3 C of charge pass from right to left each second. Therefore, it is important to specify not only the magnitude of the variable representing the current, but also its direction.
- 16. S ECTION 1.2 i(r) i(r) (a) (b) The two types of current that we encounter often in our daily lives. alternating current (ac) and direct current (dc), are shown as a function of time in Fig. 1.3. A/remming currell! is the C0l111110 11 current found in every household and is used to run the refrigerator. stove, washing machine, and so on. Batteries, which are lIsed in automobiles or flashlights, are one sourcc ofdirecr currell!. In addilion 10 these two types ofcurrents, which have a wide variety of uscs. we can generate many other types of currents. We will examine some of these other types later in the book. In the meantime, it is interesting to note that the magnitude of currents in elements familiar to us ranges from soup to nuts. as shown in Fig. IA. We have indicaled lhat charges in motion yield an cncrgy transfcr. Now wc detinc the volrage (also called the elecrromotiveforce or porenthll) between IWO points in a circuit as the difference in energy level of a unit charge located at each of the two points. Voltage is very sim- ilar to a gravitational force. Think about a bowling ball being dropped from a ladder into a tank of water. As soon as the ball is released, the force of gravity pulls it 100vard the boltom of the tank. The potential energy of the bowling ball decreases as it approaches the bottom. The grav- itational force is pushing the bowling ball through the water. Think of the bowling ball as a charge and the voltage as the force pushing the charge through a circuit. Charges in mOl ion represent a current, so the motion of the bowling ball could be thought of as a current. The water in the tank will resist the motion of the bowling ball. The motion of charges in an elec- tric circuit will be impeded or resisted as well. We will introduce the concept of resistance in Chapter 2 to describe this effec. Work or energy, w(r ) or W, is measured in joules (l ); I joule is I newton meter (N · m). Hence, voltage [v(r) or VIis measured in volts (V) and I volt is I joule per coulomb; that is, I volt ;:;:: I joule per coulomb = I newton meter per coulomb. If a unit positive charge is moved between two points, the energy req uired to move it is the difference in energy level between the two points and is the defined voltage. It is extremely imponant that the variables used to represent voltage between two points be detined in such a way that the solution will let us interpret which point is at the higher potential wilh respect to the other. 10' Lightning bolt 10' Large industrial motor current 10' ~ 100 Typical household appliance current 00 ~ 10-'~ Causes ventricular fibrillation in humans 0. E Human threshold of sensation ~ 10-4 .5 C 10-6 ~ 5 10-80 Integrated circuit (IC) memory cell current 10- 10 10- 12 Synaptic current (brain cell) 10- 14 BAS I C QUANT ITI ES .~.- Figure 1.3 Two common types of current: (a) alternating current (ae); (b) direct current (de). ~... Figure 1.4 Typica l current magnitudes. 3
- 17. 4 CHAPTER 1 BASIC CONCEPTS Figure 1.5 •••~ Voltage representations. Figure 1.6 ...~ Typical voltage magnitudes. A + o-----jC B (a) r e1 u A + V2 ~ - 5 V B (b) C A C r V2 ~ 5V r e2 e3 u u + B (e) In Fig. l.5a the variable that represents the voltage between points A and 8 has been defined as VI. and it is assumed that point A is at a higher potential than point e,as indicated by the + and - signs associated with the variable and detined in the tlgurc. The + and - signs define a reference direction for VI' If ~ = 2 Y, then the difference in potential of points A and B is 2 V and point A is at the higher potential. If a unit positive charge is moved from point A through the circuit to point B, it will give up energy to the circuit and have 2 J less energy when it reaches point B. If a unit positive charge is moved from point B to point A. extra energy must be added to the charge by the circuit, and hence the charge will end up with 2 J more energy at point A than it started with at point B. For Ihe circuil in Fig. 1.5b, V, ~ - 5 V means Ihat Ihe pOlential between points A and 8 is 5 V and point B is at the higher potential. The voltage in Fig. 1.5b can be expressed as shown in Fig. 1.5c. In this equivalent case, the difference in potential between points A and B is V2 = 5 V, and point B is at the higher potential. Note that it is important to detine a variable with a reference direction so that the answer can be interpreted to give the physical condition in the circuit. We wi ll find that it is not possible in many cases to define the variable so that the answer is positive. and we will also tind that it is not necessary to do so. As demonstrated in Figs. 1.5b and c, a negative number for a given variable, for example. V2 in Fig. 1.5b, gives exactly the same information as a positive number, that is. V2 in Fig. 1.5c, except that it has an opposite reference direction. Hence, -vhen we define either current or volt- age, it is absolutely necessary that we specify both magnitude and direction. Therefore, it is incomplete to say that the voltage between two points is 10 V or the current in a line is 2 A, since only the magnitude and not the direction for the variables has been defined. The range of magnitudes for voltage, equivalent to that for currents in Fig. lA, is shown in Fig. 1.6. Once again, note that this range spans many orders of magnitude. 10· 10· 10' ~ 102 !!! 0 100 > .~ " 10- 2 '"g g 10- 4 10- 6 10- 8 10- 10 Lightning bolt High-voltage transmission lines Voltage on a TV picture tube Large industrial motors ac oullet plug in U.S. households Car battery Voltage on integrated circuits Flashlight battery Voltage across human chest produced by the hearl (EKG) Vottage between two points on human scatp (EEG) Antenna of a radio receiver
- 18. SECT I ON 1.2 Switch - Battery Light bulb At this point we have presented the conventions that we employ in our discussions of current and voltage. Ellergy is yet another important tenn of basic significance. Let's investigate the voltage-current relationships for energy transfer using the flashlight shown in Fig. 1.7. The basic elements of a flashlight are a battery, a switch, a light bulb, and connect- ing wires. Assuming a good battery, we all know thutthe light bul b will glow when the switch is closed. A current now flows in this closed circuit as charges flow out of the positive ter- minal of the battery through the switch and light bulb and back into the negative terminal of the battery. The current heats up the filament in the bulb, causing it to glow and emit light. The light bulb converts electrical energy to thermal energy; as a result, charges passing through the bulb lose energy. These charges acquire energy as they pass through the battery as chemical energy is converted to electrical energy. An energy conversion process is occur- ring in the flashlight as the chemical energy in the banery is converted to electrical energy, which is then converted to thermal energy in the light bulb. I - BaHery - Vbauery + + V bu1b - Let's redraw the flashlight as shown in Fig. 1.8. There is a current I flowing in this dia- gram. Since we know that the light bulb uses energy, the charges coming out of the bulb have less energy than those entering the light bulb. In other words, the charges expend energy as they move through the bulb. This is indicated by the voltage shown across the bulb. The charges gain energy as they pass through the banery, which is indicated by the voltage across the battery. Note the voltage--<:urrent relationships for the battery and bulb. We know that the bulb is absorbing energy; the current is entering the positive terminal of the voltage. For the battery, the current is leaving the positive temlinal, which indicates that energy is being supplied. This is further illustrated in Fig. 1.9 where a circuit element has been extracted from a larger circuit for examination. In Fig. 1.9a, energy is being supplied to the element by whatever is attached to the terminals. Note that 2 A, that is, 2 C of charge are moving from point A to point B through the element each second. Each coulomb loses 3 J of energy as it passes through the element from point A to point B. Therefore, the element is absorbing 6 ] of energy per second. Note that when the element is absorbing energy. a positive current enters the positive terminal. In Fig. 1.9b energy is being supplied by the clement to whatever is connected to terminals A-B. In this case, note that when the element is supplying energy, a positive current enters the negative terminal and leaves via the positive terminal. In this con- vention, a negative current in one direction is equivalent to a positive current in the opposite direction, and vice versa. Similarly, a negative voltage in one direction is equivalent to a pos- itive voltage in the opposite direction. BASIC QUANTITIE S ~••• Figure 1.7 Flashlight circuit. ~... Figure 1.8 Flashlight circuit with voltages and current. A 1 ~ 2A + 3V B 1 ~ 2A (a) A 1 ~ 2A + 3V B I ~ 2 A (b) 5 .or" Figure 1.9 Voltage- current relationships for <aJ energy absorbed and (bJ energy supplied.
- 19. • 6 C H APT ER 1 BASIC CONC E PTS EXAMPLE 1.1 • SOLUTION Figure 1.10 ···t Diagram for Example 1.1. i(l) + V(I) • -<•• Figure 1.11 i Sign convention for power. [hint ] The passive sign convention is used to determine whether power is being absorbed or supplied. Suppose that your car will not start. To determine whether the battery is faulty, you turn on the light switch and fi nd that the lights are very dim, indicating a weak battery. You borrow a friend's car and a set of jumper cables. However, how do you connect his car's battery to yours? What do you want his batlery to do? Essentially, his car's battery must supply energy to yours, and therefore it should be connected in the manner shown in Fig. J. IO. Note that the positive current leaves the posi- tive termi nal of the good battery (supplyi ng energy) and enters the positive terminal of the weak battery (absorbing energy), Note that the same connections are used when charging a battery. I I In practical applications there are often considerations other than simply the electrical relations (e.g., safety). Such is the case with jump-starting an automobile. Automobile batteries produce explosive gases that can be ignited accidentally, causing severe physical injury. Be safe-follow the procedure described in your auto owner's manual. We have defined voltage in joules per coulomb as the energy required to move a positive charge of I C through an element. If we assume that we are dealing with a di fferential alllount of charge and energy, then li1V v=- dq Muhiplying this quantity by the current in the element yields 1.2 1.3 which is the time rale of change of energy or power measured in joules per second, or watts (W). Since, in general, both v and i are functions of time, p is also a time-varying quantity. Therefore, the change in energy from time I, to lime 12 can be found by integrati ng Eq. ( 1.3); that is, 1', 1"t.w = P dl = VillI '1 '1 1.4 At this point, leI us summarize our sign convention for power. To determine the sign of any of the quantities involved, the variables for the current and voltage should be arranged as shown in Fig. 1. 11 . The variable for the voltage V{ /) is defi ned as the voltage across the ele- ment with the positive reference at the same termi nal that the current variable i{/ ) is entering. This convention is called the passive sign cOllvelllioll and will be so noted in the remainder of this book. The product of V and i, with their attendant signs, will determine the magnitude and sign of the powcr. If the sign of the power is positive, power is being absorbed by the ele- ment; if the sign is ncgative. power is being supplied by the element.
- 20. SECTION 1 . 2 Given the two diagrams shown in Fig. 1.12, determine whether the element is absorbing or supplying power and how much. 2V + 4A (a) 2V + + 2V - 2A (b) + 2V BASIC QU ANTI TI ES EXAMPLE 1.2 ~... Figure 1.12 Elements for Example 1.2. • In Fig. 1.l2a the power is P = (2 V)(- 4 A) =-8 W. Therefore, the element is supplying SOLUTION power. In Fig. 1.12b, the power is P = (2 V)(- 2 A) = - 4 W. Therefore, the element is supplying power. Learning ASS ESSM ENT E1.1 Determine the amount of power absorbed or supplied by the elements in Fig. El.I. + Figure El.l (a) + 12V + (b) We wish to determine the unknown voltage or current in Fig. 1.13. SA { = ? A -A Vt =? P = - 20W SV p = 40W B +B (a) (b) SV + ANSWER: (a) P = -48 W; (b) P = 8 W. EXAMPLE 1.3 .~... Figure 1.13 Elements for Example 1.3. • In Fig. 1.13a, a power of -20 W indicates that the element is delivering power. Therefore, SOLUTION the current enters the negative terminal (terminal A), and from Eq. (1.3) the voltage is 4 V. Thus, B is the positive terminal, A is the negative terminal, and the voltage between them is 4Y. In Fig 1.1 3b, a power of +40 V indicates that the element is absorbing powerand. there- fore, the current should enter the positive terminal B. The current thus has a value of -8 A, as shown in the figure. 7 • •
- 21. 8 CHAPT E R 1 B ASIC CONCEPTS Learning ASS ESSM E N T E1.2 Determine the unknown variables in Fig. E 1.2. ANSWER: + Figure E1.2 (a) 1.3 Circuit Elements 1 = 2 A + (b) + 10 V (0) V, = -20 V; (b) I = -5 A. Finally, it is imporlum to note that ollr electrical networks satisfy the principle of conser- vation of energy. Because of the relationship between energy and power, it can be implied that power is also conserved in an electrical network. This result was formally stuted in 1952 by B. D. H. Tcllcgcn and is known as Tellegcn's theorem- the slim of the powers absorbed by all elements in an clectricalnclwork is zero. Another statement of this theorem is Ihal the power supplied in a network is exactl y equal to the power absorbed. Checking (0 verify that Tellegcn's theorem is satisfied for a particular network is one way to check our calculations when analyzing electrical networks. Thus far we have defined voltage, current, and power. In the remainder of this chapter we will define both illllt:pclldent and dependent current and voltage sources. Although we will assume ideal elements, we will try to indicate the shortcomings of these assumptions as we proceed with the discussion. In general, the elements we will define are terminal devices that are completely charac- terized by the current through the clement and/or the voltage across it. These elements, which we will employ in constructing electric circuits. will be broadly classified as being either active or passive. The distinction between these two classifications depends essentially on olle thing-whether they supply OJ' absorb energy. As the words themselves imply, an active element is capable of generating energy and a passive element cannot generate energy. However, later we will show that some passive elements are capable of storing energy. Typical active elements are batteries and generators. The three common passive elements are resistors, capacitors, and inductors. In Chapter 2 we will launch an examination of passive elements by discussing the resis- tor in detail. Before proceeding with that clement, we first present some very important active elements. 1. Independent voltage source 3. Two dependent voltage sources 2. Independent current source 4 . Two dependent current sources INDEPENDENT SOURCES An illdepellde1l1 vo/wge source is a two-Ienninal element that maintains a specified voltage between its terminals regardless oj tile CllrreW throllgh it as shown by the v-i plot in Fig. I.14a. The general symbol for an independent source, a circle. is also shown in Fig. 1.14a. As the figure indicates. terminal A is v(t ) volts positive with respect to terminal B. In contrast to the independent voltage source, the illdepel/{Iem current source is a two- terminaJ elemeill that maintains a specified current regardless oj'tlte volwge (lcros.· its termillals, as illustrated by the '1)-i plot in Fig. 1.14b. The general symbol for an independent current source is also shown in Fig. 1.1 4b, where i(t) is the specified Clirreill and the arrow indicates the positive direction of current now.
- 22. } I SECT I ON 1 . 3 'V 'V A A "(')~ '(')~ B B (a) (b) In their normal mode o f operation, independent sources supply power to the remainder of the circuit. However, they may also be connected into a circuit in such a way that they absorb power. A simple example of this latter case is a battery-charging circuit such as that shown in Example 1.1. It is important that we pause here to interject a comment concerning a shortcoming of the models. 1.11 general, mathematical models approximate actual physical syslems only under a cer- tain range of conditions. Rarely does a I1H..x.lel accuntlely represent a physical system under every set of conditions. To illustrate this point. consider the model for the voltage source in Fig. I. 14a. We assume thai the voltage source deli vers V volts regardless of what is connected 10 its tenninals. Theoretically, we could adjust the external circuit so that an intinite amount of current would tlow, and therefore the voltage source would deliver an intinite amount of power. This is, of course, physically impossible, A similar argument could be made for the independ- ent current source. Hence, the reader is cautioned to keep in mind that models have limitations and thus are valid representations of physical systems only under certain conditions. For example, can the independent voltage source be utilized to model the battery in an automobile under all operating conditions? With the headlights on, turn on the radio. Do the headlights dim with the radio on? They probably won't if the sound system in your automo· bile was installed at the factory. If you try to crank your car with the headlights on, you wi ll notice that the lights dim. The starter in your car draws considerable current, thus causing the voltage at the battery terminals to drop and dimming the headli ghts. The independent volt- age source is a good model for the battery with the radio turned on; however, an improved model is needed for your battery to predict its performance under cranking conditions. Determine the power absorbed or supplied by the elements in the network in Fig, 1,1 5, 6V + 24 V 18 V C IR C U IT ELEMENT S 9 ~,•• Figure 1,14 Symbols for (al independent voltage sou rce, (bl independ, ent current source. EXAMPLE 1.4 ~••• Figure 1,15 Network for Example 1.4. •
- 23. 10 CHA PTE R 1 BAS I C C ONC EPT S • SOLUTION [hin tj Elements that are connected In series have the same current. The current now is out of the positive terminal of the 24-V source, and therefore this element is supplying (2)(24) ~ 48 W of power. The current is into the positive terminals of elements I and 2, and therefore elements I and 2 are absorbing (2)(6) ~ 12 Wand (2)( 18) ~ 36 W, respectively. Note that the power supplied is equal to the power absorbed. Learning ASSESSM ENT E1.3 Find lhe power that is absorbed or supplied by the elements in Fig. E1.3. ANSWER: Current source supplies 36 W, element Figure E1.3 Figure 1.16 ...~ Four different types of dependent sources. I absorbs 54 W, and element 2 supplies 18 W. DEPENDENT SOURCES In contrast 10 the independent sources, which produce a particular voltage or current completely unaffected by what is happening in the remainder of [he circuit, dependent sources generate a voltage or current that is detennined by a voltage or current at a specitied location in the circuit. These sources are very important because they are an integral purt of the mathematical models used to describe the behavior of many elec- tronic circuit elements. For example, mctal-oxide-scmiconductor ficld-clfect transistors (MOSFETs) and bipolm transislOrs, both of which are commonly found in a host of electJonic equipment. are mod- eled with dependent sources, and therefore the anal ysis of electronic circuits involves the use of these controlled elements. In contrast lO the circle used to represent independent sources, a diamond is used to represent a dependent or controlled source. Figure 1.16 illustrates the four types of depend- ent sources. The input termi nals on the left represent the voltage or current that controls the dependent source. and the output terminals on the right represent the output current or volt- age orthe COil trolled source. Note that in Figs. 1.1 6a and d the quantities ~ and J3 are di men- sionless constants because we are transforming voltage to voltage and current to current. This is not the case in Figs. 1.16b and c; hence, when we employ these elements a short time later, we must describe the units of the factors rand g. E(a) (b) is + 'Us t i = gvs (c) (d) • I
- 24. SECTION 1 . 3 CIRCUIT ELEMEN TS 11 Given the two networksshown in Fig. 1.1 7, we wish to determine the outputs. EXAMPLE 1.5 • [n Fig. 1.17a the output voltage is v" = [.LVs or Va = 20 Vs = (20)(2 V) = 40 V. Note that SOLUTION the output voltage has been amplified from 2 V at the input terminals to 40 V at the output terminals; that is, the circuit is a voltage amplifier with an amplification factor of 20. IS = 1 rnA + Vs = 2V 5015 = 10 (a) (b) [n Fig. 1.I7b, the output current is 10 = f3/s = (50)(1 mAl = 50 mA; that is, the circuit has acurrent gain of 50, meaning that theoutput current is50 times greater than the input current. Learning ASS ESSM ENT £1.4 Determine the power supplied by the dependent sources in Fig. E1.4. 10 = 2A " 15 = 4A + B '"'BVs = 4V LI (a) (b) Figure E1.4 Calculate the power absorbed by each element in the network of Fig. I. IB. Also verify that Tellegen's theorem is satisfied by this network. 24 V 3A 1 A 12 V + '---~--1 3 f------, 4V Let's calculate the power absorbed by each element using the sign convemion for power. PI = (16)( 1) = 16 W P, = (4)( 1) =4W P, = (12)(1) = 12 W ~.., Figure 1.17 Circuits for Example 1.5. ANSWER: (a) Power supplied = BO W; (b) power supplied = 160 W. EXAMPLE 1.6 ~... Figure 1.18 Circuit used in Example 1.6. • SOLUTION • •
- 25. • 12 CHAP T ER 1 BASIC CONCEPTS EXAMPLE 1.7 Figure 1.19 ...~ Circuit used in Example 1.7. • P, = (8)(2) = 16 W P12V = (12)(2) = 24 W P"v = (24)(- 3) = -72 W Note that to calculate the power absorbed by the 24-V source, the current of 3 A flowing up through the source was changed to a current -3 A flowing down through the 24-V source. Let's sum up the power absorbed by all elements: 16 + 4 + 12 + 16 + 24 - 72 = 0 This sum is zero, which verifies that Tellegen's theorem is satisfied. Use Tellegen's theorem to find the current 10 in the network in Fig. 1.19. SOLUTION First, we must determine the power absorbed by each element in the network. Using the sign convention for power, we find P'A = (6)(- 2) = - 12 W P, = (6 )(10) = 6/"W P, = ( 12)(-9) = - 108 W P, = ( 10)(- 3) = -30 W PH = (4)(-8) = -32W PD, = (8/,)( 11 ) = ( 16)( 11 ) = 176W Applying Tellegen's theorem yields, -12 + 6/" - 108 - 30 - 32 + 176 = 0 or 6/,, + 176 = 12+ 108 +30 + 32 Hence, 10 = IA Learning ASS ESSM ENT E1.5 Find the power that is absorbed or supplied by the circuit elements in the network in Fig. EI.5. BV 24V Figure El.5 ANSWER: P" v = 96 W supplied; P, = 32 W absorbed; P4I , = 64 W absorbed.
- 26. SECTION 1.3 C IRCUIT ELEMENTS 13 The charge that enters the BOX is shown in Fig. 1.20. Calculate and sketch the current flow- EXAMPLE 1.8 ing into and the power absorbed by the BOX between 0 and 10 milliseconds. i (I) ~... Figure 1.20 Diagrams for Example 1.8. t2 V BOX q(t) (me) 3 2 5 6 2 3 4 7 8 9 10 I (ms) - t - 2 - 3 Recall that current is related to charge by i(l) = dq(l) The current is equal to the slope of SOLUTION dl the charge waveform. i(l) = 0 3 X 10-3 - I X 10-3 i(l) = 2 X 10 3 _ I X 10 3 = 2A i(l) = 0 -2 X 10-3 - 3 X 10-3 i(l) = 5 X 10 3 _ 3 X 10-3 = -2.5 A i(l) = 0 2 X 10-3 - (-2 X 10-3) i(l) = = 1.33 A 9 X 10 3 - 6 X 10-3 i(l) = 0 OSISlms 1St S 2 ms 2SI s 3ms 3 s t S 5 ms 5SI s 6ms 6 :5 t :5 9 ms t ~ 9ms The current is plotted with the charge waveform in Fig. 1.21. Note that the current is zero during times when the charge is a constant value. When the charge is increasing. the current is positive, and when the charge is decreasing the current is negative. • •
- 27. 14 C H A P TER 1 BAS I C CO N CEPTS Figure 1.21 ...? Charge and current waveforms for Example 1.8. Figure 1.22 •••l- Power waveform for Example 1.8. q(l) (me),i(l) (A) 3 2 2 3 - 1 - 2 - 3 The power absorbed by the BOX is 12 . i(I). p(l ) = 12*0 = 0 p(l ) = 12*2 = 24 W p(l ) = 12*0 = 0 p(l ) = 12*(-2.5) = - 30 W p(l ) = 12*0 = 0 p(l ) = 12*1.33 = 16 W p(l ) = 12*0 = 0 O StS lms 1 ::51S 2ms 2 ::5 { ::5 3 1115 3 ::5 1 ::5 5 ms 5 ::5 t s 6 illS 6 "1 ,, 9ms [ ~ 9 ms 9 10 I (ms) The power absorbed by the BOX is plotted in Fig. 1.22. For the time intervals, I " I " 2 ms and 6 s 1 ::5 9 ms, the BOX is absorbing power. During the time interval 3 ::5 t ::5 5 ms, the power absorbed by the BOX is negative, which indicates that the BOX is supplying power to the 12-V source. p(l) (W) 36 24 1-'---- 12 I 5 6 tJ 2 7 8 10 I (ms) - 12 - 24 9 -36
- 28. SECTION 1 . 3 CIRCUIT ELE MEN T S 15 A Universal Serial Bus (USB) port is a common feature on both desklop and nOlebook compulers as well as many handheld devices such as MP3 players. digilal cameras, and cell phones. The new USB 2.0 specification (www.usb.org) permits data transfer between a computer and a peripheral device at rates up to 480 Megabits persecond. One important fea- ture of USB is the ability to swap peripherals without having to power down a computer. USB ports are also capable of supplying power 10 eXlernal peripherals. Figure 1.23 shows a MOlorola RAZR® and Apple iPod® being charged from the USB ports on a nOlebook computer. A USB cable is a four-conductorcable with two signal conductors and two con- ductors for providing power. The amount of current that can be provided over a USB port is defined in the USB specification in terms of unit loads, where one unit load is specified 10 be 100 rnA. All USB ports defauillo low-power parIS al one unilload, bUI can be changed under software control 10 high-power ports capable of supplying up 10 five unil loads or 500mA. 1. A 680 mAh Lilhium-ion battery is standard in a Motorola RAZR®. If Ihis battery is completely discharged (Le., 0 mAh), how long will it take to recharge the baltery to its full capacilY of 680 mAh from a low-power USB port? How much charge is stored in the battery at the end of the charging process? 2. A Ihird-generation iPod® wilh a 630 mAh Lithium-ion battery is 10 be recharged from a high-power USB port supplying 150 mA of current. Al the beginning of Ihe recharge, 7.8 C ofcharge are stored in the battelY, The recharging process halts when the stored charge reaches 35.9 C. How long does illake to recharge Ihe battery? 1. A low-power USB port operates at 100 rnA. Assumjng that the charging current from the USB port remains at 100 rnA throughout the charging process, the time required to recharge Ihe battery is 680 mAh/ IOO mA = 6.8 h. The charge stored in the battery when fully charged is 680mAh • 60 s/h = 40,800 mAs = 40.8 As = 40.8 C. 2. The charge supplied 10 Ihe battery during the recharging process is 35.9 - 7.8 = 28.1C. This corresponds 10 28.1 As = 28,100 mAs ' Ih/ 60s = 468.3 mAh. Assuming a constant charging current of 150 rnA from the high-power USB port, the time required 10 recharge the battery is 468.3 mAh/ ISO mA = 3.12 h. EXAMPLE 1.9 ~". Figure 1.23 Charging a Motorola RAZXR® and Apple iPod® from USB ports. (Courtesy of Mark Nelms and Jo Ann Loden) • SOLUTION •
- 29. • • 16 C H APT ER 1 BASIC CONCEPTS SUMMARY • The standard prefixes employed p = 10-12 k 103 n = 10-9 M 106 fJ. 10-6 G 10' m 10-3 T= 1012 • The relationships between current and charge dq (l ) i(l) = - - <II or q(l ) = J~i(X) <Ix • The relationships among power, energy, current, and voltage dw . p = - = V I dl 1"Ih v = p dl = " PROBLEMS 1 ','VI df " 1.1 If the currem in an electric conductor is 2.4 A, how many coulombs of charge pass any point in a 30-second interval? 1.2 Determine the time interval required for a I2-A battery charger '0 deliver 4800 C. 1.3 A lightning bolt carrying 30,000 A lasts for 50 micro- seconds. If the lightning strikes an airplane flying at 20,000 feel, what is the charge deposited on the plane? 1,4 If a 12-V battery delivers 100 J in 5 s, find (a) 'he amount of charge delivered and (b) the current produced. 0 '.5 The current in a conductor is 1.5 A. How many coulombs of charge pass any point in a time interval of 1.5 min? o 1.6 If 60 C of charge pass through an electric conductor in 30 seconds, determine the currem in the conductor. 0 1.7 0 ,.8 Determine the number of coulombs of charge produced by a 12-A battery charger in an hour. Five coulombs of charge pass through the elemem in Fig. PI.8 from point A to point B. If the energy absorbed by the element is 120 J, determine the voltage across the element. B + A Figure P1,S • The passive sign convention The passive sign convention states that if the voltage and current associated with an element are as shown in Fig. 1.11 . the product of v and i, with their 3t1cndant signs. determines the magnitude and sign of the power. If the sign is positive, power is being absorbed by the element, and if the sign is negative, the clemem is supplying power. • Independent and dependent sources An ideal independent voltage (current) source is a two-terminal element that maintains a specified voltage (current) between its terminals regardless of the current (voltage) through (across) the element. Dependent or controlled sources generate a voltage or current that is detcnnined by a voltage or current at a specified location in the circuit. • Conservation of energy The electric circuits under investigation satisfy the conservation of energy. • Tellegen's Theorem The Slim of the powers absorbed by all elements in an electrical network is zero. 1.9 The charge entering an element is shown in Fig. P1.9. 1.10 Find the current in the element in the time interval o~ I ~ 0.5 s. [Him: The equation for '1(1) is '1 (1) = I + (1/ 0.5)1, I ~ 0.1 q (e) 2 o 0.5 r (s) Figure P1.9 The current that enters an element is shown in Fig. P1.1O. Find the charge that enters the element in the lime interval 0 < I < 20 s. i(l) rnA 10 o 20 I (s) Figure Puo o
- 30. 1 .11 The charge entering the positive terminal of an element is q(r) = -30e-41 me. If the vollage across the element is 120e-21 y , determine the energy delivered to the element in the time interval 0 < t < 50 ms. PR O B L E MS 17 1.14 The waveform for the current flowing illlo a circuit element is shown in Fig. P1. 14. Calculate the amoum of charge which enters the element between(a) 0 and 3 sec- onds, (b) 1 and 5 seconds, and (c) 0 and 6 seconds. £1 1.12 The charge emering the positive terminal of an element is given by the expression q(t) = - J2e-2r me. The power delivered to the element is p(r) = 2.4e-31 W. Compute the currem in the element, the voltage across the element, and the energy delivered to the element in the time interval 0 < t < 100 InS. ( ) (A)- t t 2 -- -- -- -- -------- 1.13 The voltage across an element is 12e-2r V. The current entering the positive terminal of the elemem is 2e-z, A. Find the energy absorbed by the element in 1.5 s starting from t = O. .5 1 1 Figure Pl.14 2 3 1.15 The current flowing into a box is given by the waveform shown in Fig. PI .IS. Calculate the following quantities: (a) the amount of charge which has entered the box at 2V t = 1 s, t = 3 s, and t = 4.5 s, (b) the power absorbed by the box at t = I s, 2.5 s, 4.5 s, and 5.5 s and (c) the amount of energy absorbed by the box between 0 and 6 s. t I.( ) (A) 2 i (I) 1 - 2 4 , , 1 3 5 6 1 Figure P1.1S t (s 4 5 6 t (s)

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