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Contents 5

Contents

Preface xTo the Student xvii

I Foundation dc concepts 01

1 Introduction 3

1.1 Introduction 41.2 The SI System of Units 61.3 Converting Units 81.4 Power of Ten Notation 101.5 Prefixes, Engineering Notation, and

Numerical Results 121.6 Circuit Diagrams 141.7 Circuit Analysis Using Computers and

Calculators 16Problems 18

2 Voltage and Current 25

2.1 Atomic Theory Review 262.2 The Unit of Electrical Charge: The Coulomb 302.3 Voltage 312.4 Current 342.5 Practical DC Voltage Sources 362.6 Measuring Voltage and Current 412.7 Switches, Fuses, and Circuit Breakers 44Problems 46

3 Resistance 51

3.1 Resistance of Conductors 523.2 Electrical Wire Tables 553.3 Resistance of Wires—Circular Mils 573.4 Temperature Effects 61

3.5 Types of Resistors 633.6 Color Coding of Resistors 673.7 Measuring Resistance—The Ohmmeter 693.8 Thermistors 723.9 Photoconductive Cells 733.10 Nonlinear Resistance 743.11 Conductance 763.12 Superconductors 77Problems 78

4 Ohm’s Law, Power, and Energy 85

4.1 Ohm’s Law 864.2 Voltage Polarity and Current Direction 904.3 Power 924.4 Power Direction Convention 964.5 Energy 974.6 Efficiency 994.7 Nonlinear and Dynamic Resistances 1024.8 Computer-Aided Circuit Analysis 103Problems 108

I I Basic dc Analysis 116

5 Series Circuits 117

5.1 Series Circuits 1185.2 Kirchhoff’s Voltage Law 1205.3 Resistors in Series 1215.4 Voltage Sources in Series 1245.5 Interchanging Series Components 1245.6 The Voltage Divider Rule 1265.7 Circuit Ground 128

5

Contents 76 Contents

12.5 Air Gaps, Fringing, and Laminated Cores 39012.6 Series Elements and Parallel Elements 39112.7 Magnetic Circuits with DC Excitation 39112.8 Magnetic Field Intensity and Magnetization

Curves 39212.9 Ampere’s Circuital Law 39512.10 Series Magnetic Circuits: Given , Find NI 39612.11 Series-Parallel Magnetic Circuits 40012.12 Series Magnetic Circuits: Given NI, Find 40112.13 Force Due to an Electromagnet 40312.14 Properties of Magnetic Materials 40412.15 Measuring Magnetic Fields 405Problems 406

13 Inductance and Inductors 411

13.1 Electromagnetic Induction 41213.2 Induced Voltage and Induction 41313.3 Self-Inductance 41613.4 Computing Induced Voltage 41813.5 Inductances in Series and Parallel 41913.6 Practical Considerations 42013.7 Inductance and Steady State DC 42213.8 Energy Stored by an Inductance 42413.9 Inductor Troubleshooting Hints 425Problems 425

14 Inductive Transients 433

14.1 Introduction 43414.2 Current Buildup Transients 43614.3 Interrupting Current in an Inductive Circuit 44014.4 De-energizing Transients 44214.5 More Complex Circuits 44414.6 RL Transients Using Computers 449Problems 453

I V Foundation Ac concepts 460

15 AC Fundamentals 461

15.1 Introduction 46215.2 Generating AC Voltages 463

15.3 Voltage and Current Conventions for AC 46515.4 Frequency, Period, Amplitude, and Peak

Value 46715.5 Angular and Graphic Relationships for Sine

Waves 47115.6 Voltages and Currents as Functions of Time 47515.7 Introduction to Phasors 47915.8 AC Waveforms and Average Value 48715.9 Effective (RMS) Values 49215.10 Rate of Change of a Sine Wave (Derivative) 49715.11 AC Voltage and Current Measurement 49715.12 Circuit Analysis Using Computers 499Problems 501

16 R, L, and C Elements and the Impedance Concept 511

16.1 Complex Number Review 51216.2 Complex Numbers in AC Analysis 51816.3 R, L, and C Circuits with Sinusoidal Excitation 52316.4 Resistance and Sinusoidal AC 52316.5 Inductance and Sinusoidal AC 52416.6 Capacitance and Sinusoidal AC 52716.7 The Impedance Concept 53016.8 Computer Analysis of AC Circuits 533Problems 536

17 Power in AC Circuits 543

17.1 Introduction 54417.2 Power to a Resistive Load 54517.3 Power to an Inductive Load 54617.4 Power to a Capacitive Load 54717.5 Power in More Complex Circuits 54917.6 Apparent Power 55117.7 The Relationship Between P, Q, and S 55217.8 Power Factor 55517.9 AC Power Measurement 55917.10 Effective Resistance 56117.11 Energy Relationships for AC 56217.12 Circuit Analysis Using Computers 563Problems 564

5.8 Voltage Subscripts 1295.9 Internal Resistance of Voltage Sources 1335.10 Ammeter Loading Effects 1355.11 Circuit Analysis Using Computers 137Problems 140

6 Parallel Circuits 151

6.1 Parallel Circuits 1526.2 Kirchhoff’s Current Law 1536.3 Resistors in Parallel 1566.4 Voltage Sources in Parallel 1626.5 Current Divider Rule 1626.6 Analysis of Parallel Circuits 1676.7 Voltmeter Loading Effects 1696.8 Computer Analysis 171Problems 174

7 Series-Parallel Circuits 185

7.1 The Series-Parallel Network 1867.2 Analysis of Series-Parallel Circuits 1877.3 Applications of Series-Parallel Circuits 1937.4 Potentiometers 2007.5 Loading Effects of Instruments 2027.6 Circuit Analysis Using Computers 206Problems 212

8 Methods of Analysis 223

8.1 Constant-Current Sources 2248.2 Source Conversions 2268.3 Current Sources in Parallel and Series 2298.4 Branch-Current Analysis 2318.5 Mesh (Loop) Analysis 2358.6 Nodal Analysis 2428.7 Delta-Wye (Pi-Tee) Conversion 2488.8 Bridge Networks 2548.9 Circuit Analysis Using Computers 261Problems 264

9 Network Theorems 273

9.1 Superposition Theorem 2749.2 Thévenin’s Theorem 277

9.3 Norton’s Theorem 2839.4 Maximum Power Transfer Theorem 2909.5 Substitution Theorem 2959.6 Millman’s Theorem 2979.7 Reciprocity Theorem 2989.8 Circuit Analysis Using Computers 300Problems 306

I I I capacitance and Inductance 316

10 Capacitors and Capacitance 317

10.1 Capacitance 31810.2 Factors Affecting Capacitance 31910.3 Electric Fields 32210.4 Dielectrics 32410.5 Nonideal Effects 32510.6 Types of Capacitors 32610.7 Capacitors in Parallel and Series 33010.8 Capacitor Current and Voltage 33310.9 Energy Stored by a Capacitor 33610.10 Capacitor Failures and Troubleshooting 336Problems 337

11 Capacitor Charging, Discharging, and Simple Waveshaping Circuits 345

11.1 Introduction 34611.2 Capacitor Charging Equations 34911.3 Capacitor with an Initial Voltage 35411.4 Capacitor Discharging Equations 35511.5 More Complex Circuits 35611.6 An RC Timing Application 36311.7 Pulse Response of RC Circuits 36511.8 Transient Analysis Using Computers 369Problems 374

12 Magnetism and Magnetic Circuits 383

12.1 The Nature of a Magnetic Field 38412.2 Electromagnetism 38612.3 Magnetic Flux and Flux Density 38712.4 Magnetic Circuits 388

Contents 98 Contents

24.2 Basic Three-Phase Circuit Connections 84124.3 Basic Three-Phase Relationships 84424.4 Examples 85224.5 Power in a Balanced System 85624.6 Measuring Power in Three-Phase Circuits 86124.7 Unbalanced Loads 86324.8 Power System Loads 86724.9 Circuit Analysis Using Computers 867Problems 870

25 Nonsinusoidal Waveforms 879

25.1 Composite Waveforms 88125.2 Fourier Series 88225.3 Fourier Series of Common Waveforms 88725.4 Frequency Spectrum 89225.5 Circuit Response to a Nonsinusoidal

Waveform 89725.6 Circuit Analysis Using Computers 901Problems 903

APPENDIX APSpice and Multisim 909

APPENDIX BMathematics in Circuit Analysis: A Brief Tutorial 914

APPENDIX CMaximum Power Transfer Theorem 922

APPENDIX DAnswers to Odd-Numbered Problems 925Glossary 937Index 942

V Impedance Networks 570

18 AC Series-Parallel Circuits 573

18.1 Ohm’s Law for AC Circuits 57418.2 AC Series Circuits 57918.3 Kirchhoff’s Voltage Law and the Voltage

Divider Rule 58618.4 AC Parallel Circuits 58818.5 Kirchhoff’s Current Law and the Current

Divider Rule 59318.6 Series-Parallel Circuits 59618.7 Frequency Effects 59918.8 Applications 60418.9 Circuit Analysis Using Computers 607Problems 613

19 Methods of AC Analysis 627

19.1 Dependent Sources 62819.2 Source Conversion 62919.3 Mesh (Loop) Analysis 63219.4 Nodal Analysis 63719.5 Delta-to-Wye and Wye-to-Delta Conversions 64319.6 Bridge Networks 64619.7 Circuit Analysis Using Computers 651Problems 655

20 AC Network Theorems 663

20.1 Superposition Theorem—Independent Sources 664

20.2 Superposition Theorem—Dependent Sources 667

20.3 Thévenin’s Theorem—Independent Sources 669

20.4 Norton’s Theorem—Independent Sources 67320.5 Thévenin’s and Norton’s Theorems for Dependent

Sources 67820.6 Maximum Power Transfer Theorem 68620.7 Circuit Analysis Using Computers 690Problems 695

21 Resonance 705

21.1 Series Resonance 70721.2 Quality Factor, Q 70821.3 Impedance of a Series Resonant Circuit 71121.4 Power, Bandwidth, and Selectivity of a Series

Resonant Circuit 71221.5 Series-to-Parallel RL and RC Conversion 71921.6 Parallel Resonance 72521.7 Circuit Analysis Using Computers 733Problems 737

22 Filters and the Bode Plot 747

22.1 The Decibel 74822.2 Multistage Systems 75422.3 Simple RC and RL Transfer Functions 75622.4 The Low-Pass Filter 76622.5 The High-Pass Filter 77222.6 The Band-Pass Filter 77722.7 The Band-Reject Filter 78022.8 Circuit Analysis Using Computers 781Problems 785

23 Transformers and Coupled Circuits 795

23.1 Introduction 79623.2 Iron-Core Transformers: The Ideal

Model 79923.3 Reflected Impedance 80523.4 Power Transformer Ratings 80723.5 Transformer Applications 80823.6 Practical Iron-Core Transformers 81423.7 Transformer Tests 81723.8 Voltage and Frequency Effects 81923.9 Loosely Coupled Circuits 82023.10 Magnetically Coupled Circuits with Sinusoidal

Excitation 82423.11 Coupled Impedance 82623.12 Circuit Analysis Using Computers 827Problems 830

24 Three-Phase Systems 839

24.1 Three-Phase Voltage Generation 840

10

Preface

Preface 11

The Book and Who It Is For

The objective of Circuit Analysis: Theory and Practice continues to be to pro-vide students with a solid grounding in the principles of circuit analysis, and to assist instructors in the task of teaching by providing them with a textbook and a broad range of supporting tools. Developed specifically for use in intro-ductory circuit analysis courses, this book was written primarily for electron-ics technology students at higher education colleges, universities, and career schools, as well as industry training programs. It covers fundamentals of dc and ac circuits, methods of analysis, capacitance, inductance, magnetic circuits, basic transients, Fourier analysis, and other topics. When students successfully complete a course using this book, they will have a good working knowledge of basic circuit principles and a demonstrated ability to solve a variety of circuit-related problems.

Text Organization

The book contains 25 chapters and is divided into five main parts: Foundation DC Concepts, Basic DC Analysis, Capacitance and Inductance, Foundation AC Concepts, and Impedance Networks. Chapters 1 through 4 are introduc-tory. They cover the foundation concepts of voltage, current, resistance, Ohm’s law, and power. Chapters 5 through 9 focus on dc analysis methods. Included are Kirchhoff’s laws, series and parallel circuits, mesh and nodal analysis, Y and transformations, source transformations, Thévenin’s and Norton’s theo-rems, the maximum power transfer theorem, and so on. Chapters 10 through 14 cover capacitance, magnetism, and inductance, plus magnetic circuits and simple dc transients. Chapters 15 through 17 cover foundation ac concepts; ac voltage generation; and the basic ideas of frequency, period, phase, and so on. Phasors and the impedance concept are introduced and used to solve simple problems. Power in ac circuits is investigated and the concept of power fac-tor and the power triangle are introduced. Chapters 18 through 23 then apply these ideas. Topics include ac versions of earlier dc techniques such as mesh and nodal analysis, Thévenin’s theorem, and so on, as well as new ideas such as resonance, filters, Bode techniques, three-phase systems, transformers, and non sinusoidal waveform analysis.

Several appendices round out the book. Appendix A provides operational instructions, reference material and tips for PSpice and Multisim users; Appen-dix B is a math-and-calculator tutorial that describes typical mathematical and calculator usage in circuit analysis—including methods for solving simultane-ous equations that have both real and complex coefficients; Appendix C shows how to apply calculus to derive the maximum power transfer theorem for both

dc circuits and ac circuits while Appendix D contains answers to odd-numbered end-of-chapter problems.

Required Background

Students need a working knowledge of basic algebra and trigonometry and the ability to solve second-order linear equations such as those found in mesh analy-sis. They should be familiar with the SI metric system and the atomic nature of matter. Calculus is introduced gradually into later chapters for those who need it. However, calculus is not an essential prerequisite or corequisite, as all topics can be readily understood without it. Thus, students who know (or are studying) calculus can use this knowledge to enrich their understanding of circuit theory, whereas, because the calculus parts of the book can be omitted without any loss of continuity, students unfamiliar with calculus can comfortably navigate around it as they work through the chapters. (Calculus-based material is flagged by an icon to identify it as optional material for advanced learners.)

Features of the Book

• A clearly written, easy-to-understand style emphasizes principles and concepts.

• Over 1200 diagrams and photos. Color and 3D visual effects are used to illustrate and clarify ideas and to aid visual learners.

• Examples. Hundreds of examples worked out in step-by-step detail help promote understanding and guide the student in problem solving.

Each chapter opens with Key Terms, Outline, Objectives, Chapter Preview, and Putting It in Perspective.

■ KEY TERMS

Application PackagesBaseBlock DiagramCircuit TheoryConversion FactorEngineering NotationExponentHorsepowerJouleNewtonPictorial DiagramPower of Ten NotationPrefixesProgramming LanguageResistanceSchematic DiagramScientific NotationSI SystemSPICEWatt

■ OUTLINE

IntroductionThe SI System of UnitsConverting UnitsPower of Ten NotationPrefixesCircuit DiagramsCircuit Analysis Using

Computers

■ OBJECTIVES

After studying this chapter, you will be able to• describetheSIsystemofmeasurement,• convertbetweenvarioussetsofunits,• usepoweroftennotationtosimplify

handling of large and small numbers,• expresselectricalunitsusingstandard

prefix notation such as A, kV, mW, etc.,• useasensiblenumberofsignificantdigits

in calculations,• describewhatblockdiagramsareandwhy

they are used,• convertasimplepictorialcircuittoits

schematic representation,• describegenerallyhowcomputersand

calculators fit in the electrical and electronic circuit analysis picture.

11CAPACITOR CHARGING, DISCHARGING AND SIMPLE WAVESHAPING CIRCUITS

A n electrical circuit is a system of interconnected components such as resistors, capaci-

tors, inductors, voltage sources, and so on. The electrical behavior of these components

is described by a few basic experimental laws. These laws and the principles, concepts, math-

ematical relationships, and methods of analysis that have evolved from them are known as

circuit theory.

Much of circuit theory deals with problem solving and numerical analysis. When you ana-

lyze a problem or design a circuit, for example, you are typically required to compute val-

ues for voltage, current, and power. In addition to a numerical value, your answer must include

a unit. The system of units used for this purpose is the SI system (Systéme International). The

SI system is a unified system of metric measurement; it encompasses not only the familiar MKS

(meters, kilograms, seconds) units for length, mass, and time, but also units for electrical and

magnetic quantities as well.

Quite frequently, however, the SI units yield numbers that are either too large or too small for

convenient use. To handle these, engineering notation and a set of standard prefixes have

been developed. Their use in representation and computation is described and illustrated.

Since circuit theory is somewhat abstract, diagrams are used to help present ideas. We

look at several types—schematic, pictorial, and block diagrams—and show how to use

them to represent circuits and systems.

We conclude the chapter with a brief look at computer and calculator usage in circuit

analysis. Several popular software packages are described, including Electronics Work-

bench’s Multisim®, Orcad’s PSpice®, and Mathsoft’s Mathcad®. ■

CHAPTER PREVIEW

13

To the Student

12 Preface

Web Tutor™

This is an online study guide that provides additional learning aids such as notes, flashcards, quizzes, Web links, and discussion questions. ISBN: 1418054577

OnLine Companion™This is a Web site that supports our book. From time to time, we will add ad-ditional material, text updates, online quizzes, etc. Please visit us at http://www. electronictech.com.

PSpice and Multisim Versions used in this Book

The versions of PSpice and Multisim used throughout this text are the versions current at the time of writing—see Appendix A. Also shown in Appendix A are operational details for these products, as well as details about downloads, Web sites, helpful tutorials, etc.

TextChoice—Build Your Perfect Course Solution

If you would like to customize a text for your Circuits and Devices classes that uses the Robbins Circuits chapters plus selected Devices chapters available through our custom database, contact your local sales representative or Visit TextChoice at www.textchoice.com and learn how Thomson Custom Solutions can help you teach your course, your way.

L earning circuit theory should be challenging, interesting, and (hopefully) fun. However, it is also hard work, since the knowledge and skills that you

seek can only be gained through practice. We offer a few guidelines.

1. As you go through the material, try to gain an appreciation of where the theory comes from—i.e., the basic experimental laws on which it is based. This will help you better understand the foundation ideas on which the theory is built.

2. Learn the terminology and definitions. Important new terms are introduced frequently. Learn what they mean and where they are used.

3. Study each new section carefully and be sure that you understand the basic ideas and how they are put together. Work your way through the examples with your calculator. Try the practice problems, then the end-of-chapter problems. Not every concept will be clear immediately and most likely many will require several readings before you gain an adequate under-standing.

4. When you are ready, test your understanding using the In-Process Learn-ing Checks (self-quizzes) located in each chapter.

5. When you have mastered the material, move on to the next block. For those concepts that you are having difficulty with, consult your instructor or some other authoritative source.

Calculators for Circuit Analysis and Electronics

You will need a good scientific calculator. A good calculator will permit you to more easily master the numerical aspects of problem solving, thereby leaving you more time to concentrate on the theory itself. This is especially true for ac, where complex number work dominates. There are some powerful calcula-tors on the market that handle complex-number arithmetic almost as easily as real-number arithmetic—and there are some less expensive calculator models that also do a credible job. You should acquire an appropriate calculator (after consulting with your instructor), and learn to use it proficiently.

Acknowledgments 15

14

Acknowledgments

M any people have contributed to the development of this text. We begin by expressing our thanks to our students for providing subtle (and sometimes

not-so-subtle) feedback. Next, the reviewers and accuracy checkers: no text-book can be successful without the dedication and commitment of such people. We thank the following:

ReviewersSami Antoun, DeVry University, Columbus, OH

G. Thomas Bellarmine, Florida A & M University

Harold Broberg, Purdue University

William Conrad, IUPUI—Indiana University, Purdue University

Franklin David Cooper, Tarrant County College, Fort Worth, TX

David Delker, Kansas State University

Timothy Haynes, Haywood Community College

Bruce Johnson, University of Nevada

Jim Pannell, DeVry University, Irving, TX

Alan Price, DeVry University, Pomona, CA

Philip Regalbuto, Trident Technical College

Carlo Sapijaszko, DeVry University, Orlando, FL

Jeffrey Schwartz, DeVry University, Long Island City, NY

John Sebeson, DeVry University, Addison, IL

Parker Sproul, DeVry University, Phoenix, AZ

Lloyd E. Stallkamp, Montana State University

Roman Stemprok, University of Texas

Richard Sturtevant, Springfield Tech Community College

Technical Accuracy ReviewersChia-chi Tsui, DeVry University, Long Island City, NY

Rudy Hofer, Conestoga College, Kitchener, Ontario, Canada

Marie Sichler, Red River College, Winnipeg, Manitoba, Canada

Reviewers for the 4th EditionDavid Cooper, Tarrant County College, Fort Worth, TX

Lance Crimm, Southern Polytechnic State University, Marietta, GA

Fred Dreyfuss, Pace University, White Plains, NY

Bruce Johnson, University of Nevada, Reno, NV

William Routt, Wake Tech Community College, Raleigh, NC

Dr. Hesham Shaalan, Texas A&M University, Corpus Christi, TX

Richard Sturtevant, Springfield Technical Community College, Springfield, MA

The following firms and individuals supplied photographs, diagrams, and other useful information:

Allen-Bradley Illinois Capacitor Inc.

AT & T Electronics Workbench

AVX Corporation JBL Professional

B K Precision Fluke Corporation

Bourns Inc. Shell Solar Industries

Butterworth & Co. Ltd. Tektronix

Cadence Design Systems Inc. Transformers Manufacturers Inc.

Condor DC Power Supplies Inc. Vansco Electronics

We express our deep appreciation to the staff at Thomson Delmar Learning for their tireless efforts in putting this book together: To Steve Helba, Senior Acquisitions Editor, for helping to define the project and smooth the way; Mi-chelle Ruelos Cannistraci, Senior Product Manager, for direction, encourage-ment, advice, and generally pulling the project together; Francis Hogan, Art & Design Coordinator, for ensuring that the art was done right; Benjamin Gleeks-man, Production Coordinator, and Larry Main, Senior Production Manager, for helping to make the project work on the usual short deadline; Dennis Williams, Marketing Manager, for helping get the book to its intended clientele; Dawn Daugherty, Editorial Assistant, for providing answers and timely assistance; and Allyson Powell, freelance developmental editor, for pulling together the e.resource project and ably guiding it to the production stage. We also wish to thank Panchi Das, Project Manager at Interactive Composition Corporation, and her colleagues (in particular Michelle Gaudreau, copyeditor), for guiding the book through the copyediting, page layout, and all such related tasks re-quired for the production of this edition of the book. To all these people and their staffs, a special thank-you.

Lastly, we thank our wives and families for their support and perseverance during the preparation of this edition.

Allan H. RobbinsWilhelm C. Miller

June, 2006

I

1616

A llan H. Robbins graduated in Electrical Engineering, earning both a Bachelor’s degree and with circuit theory as his specialty a Master’s degree.

After gaining industrial experience, he joined Red River College where he served as head of the Department of Electrical and Computer Technology. As of this writing, he has over thirty-five years of experience in teaching and depart-ment leadership. In addition to his academic career, Allan has been a consultant and a small-business partner in the electronics/microcomputer field. He began writing as a contributing author for Osborne-McGraw-Hill in the early stages of the newly emerging microcomputer field and, in addition to the Delmar titles, is also joint author of one other textbook. He has served as Section Chairman for the IEEE and as a member of the board for the Electronics Industry Association of Manitoba.

Wilhelm (Will) C. Miller obtained a diploma in Electronic Engineering Technology from Red River Community College (now Red River College) and later graduated from the University of Winnipeg with a degree in Phys-ics and Mathematics. He worked in the communications field for ten years, including a one-year assignment with Saudi PTT in Jeddah, Saudi Arabia. Will was an instructor in the electronics and computer engineering technologies for twenty years, having taught at Red River College and College of The Bahamas (Nassau, Bahamas). He currently serves as Chair of the EET programs at Red River College. In addition to providing academic consulting (most recently in Doha, Qatar), Will is an active member on the board of directors of the Ca-nadian Technology Accreditation Board. The CTAB is a standing committee of the Canadian Council of Technicians and Technologists, and is responsible for ensuring that technician and technology programs across Canada meet the Canadian Technology Standards. In addition, Will is the Chair of the Panel of Examiners for CTTAM (the Certified Technicians and Technologists Associa-tion of Manitoba).

17

c ircuit theory provides the tools and concepts needed to understand and ana-

lyze electrical and electronic circuits. The foundations of this theory were laid

down over the past several hundred years by a number of pioneer researchers. In

1780, Alessandro Volta of Italy developed an electric cell (battery) that provided the

first source of what we now call dc voltage. Around the same time, the concept of

current was evolved (even though nothing was known about the atomic structure

of matter until much later). In 1826, Georg Simon Ohm of Germany brought the two

ideas together and experimentally determined the relationship between voltage

and current in a resistive circuit. This result, known as Ohm’s law, set the stage for

the development of modern-day circuit theory.

In Part I, we examine the foundation of this theory. We look at voltage, current,

power, energy, and the relationships between them. The ideas developed here

are used throughout the remainder of the book and in practice. They constitute the

fundamental ideas upon which all electrical and electronic circuit theory is built. ■

1 Introduction

2 Voltage and Current

3 Resistance

4 Ohm’s Law, Power,

and Energy

FouNdAtIoN dc coNcepts

About the Authors

■ KEY TERMSApplication PackagesBaseBlock DiagramCircuit TheoryConversion FactorEngineering NotationExponentHorsepowerJouleNewtonPictorial DiagramPower of Ten NotationPrefixesProgramming LanguageResistanceSchematic DiagramScientific NotationSI SystemSPICEWatt

■ OUTLINE

IntroductionThe SI System of UnitsConverting UnitsPower of Ten NotationPrefixesCircuit DiagramsCircuit Analysis Using

Computers

■ OBJECTIVES

After studying this chapter, you will be able to• describetheSIsystemofmeasurement,• convertbetweenvarioussetsofunits,• usepoweroftennotationtosimplify

handling of large and small numbers,• expresselectricalunitsusingstandard

prefix notation such as A, kV, mW, etc.,• useasensiblenumberofsignificantdigits

in calculations,• describewhatblockdiagramsareandwhy

they are used,• convertasimplepictorialcircuittoits

schematic representation,• describegenerallyhowcomputers

and calculators fit in the electrical and electronic circuit analysis picture.

1INtroductIoN

A n electrical circuit is a system of interconnected components such as resistors, capaci-

tors, inductors, voltage sources, and so on. The electrical behavior of these components

is described by a few basic experimental laws. These laws and the principles, concepts, math-

ematical relationships, and methods of analysis that have evolved from them are known as

circuit theory.

Much of circuit theory deals with problem solving and numerical analysis. When you ana-

lyze a problem or design a circuit, for example, you are typically required to compute val-

ues for voltage, current, and power. In addition to a numerical value, your answer must include

a unit. The system of units used for this purpose is the SI system (Systéme International). The

SI system is a unified system of metric measurement; it encompasses not only the familiar MKS

(meters, kilograms, seconds) units for length, mass, and time, but also units for electrical and

magnetic quantities as well.

Quite frequently, however, the SI units yield numbers that are either too large or too small for

convenient use. To handle these, engineering notation and a set of standard prefixes have

been developed. Their use in representation and computation is described and illustrated.

Since circuit theory is somewhat abstract, diagrams are used to help present ideas. We

look at several types—schematic, pictorial, and block diagrams—and show how to use

them to represent circuits and systems.

We conclude the chapter with a brief look at computer and calculator usage in circuit

analysis. Several popular software packages are described, including Electronics Work-

bench’s Multisim®, Orcad’s PSpice®, and Mathsoft’s Mathcad®. ■

ChAPTER PREVIEw

Technology has dramatically changed the way we do things; we now have com-puters and sophisticated electronic entertainment systems in our homes, elec-tronic control systems in our cars, cellular phones that can be used just about anywhere, robots that assemble products on production lines, and so on.

A first step to understanding these technologies is electric circuit theory. Circuit theory provides you with the knowledge of basic principles that you need to understand the behavior of electric and electronic devices, circuits, and systems. In this book, we develop and explore its basic ideas—see Note 1.

Examples of the Technology at work

Before we begin, let us look at a few examples of the technology at work (see Note 2).

First, consider Figure 1 –1, which shows a home theater system. This system relies on electrical and electronic circuits, magnetic circuits, and laser technol-ogy for its operation. For example, resistors, capacitors, and integrated circuits are used to control the voltages and currents that operate its motors and to am-plify its audio and video signals, while laser circuitry is used to read data from the disks. The speaker system relies on magnetic circuits for its operation, while other magnetic circuits (the power transformers) drop the ac voltage from the 120-volt wall outlet voltage to the lower levels required to power the system.

Figure 1–2 shows another example. Here, a computer-generated screen shot of the magnetic flux pattern for an electric motor illustrates the use of computers in research and design. Programmed to apply basic magnetic circuit fundamentals to complex shapes, software packages such as that used here help make it possible to develop more efficient and better performing motors, com-puter disk drives, audio speaker systems, and the like.

Figure 1–3 shows another application, a manufacturing facility where fine pitch surface-mount (SMT) components are placed on printed circuit boards

Section 1.1 | Introduction 2120 Chapter 1 | Introduction

FIGure 1–1 A home theater system.

FIGure 1–2 Computer-generated magnetic flux pattern for a dc motor, armature only excited.

1.1 Introduction

Notes... 1. The back of the book CD

contains a selection of audio clips that expand on various topics throughout the book. To listen to these on your computer, insert the CD, click Button 3 and select the clip of interest. (Clips are organized by chapter and may be played on any mp3 player. When you see this icon, check the CD for an audio clip.)

2. As you go through the examples here, you will see components, devices and electrical quantities that have not yet been discussed. You will learn about these later. For the moment, just concentrate on the general ideas.

Robe

rt A.

Fow

kes

Putting it in PerspectiveHints on Problem Solving

During the analysis of electrical and electronic circuits, you will find yourself solving quite a few problems. An organized approach helps. Listed below are some useful guidelines:

1. Make a sketch (e.g., a circuit diagram), mark on it what you know, then identify what it is that you are trying to determine. Watch for “implied data” such as the phrase “the capacitor is initially uncharged”. (As you will find out later, this means that the initial voltage on the capacitor is zero.) Be sure to convert all implied data to explicit data e.g., Vo 0V.

2. Think through the problem to identify the principles involved, then look for relationships that tie together the unknown and known quantities.

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013

almost totally superseded. In its place the SI system is used. Table 1–1 shows a few frequently encountered quantities with units expressed in both systems.

The SI system combines the MKS metric units and the electrical units into one unified system: See Table 1–2 and Table 1–3. (Do not worry about the electrical units yet. We define them later, starting in Chapter 2.) Note that some symbols and abbreviations use capital letters while others use lowercase letters.

A few non-SI units are still in use. For example, electric motors are com-monly rated in horsepower, and wires are frequently specified in AWG sizes (American Wire Gage, Section 3.2). On occasion, you will need to convert non-SI units to SI units. Table 1–4 may be used for this purpose.

Definition of Units

When the metric system came into being in 1792, the meter was defined as one ten-millionth of the distance from the north pole to the equator and the second as

Section 1.2 | The SI System of Units 23

at high speed using laser centering and optical verification. The bottom row of Figure 1–4 shows how small these components are. Computer control pro-vides the high precision needed to accurately position parts as tiny as these. The speaker system relies on magnetic circuits for its operation, drop the ac voltage from the 120-volt wall outlet voltage required to power the system.

The solution of technical problems requires the use of units. At present, two major systems—the English (US Customary) and the metric—are in everyday use. For scientific and technical purposes, however, the English system has been

22 Chapter 1 | Introduction

Surface mountparts

FIGure 1–3 Laser centering and optical verification in a manufacturing process.

FIGure 1–4 Some typical electronic components. The small components at the bottom are surface mount parts that are installed on printed circuit boards by the machine shown in Figure 1–3.

Quantity Symbol Unit Abbreviation

Length l meter mMass m kilogram kgTime t second sElectric current I, i ampere ATemperature T kelvin K

TABLE 1–2 Some SI Base Units

Quantity Symbol Unit Abbreviation

Force F newton NEnergy W joule JPower P, p watt WVoltage V, v, E, e volt VCharge Q, q coulomb CResistance R ohm Capacitance C farad FInductance L henry HFrequency f hertz HzMagnetic flux weber WbMagnetic flux density B tesla T

TABLE 1–3 Some SI Derived Units*

*Electrical and magnetic quantities will be explained as you progress through the book. As in Table 1–2, the distinction between capitalized and lowercase letters is important.

1.2 The SI System of Units

1 meter 100 centimeters 39.37 inches1 millimeter 39.37 mils1 inch 2.54 centimeters1 foot 0.3048 meter1 yard 0.9144 meter1 mile 1.609 kilometers1 kilogram 1000 grams 2.2 pounds1 gallon (US) 3.785 liters

TABLE 1–1 Common Quantities

When You Know Multiply By To Find

Length inches (in) 0.0254 meters (m) feet (ft) 0.3048 meters (m) miles (mi) 1.609 kilometers (km)Force pounds (lb) 4.448 newtons (N)Power horsepower (hp) 746 watts (W)Energy kilowatthour (kWh) 3.6 106 joules† (J) foot-pound (ft-lb) 1.356 joules† (J)† 1 joule 1 newton-meter.

TABLE 1–4 Conversions

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PRACtICAL Note...

When a digital ohmmeter measures an open circuit, the display on the meter will usually be the digit 1 at the left-hand side, with no following digits. This reading should not be confused with a reading of 1 V, 1 kV, or 1 MV, which would appear on the right-hand side of the display.

Source: Vansco Electronics




Notes... 1. Software for technical use falls

into two broad categories—application software (such as Multisim and PSpice) and programming languages (such as Java and C11). Application software is designed to solve problems without requiring programming on the part of the user, whereas programming languages require that you write code for each type of problem to be solved. In this book, we do not consider programming languages.

2. Software tools should always be used wisely. Before you use Multisim or PSpice for example, be sure you understand the basics of the subject that you are studying, as the uninformed

of such software can result in answers that make no sense—and you need to be able to recognize this fact. This is why you should solve many problems manually with your calculator.

(continued)

The quantities in Equation 1–1 are called conversion factors. As you can see, conversion factors have a value of 1 and thus you can multiply them times any expression without changing the value of that expression. For example, to com-plete the conversion of 12 cm to inches, choose the second ratio (so that units cancel), then multiply. Thus,

12 cm 12 cm 4.72 in

When you have a chain of conversions, select factors so that all unwanted units cancel. This provides an automatic check on the final result as illustrated in part (b) of Example 1–1.

Section 1.3 | Converting Units 2524 Chapter 1 | Introduction

1.3 Converting Units

*Paraphrased from Edward C. Jordan and Keith Balmain, Electromagnetic Waves and Radi-ating Systems, Second Edition. (Englewood Cliffs, New Jersey: Prentice-Hall, Inc, 1968).

Given a speed of 60 miles per hour (mph),

a. convert it to kilometers per hour,b. convert it to meters per second.

Solution

a. 10 104 V 100 103 V 100 kilovolts 100 kV

b. 0.1 103 W 0.1 milliwatts 0.1 mW

c. 250 107 s 25 106 s 25 microseconds 25 s

You can also solve this problem by treating the numerator and denominator separately. For example, you can convert miles to meters and hours to seconds, then divide (see Example 1–2). In the final analysis, both methods are equiva-lent.The watt is also the SI unit for electrical power.

The link between electrical and mechanical units can be easily established. Consider an electrical generator. Mechanical power input produces electrical power output. If the generator were 100% efficient, then one watt of mechanical power input would yield one watt of electrical power output.

However, just how big is a watt? While the above examples suggest that the watt is quite small, in terms of the rate at which a human can work it is actu-ally quite large. For example, a person can do manual labor at a rate of about 60 watts when averaged over an 8-hour day—just enough to power a standard 60-watt electric lamp continuously over this time! A horse can do considerably better. Based on experiment, James Watt determined that a strong dray horse could average 746 watts. From this, he defined the horsepower (hp) as 1 horse-power 746 watts. This is the figure that we still use today.

Do Example 1–1(b) by expanding the top and bottom separately.

Solution

a. 10 104 V 100 103 V 100 kilovolts 100 kV



EXAMPLE 1–2

EXAMPLE 1–1

1⁄60 1⁄60 1⁄24 of the mean solar day. Later, more accurate definitions based on physical laws of nature were adopted. The meter is now defined as the distance travelled by light in a vacuum in 1/299 792 458 of a second, while the second is defined in terms of the period of a cesium-based atomic clock. The definition of the kilogram is the mass of a specific platinum-iridium cylinder (the international pro-totype), preserved at the International Bureau of Weights and Measures in France.

Relative Size of the Units*

To gain a feel for the SI units and their relative size, refer to Table 1–1 and Table 1–4. Note that 1 meter is equal to 39.37 inches; thus, 1 inch equals 1/39.37 5 0.0254 meter or 2.54 centimeters. A force of one pound is equal to 4.448 new-tons; thus, 1 newton is equal to 1/4.448 5 0.225 pound of force, which is about the force required to lift a 1⁄4-pound weight. One joule is the work done in mov-ing a distance of one meter against a force of one newton. This is about equal to the work required to raise a quarter-pound weight one meter. Raising the weight one meter in one second requires about one watt of power.

The watt is also the SI unit for electrical power. A typical electric lamp, for example, dissipates power at the rate of 60 watts, and a toaster at a rate of about 1000 watts.

The link between electrical and mechanical units can be easily established. Consider an electrical generator. Mechanical power input produces electrical power output. If the generator were 100% efficient, then one watt of mechanical power input would yield one watt of electrical power output. This clearly ties the electrical and mechanical systems of units together.


Sometimes quantities expressed in one unit must be converted to another. For example, suppose you want to determine how many kilometers there are in ten miles. Given that 1 mile is equal to 1.609 kilometers (Table 1–1), you can write 1 mi 1.609 km, using the abbreviations in Table 1–4. Now multiply both sides by 10. Thus, 10 mi 16.09 km.

This procedure is quite adequate for simple conversions. However, for complex conversions, it may be difficult to keep track of units. The procedure outlined next helps. It involves writing units into the conversion sequence, can-celling where applicable, then gathering up the remaining units to ensure that the final result has the correct units.

To get at the idea, suppose you want to convert 12 centimeters to inches. From Table 1–1, 2.54 cm 1 in. From this, you can write

10 104 V 100 103 V 100 kilovolts 100 kV (1–1)

Notes... 3. Computer software is frequently

updated, and the versions used in this book are the versions current at the time of writing (Multisim 9 and Orcad 10.).

4. Multisim® is a trademark of Electronics Workbench, a National Instruments Company, OrCAD®, OrCAD Capture® and PSpice® are all registered trademarks of Cadence Design Systems Inc., and Mathcad® is a product of Mathsoft Engineering and Education Inc.

Section 1.4 | Power of Ten Notation 2726 Chapter 1 | Introduction

PRACTICE PROBLEMS 1

1. Area pr2. Given r 8 inches, determine area in square meters (m2).

2. A car travels 60 feet in 2 seconds. Determine

a. its speed in meters per second,

b. its speed in kilometers per hour.

For part (b), use the method of Example 1–1, then check using the method of Example 1–2.

Answers1. 0.130 m2; 2. a. 9.14 ms, b. 32.9 kmh

Electrical values vary tremendously in size. In electronic systems, for example, voltages may range from a few millionths of a volt to several thousand volts, while in power systems, voltages of up to several hundred thousand are com-mon. To handle this large range, the power of ten notation (Table 1–5) is used.

To express a number in power of ten notation, move the decimal point to where you want it, then multiply the result by the power of ten needed to restore the number to its original value. Thus, 247 000 2.47 105. (The number 10 is called the base, and its power is called the exponent.) An easy way to determine the exponent is to count the number of places (right or left) that you moved the decimal point. Thus,

247 000 2 4 7 0 0 0 2.47 105

5 4 3 2 1

Similarly, the number 0.003 69 may be expressed as 3.69 103 as illustrated below.

0.003 69 0.0 0 3 6 9 3.69 103

1 2 3

Multiplication and Division Using Powers of Ten

To multiply numbers in power of ten notation, multiply their base numbers, then add their exponents. Thus,

(1.2 103)(1.5 104) (1.2)(1.5) 10(34) 1.8 107

For division, subtract the exponents in the denominator from those in the nu-merator. Thus,

1.4 Power of Ten Notation

1 000 000 106 0.000001 106

100 000 105 0.00001 105

10 000 104 0.0001 104

1 000 103 0.001 103

100 102 0.01 102

10 101 0.1 101

1 100 1 100

TABLE 1–5 Common Power of Ten Multipliers

In scientific work, it is common to find very large and very small numbers expressed in power of 10 notation. However, in engineering, certain elements of style and standard practices have evolved giving rise to what is referred to as engineering notation. In engineering notation, it is more common to use prefixes than powers of 10. The most common prefixes (along with their symbols) are listed in Table 1–6 (Note: The notation goes in powers of 10 by threes.). As an example, while a current of 0.0045 A (amperes) may be expressed as 4.5 103 A, it is preferable to express it as 4.5 mA or as 4.5 milliamps. Note also that there are often several equally ac-ceptable choices. For example, a time interval of 15 105 s may be expressed as 150 s, or as 150 microseconds, or as 0.15 ms, or as 0.15 milliseconds. Note also that it is not wrong to express the number as 15 105; it is simply not common engineering practice. From here onward, we will use engineering notation almost exclusively.

Numerical Results

While computers and calculators typically display many digits, the question is how many should you actually retain in your answer? While it is tempting to write them all down, a closer inspection shows that this may not be sensible. To see why, note that much of engineering is based on measurement. In practice for example, voltage is measured with a voltmeter and current with an ammeter. Such measured values are approximate since it is impossible to measure anything exactly. Since measured values have an element of uncertainty, computations based on them also have an element of uncertainty—see Notes. To illustrate, suppose you want to know the area of a garden and you measure the length and width as L 5.76 m and W 3.72 m.

1.5 Prefixes, Engineering Notation, and Numerical Results

Express the following in engineering notation:

a. 10 104 volts b. 0.1 103 watts c. 250 107 seconds

Solution

a. 10 104 V 100 103 V 100 kilovolts 100 kV



1. Convert 1800 kV to megavolts (MV).

2. In Chapter 4, we show that voltage is the product of current times resistance—that is, V I R, where V is in volts, I is in amperes, and R is in ohms. Given I 25 mA and R 4 k, convert these to power of ten notation, then determine V.

3. If I1 520 A, I2 0.157 mA, and I3 2.75 104 A, what is I1 I2 I3 in mA? In microamps?

Answers1. 1.8 MV; 2. 100 V; 3. 0.952 mA, 952 A

PRACTICE PROBLEMS 2

EXAMPLE 1–3


Section 1.5 | Prefixes, Engineering Notation, and Numerical Results 2928 Chapter 1 | Introduction

1. All conversion factors have a value of what?

2. Convert 14 yards to centimeters.

3. What units does the following reduce to?

4. Express each of the following as indicated.

a. 752 A in mA.

b. 0.98 mV in V.

c. 270 s 0.13 ms in s and in ms.

Electrical and electronic circuits are constructed using components such as bat-teries, switches, resistors, capacitors, transistors, interconnecting wires, etc. To represent these circuits on paper, diagrams are used. In this book, we use three types: block diagrams, schematic diagrams, and pictorials.

Block Diagrams

Block diagrams describe a circuit or system in simplified form. The overall problem is broken into blocks, each representing a portion of the system or circuit. Blocks are labelled to indicate what they do or what they contain, then interconnected to show their relationship to each other. General signal flow is usually from left to right and top to bottom. Figure 1–5, for example, represents an audio amplifier. Although you have not covered any of its circuits yet, you should be able to follow the general idea quite easily—sound is picked up by the microphone, converted to an electrical signal, amplified by a pair of ampli-fiers, then output to the speaker, where it is converted back to sound. A power supply energizes the system. The advantage of a block diagram is that it gives you the overall picture and helps you understand the general nature of a prob-lem. However, it does not provide detail.

Pictorial Diagrams

Pictorial diagrams are one of the types of diagrams that provide detail. They help you visualize circuits and their operation by showing components as they actually look physically. For example, the circuit of Figure 1–6 consists of a battery, a switch, and an electric lamp, all interconnected by wire. Operation is easy to visualize—when the switch is closed, the battery causes current in the circuit, which lights the lamp. The battery is referred to as the source and the lamp as the load.

Schematic Diagrams

While pictorial diagrams help you visualize circuits, they are cumbersome to draw. Schematic diagrams get around this by using simplified, standard sym-bols to represent components; see Table 1–7. (The meaning of these symbols will be made clear as you progress through the book.) In Figure 1–7(a), for example, we have used some of these symbols to create a schematic for the

circuit of Figure 1–6. Each component has been replaced by its corresponding circuit symbol.

When choosing symbols, choose those that are appropriate to the occasion. Consider the lamp of Figure 1–7(a). As we will show later, the lamp possesses a property called resistance. When you wish to emphasize this property, use the resistance symbol rather than the lamp symbol, as in Figure 1–7(b).

Relative Size of the Units*

To gain a feel for the SI units and their relative size, refer to Table 1–1 and Table 1–4. Note that 1 meter is equal to 39.37 inches; thus, 1 inch equals 1/39.37 0.0254 meter or 2.54 centimeters. A force of one pound is equal to 4.448 new-tons; thus, 1 newton is equal to 1/4.448 0.225 pound of force, which is about the force required to lift a 1⁄4-pound weight. One joule is the work done in mov-ing a distance of one meter against a force of one newton. This is about equal to the work required to raise a quarter-pound weight one meter. Raising the weight one meter in one second requires about one watt of power.

The watt is also the SI unit for electrical power. A typical electric lamp, for example, dissipates power at the rate of 60 watts, and a toaster at a rate of about 1000 watts.

The link between electrical and mechanical units can be easily established. Consider an electrical generator. Mechanical power input produces electrical power output. If the generator were 100% efficient, then one watt of mechanical power input would yield one watt of electrical power output. This clearly ties the electrical and mechanical systems of units together.


Examples of the Technology at work

Before we begin, let us look at a few examples of the technology at work (see Note 2).

First, consider Figure 1 –1, which shows a home theater system. This system relies on electrical and electronic circuits, magnetic circuits, and laser technol-ogy for its operation. For example, resistors, capacitors, and integrated circuits are used to control the voltages and currents that operate its motors and to am-plify its audio and video signals, while laser circuitry is used to read data from the disks. The speaker system relies on magnetic circuits for its operation, while other magnetic circuits (the power transformers) drop the ac voltage from the 120-volt wall outlet voltage to the lower levels required to power the system.

Figure 1–2 shows another example. Here, a computer-generated screen shot of the magnetic flux pattern for an electric motor illustrates the use of computers in research and design. Programmed to apply basic magnetic circuit fundamentals to complex shapes, software packages such as that used here help make it possible to develop more efficient and better performing motors, com-puter disk drives, audio speaker systems, and the like. The advantage of a block diagram is that it gives you the overall picture and helps you understand the general nature of a problem. However, it does not provide detail.

1.6 Circuit Diagrams

in-process LeArninG cHecK 1(Answers are at the end of the chapter.)

✓

c

17. You walk for 15 minutes at a rate of 2 kmh, then 18 minutes at 5 kmh, and for the remainder, your speed is 2.5 kmh. If the total distance covered is 2.85 km, how many minutes did you spend walking at 2.5 kmh?

18. You walk for 16 minutes at a rate of 1.5 mph, speed up to 3.5 mph for awhile, then slow down to 3 mph for the last 12 minutes. If the total distance covered is 1.7 miles, how long did you spend walking at 3.5 mph?

19. Your plant manager asks you to investigate two machines. The cost of electricity for operating machine #1 is 43 centsminute, while that for ma-chine #2 is $200.00 per 8-hour shift. The purchase price, production ca-pacities, maintenance costs, and long term reliability for both machines are identical. Based on this information, which machine should you purchase and why?

20. Given that 1 hp 550 ft-lbs, 1 ft 0.3048 m, 1 lb 4.448 N, 1 J 1 N-m, and 1 W 1 Js, show that 1 hp 746 W.

1.4 Power of Ten Notation

21. Express each of the following in power of ten notation with one nonzero digit to the left of the decimal point:

a. 8675 e. 0.003 48 105

b. 0.008 72 f. 0.000 215 103

c. 12.4 102 g. 14.7 100

d. 37.2 102

22. Express the answer for each of the following in power of ten notation with one nonzero digit to the left of the decimal point.

a. (17.6)(100) d. 1 107 104 10.65

b. (1400)(27 103) e. (12.5)(1000)(0.01)

c. (0.15 106)(14 104) f. (18.4 100)(100)(1.5 105)(0.001)

23. An electric fan rotates at 300 revolutions per minute. How many degrees is this per second?

24. If the surface mount robot machine of Figure 1–3 places 15 parts every 12 s, what is its placement rate per hour?

25. If your laser printer can print 8 pages per minute, how many pages can it print in one tenth of an hour?

26. A car gets 27 miles per US gallon. What is this in kilometers per liter?

27. The equatorial radius of the earth is 3963 miles. What is the earth’s circumfer-ence in kilometers at the equator?

28. A wheel rotates 18° in 0.02 s. How many revolutions per minute is this?

29. The height of horses is sometimes measured in “hands,” where 1 hand 4 inches. How many meters tall is a 16-hand horse? How many centimeters?

30. Suppose s vt is given, where s is distance travelled, v is velocity, and t is time. If you travel at v 60 mph for 500 seconds, you get upon unthinking substitution s vt (60)(500) 30,000 miles. What is wrong with this calculation? What is the correct answer?

31. A round pizza has a circumference of 47 inches. How long does it take for a pizza cutter traveling at 0.12 ms to cut diagonally across it?

32. Joe S. was asked to convert 2000 ydh to meters per second. Here is Joe’s work: velocity 2000 0.9144 6060 1828.8 ms. Determine conver-sion factors, write units into the conversion, and find the correct answer.

Problems 3130 Chapter 1 | Introduction

1.3 Converting Units

1. Perform the following conversions:

a. 27 minutes to seconds d. 35 horsepower to watts

b. 0.8 hours to seconds e. 1827 W to hp

c. 2 h 3 min 47 s to s f. 23 revolutions to degrees

2. Perform the following conversions:

a. 27 feet to meters e. 100 sq. ft to m2

b. 2.3 yd to cm f. 124 sq. in. to m2

c. 36 F to degrees C g. 47-pound force to newtons

d. 18 (US) gallons to liters

3. Set up conversion factors, compute the following, and express the answer in the units indicated.

a. The area of a plate 1.2 m by 70 cm in m2.

b. The area of a triangle with base 25 cm, height 0.5 m in m2.

c. The volume of a box 10 cm by 25 cm by 80 cm in m3.

d. The volume of a sphere with 10 in. radius in m3.

4. An electric fan rotates at 300 revolutions per minute. How many degrees is this per second?

5. If the surface mount robot machine of Figure 1–3 places 15 parts every 12 s, what is its placement rate per hour?

6. If your laser printer can print 8 pages per minute, how many pages can it print in one tenth of an hour?

7. A car gets 27 miles per US gallon. What is this in kilometers per liter?

8. The equatorial radius of the earth is 3963 miles. What is the earth’s circumfer-ence in kilometers at the equator?

9. A wheel rotates 18° in 0.02 s. How many revolutions per minute is this?

10. The height of horses is sometimes measured in “hands,” where 1 hand 4 inches. How many meters tall is a 16-hand horse? How many centimeters?

11. Suppose s vt is given, where s is distance travelled, v is velocity, and t is time. If you travel at v 60 mph for 500 seconds, you get upon unthinking substitution s vt (60)(500) 30,000 miles. What is wrong with this calculation? What is the correct answer?

12. A round pizza has a circumference of 47 inches. How long does it take for a pizza cutter traveling at 0.12 ms to cut diagonally across it?

13. Joe S. was asked to convert 2000 ydh to meters per second. Here is Joe’s work: velocity 2000 0.9144 6060 1828.8 ms. Determine conver-sion factors, write units into the conversion, and find the correct answer.

14. The mean distance from the earth to the moon is 238 857 miles. Radio signals travel at 299 792 458 ms. How long does it take a radio signal to reach the moon?

15. If you walk at a rate of 3 kmh for 8 minutes, 5 kmh for 1.25 h, then continue your walk at a rate of 4 kmh for 12 minutes, how far will you have walked in total?

16. Suppose you walk at a rate of 2 mph for 12 minutes, 4 mph for 0.75 h, then finish off at 5 mph for 15 minutes. How far have you walked in total?

problems

CircuitSim 1-1 PSPICE

MultiSim

Contents 3332 Chapter 1 | Introduction

Appendix D

CHAPTER 1

1. a. 1620 s c. 7427 s e. 2.45 hp

b. 2880 s d. 26 110 W f. 8280

3. a. 0.84 m2 c. 0.02 m3

b. 0.0625 m2 d. 0.0686 m3

5. 4500 parts/h

7. 11.5 km/l

9. 150 rpm

11. 8.33 mi

13. 0.508 m/s

15. 7.45 km

17. 20.4 min

19. Machine 1: $25.80/h; Machine 2: $25.00/h; Machine 2

21. a. 8.675 103 d. 3.72 101 g. 1.47 101

b. 8.72 103 e. 3.48 102

c. 1.24 103 f. 2.15 107

23. a. 1.25 101 c. 2.0 102

b. 8 107 d. 2.05 104

25. a. 10 c. 3.6 103 e. 12.0

b. 10 d. 15 104

29. 6.24 1018

31. 62.6 1021

33. 1.16 s

35. 13.4 1010 l/h

37. a. kilo, k c. giga, G e. milli, m

b. mega, M d. micro, f. pico, p

39. a. 1.5 ms b. 27 s c. 350 ns

41. a. 150, 0.15 b. 0.33, 33

43. a. 680 V b. 162.7 W

45. 1.5 kW

47. 187 A

49. 39 pF

53. a. 2.083 k

b. The actual value of R lies somewhere between 2.07 k and 2.10 k.

CHAPTER 2

1. a. 1029 b. 10.4 1023

3. Increases by a factor of 24.

5. a. Material with many free electrons (i.e., material with 1 electron in the valence shell).

b. Inexpensive and easily formed into wires.

c. Full valence shell. Therefore, no free electrons.

d. The large electrical force tears electrons out of orbit.

7. a. 630 N (repel) d. 8.22 108 N (attract)

b. 20 N (attract) e. Neutron is uncharged, thus F 0

c. 1.6 1014 N (repel)

9. 2 C; (Attraction)

11. 0.333 C, 1.67 C; both () or both ()

13. 30.4 C

15. 27.7 C ()

17. 24 V

19. 2400 V

21. 4.25 mJ

23. 4.75 C

25. 50 mA

27. 334 C

29. 3 mA

31. 80 A

33. 18 V, 0.966 A

35. a. 4.66 V b. 1.50 V

37. 50 h

39. 11.7 h

41. 267 h

43. (c) Both

45. The voltmeter and ammeter are interchanged.

47. If you exceed a fuse’s voltage rating, it may arc over when it “blows.”

33

33. The mean distance from the earth to the moon is 238 857 miles. Radio signals travel at 299 792 458 ms. How long does it take a radio signal to reach the moon?

34. If you walk at a rate of 3 kmh for 8 minutes, 5 kmh for 1.25 h, then continue your walk at a rate of 4 kmh for 12 minutes, how far will you have walked in total?

35. Suppose you walk at a rate of 2 mph for 12 minutes, 4 mph for 0.75 h, then finish off at 5 mph for 15 minutes. How far have you walked in total?

36. You walk for 15 minutes at a rate of 2 kmh, then 18 minutes at 5 kmh, and for the remainder, your speed is 2.5 kmh. If the total distance covered is 2.85 km, how many minutes did you spend walking at 2.5 kmh?

37. You walk for 16 minutes at a rate of 1.5 mph, speed up to 3.5 mph for awhile, then slow down to 3 mph for the last 12 minutes. If the total distance covered is 1.7 miles, how long did you spend walking at 3.5 mph?

38. Your plant manager asks you to investigate two machines. The cost of electricity for operating machine #1 is 43 centsminute, while that for ma-chine #2 is $200.00 per 8-hour shift. The purchase price, production ca-pacities, maintenance costs, and long term reliability for both machines are identical. Based on this information, which machine should you purchase and why?

39. Given that 1 hp 550 ft-lbs, 1 ft 0.3048 m, 1 lb 4.448 N, 1 J 1 N-m, and 1 W 1 Js, show that 1 hp 746 W.

in-process LeArninG cHecK 1

1. One

2. 1280 cm

3. ms

4. a. 4.27 s

b. 1.53 mV

c. 1.23 ms

5. a. 1.8 104 18 103

b. 36 104 3.6 105 0.36 106

c. 4.45 102 44.5 101

d. 27 106 2.7 105

6. a. 0.752 mA

b. 980 V

c. 400 s 0.4 ms

Answers to in-process LeArninG cHecKs✓

Contents 3534 Appendix D

CHAPTER 3

1. a. 3.6 c. 36.0 k

b. 0.90 d. 36.0 m

3. 0.407 inch

5. 300 m 986 feet

7. 982 108 m (Resistivity is less than for carbon.)

9. 2.26 108 m (This alloy is not as good a conductor as copper.)

11. AWG 22: 4.86

AWG 19: 2.42

Diameter of AWG 19 is 1.42 times the diameter of AWG 22. The resistance of AWG 19 is half the resistance of an equal length of AWG 22.

13. AWG 19 should be able to handle 4 A.

AWG 30 can handle about 0.30 A.

15. 405 meters

17. a. 256 CM b. 6200 CM c. 1910 MCM

19. a. 16.2 b. 0.668 c. 2.17 103

21. a. 4148 CM 3260 sq mil b. 0.0644 inch

23. a. 1600 CM 1260 sq mil b. 1930 feet

25. R30C 40.2 R0C 46.1 R200C 85.2

27. a. Positive temperature coefficient

b. 0.00385 (C)1

c. R0C 18.5 R100C 26.2

29. 16.8

31. T 260C

33. a. Rab 10 k Rbc 0

b. Rab 8 k Rbc 2 k

c. Rab 2 k Rbc 8 k

d. Rab 0 k Rbc 10 k

35. a. 150 k 10%

b. 2.8 5% with a reliability of 0.001%

c. 47 M 5%

d. 39 5% with a reliability of 0.1%

37. Connect the ohmmeter between the two terminals of the light bulb. If the ohmmeter indicates an open circuit, the light bulb is burned out.

41. a. 380

b. 180

c. Negative temperature coefficient. Resistance decreases as temperature increases.

43. a. 4.0 S c. 4.0 S

b. 2.0 mS d. 0.08 S

45 2.93 mS

CHAPTER 4

1. a. 2 A c. 5 mA e. 3 mA

b. 7.0 A d. 4 A f. 6 mA

3. a. 40 V c. 400 V

b. 0.3 V d. 0.36 V

5. 96

7. 28 V

9. 6 A

11. Red, Red, Red

13. 22 V

15. a. 2.31 A b. 2.14 A

17. 2.88 V

19. 4

21. 400 V

23. 3.78 mA

25. a. 45 V c. 90 V

b. 4 A (→) d. 7 A (←)

27. 3.19 J/s; 3.19 W

29. 36 W

31. 14.1 A

33. 47.5 V

35. 50 V, 5 mA

37. 37.9 A

39. 2656 W

41. 23.2 V; 86.1 mA

43. 361 W → 441 W

45. a. 48 W (→) c. 128 W (←)

b. 30 W (←) d. 240 W (→)

47. a. 1.296 106 J b. 360 Wh c. 2.88 cents

49. 26 cents

51. $5256

53. 5 cents

55. 51.5 kW

57. 82.7%

59. 2.15 hp

61. 8.8 hp

63. 1.97 hp

65. $137.45

67. a. 10 b. 13.3

CHAPTER 5

1. a. 30 V b. 90 V

3. a. 45 V b. 60 V

c. 90 V d. 105 V

5. a. 7 V b. V2 4 V V1 4 V

7. V3 12 V V4 2 V

9. a. 10 k b. 2.94 M c. 23.4 k

11. Circuit 1: 1650 , 6.06 mA Circuit 2: 18.15 k, 16.5 mA

13. a. 10 mA

b. 13 k

ac Abbreviation for alternating current; used to denote periodi-cally varying quantities such as ac current, ac voltage, and so on.

admittance (Y) A vector quantity (measured in siemens, S) that is the reciprocal of impedance. Y 1/Z.

alternating current Current that periodically reverses in direc-tion, commonly called an ac current.

alternating voltage Voltage that periodically changes in polarity, commonly called an ac voltage. The most common ac voltage is the sine wave.

American Wire Gauge (AWG) An American standard for clas-sifying wire and cable.

ammeter An instrument that measures current.

ampere (A or amp) The SI unit of electrical current, equal to a rate of flow of one coulomb of charge per second.

ampere-hour (Ah) A measure of the storage capacity of a battery.

angular frequency (v) Frequency of an ac waveform in radians/s. q 2pf where f is frequency in Hz.

apparent power (S) The power that apparently flows in an ac circuit. It has components of real power and reactive power, related by the power triangle. The magnitude of apparent power is equal to the product of effective voltage times effective current. Its unit is the VA (volt-amp).

atom The basic building block of matter. In the Bohr model, an atom consists of a nucleus of positively charged protons and un-charged neutrons, surrounded by negatively charged orbiting elec-trons. An atom normally consists of equal numbers of electrons and protons and is thus uncharged.

attenuation The amount that a signal decreases as it passes through a system. The attenuation is usually measured in decibels, dB.

audio frequency A frequency in the range of human hearing, which is typically from about 15 Hz to 20 kHz.

autotransformer A type of transformer with a partially common primary and secondary winding. Part of its energy is transferred magnetically and part conductively.

average of a waveform The mean value of a waveform, obtained by algebraically summing the areas above and below the zero axis of the waveform, divided by the cycle length of the waveform. It is equal to the dc value of the waveform as measured by an ammeter or a voltmeter.

balanced (1) For a bridge circuit, the voltage between midpoints on its arms is zero. (2) In three-phase systems, a system (or a load) that is identical for all three phases.

band-pass filter A circuit that permits signals within a range of frequencies to pass through a circuit. Signals of all other frequen-cies are prevented from passing through the circuit.

band-stop filter (or notch filter) A circuit designed to prevent signals within a range of frequencies from passing through a cir-cuit. Signals of all other frequencies freely pass through the circuit.

bandwidth (BW) The difference between the half-power fre-quencies for any resonant, band-pass, or band-stop filter. The band-width may be expressed in either hertz or radians per second.

Bode plot A straight line approximation that shows how the volt-age gain of a circuit changes with frequency.

branch A portion of a circuit that occurs between two nodes (or terminals).

branch current The current through a branch of a circuit.

buffer An amplifier having a unity voltage gain (Av = 1), very high input impedance, and very low output impedance. A buffer circuit is used to prevent loading effect.

capacitance A measure of charge storage capacity, for example, of a capacitor. A circuit with capacitance opposes a change in volt-age. Unit is the farad (F).

capacitor A device that stores electrical charges on conductive “plates” separated by an insulating material called a dielectric.

cascade Two stages of a circuit are said to be in a cascade con-nection when the output of one stage is connected to the input of the next stage.

CGS system A system of units based on centimeters, grams, and seconds.

characteristic curve(s) A relationship between output current and output voltage of a semiconductor device. Characteristic curves may also show how output varies as a function of some other param-eter such as input current, input voltage, and temperature.

charge (1) The electrical property of electrons and protons that causes a force to exist between them. Electrons are negatively charged while protons are positively charged. Charge is denoted by Q and is defined by Coulomb’s law. (2) An excess or deficiency of electrons on a body. (3) To store electric charge as in to charge a capacitor or charge a battery.

choke Another name for an inductor.

circuit A system of interconnected components such as resistors, capacitors, inductors, voltages sources, and so on.

35

Glossary

36 Glossary

circuit common The reference point in a electrical circuit from which voltages are measured.

circular mil (CM) A unit used to specify the cross-section area of a cable or wire. The circular mil is defined as the area contained in a circle having a diameter of 1 mil (0.001 inch).

coefficient of coupling (k) A measure of the flux linkage between circuits such as coils. If k 0, there is no linkage; if k 1, all of the flux produced by one coil links another. The mutual inductance M between coils is related to k by the relationship M k √

—–L1L2, where

L1 and L2 are the self-inductances of the coils.

coil A term commonly used to denote inductors or windings on transformers.

common-mode signal A signal that appears at both inputs of a differential amplifier.

conductance (G) The reciprocal of resistance. Unit is the sie-mens (S).

conductor A material through which charges move easily. Cop-per is the most common metallic conductor.

continuity of current This refers to the fact that current cannot change abruptly (i.e., in step-wise fashion) from one value to an-other in an isolated (i.e., non-coupled) inductance.

copper loss The I2R power loss in a conductor due to its resis-tance, for example the power loss in the windings of a transformer.

core The form or structure around which an inductor or the coils of a transformer are wound. The core material affects the magnetic properties of the device.

core loss Power loss in the core of a transformer or inductor due to hysteresis and eddy currents.

coulomb (C) The SI unit of electrical charge, equal to the charge carried by 6.24 1018 electrons.

Coulomb’s law An experimental law that states that the force (in Newtons) between charged particles is F Q1Q2/4pr2, where Q1 and Q2 are the charges (in coulombs), r is the distance between their centers in meters, and e is the permittivity of the medium. For air, 8.854 1012F/m.

critical temperature The temperature below which a material becomes a superconductor.

current (I or i) The rate of flow of electrical charges in a circuit, measured in amperes.

current source A practical current source can be modeled as an ideal current source in parallel with an internal impedance.

cutoff frequency, fc or vc The frequency at which the output power of a circuit is reduced to half of the maximum output power. The cutoff frequency may be measured in either hertz, (Hz) or ra-dians per second, (rad/s).

cycle One complete variation of an ac waveform.

decade A tenfold change in frequency.

decibel (dB) A logarithmic unit used to represent an increase (or decrease) in power levels or sound intensity.

delta () A small change (increment or decrement) in a variable. For example, if current changes a small amount from i1 to i2, its in-crement is i i2 i1, while if time changes a small amount from t1 to t2, its increment is t t2 t1.

delta load A configuration of circuit components connected in the shape of a (Greek letter delta). Sometimes called a pi (p) load.

derivative The instantaneous rate of change of a function. It is the slope of the tangent to the curve at the point of interest.

dielectric An insulating material. The term is commonly used with reference to the insulating material between the plates of a capacitor.

dielectric constant () A common name for permittivity.

differentiator A circuit whose output is proportional to the de-rivative of its input.

diode A two-terminal component made of semiconductor mate-rial, which permits current in one direction while preventing cur-rent in the opposite direction.

direct current (dc) Unidirectional current such as that from a battery.

DMM A digital multimeter that displays results on a numeric readout. In addition to voltage, current, and resistance, some dmms measure other quantities such as frequency and capacitance.

duty cycle The ratio of on time to the duration of a pulse wave-form, expressed in percent.

eddy current A small circulating current. Usually refers to the unwanted current that is induced in the core of an inductor or trans-former by changing core flux.

effective resistance Resistance defined by R P/I2. For AC, ef-fective resistance is larger than dc resistance due to skin effect and other effects such as power losses.

effective value An equivalent dc value of a time varying wave-form, hence, that value of dc that has the same heating effect as the given waveform. Also called rms (root mean square) value. For sinusoidal current, Ieff 0.707 Im, where Im is the amplitude of the ac waveform.

efficiency (h) The ratio of output power to input power, usually expressed as a percentage. h Pout/Pin 100%.

electron A negatively charged atomic particle. See atom.

energy (W) The ability to do work. Its SI unit is the joule; electri-cal energy is also measured in kilowatt-hours (kWh).

engineering notation A method of representing certain common powers of 10 via standard prefixes—for example, 0.125 A as 125 mA.

fall time (tf) The time it takes for a pulse or step to change from its 90% value to its 10% value.

farad (F) The SI unit of capacitance, named in honor of Michael Faraday.

ferrite A magnetic material made from powdered iron oxide. Provides a good path for magnetic flux and has low enough eddy current losses that it is used as a core material for high frequency inductors and transformers.

field A region in space where a force is felt, hence a force field. For example, magnetic fields exist around magnets and electric fields exist around electric charges.

field intensity The strength of a field.

filter A circuit that passes certain frequencies while rejecting all other frequencies.

flux A way of representing and visualizing force fields by draw-ing lines that show the strength and direction of a field at all points in space. Commonly used to depict electric or magnetic fields.

free electron An electron that is weakly bound to its parent atom and is thus easily broken free. For materials like copper, there are

ABC phase sequence, 843–844Absolute

dielectric constant, 321–322temperature, inferred, 61zero, 61

Absorption, dielectric, 326AC adaptors, 40–41AC circuits

active power, 545amplitude, 470angle, 471–474apparent power, 551–552applications, impedance, 604–607average values, 487–492band-pass filters, 777–780band-reject filters, 780–781bridge, 646–651capacitive load, power to, 547–548computer analysis, 499–501decibels, multistage systems, 754–756decibels, overview, 748–754Delta, 643–646dependent sources, 628–629dependent sources, Norton’s theorem, 678–686dependent sources, superposition theorem, 667–669dependent sources, Thévenin’s theorem, 678–686derivative, sine wave, 497effective resistance, 561–562effective values, 492–497energy formulas, 562–563formula, 471frequency, 468, 599–603graphing, 474–475high-pass filters, 772–776impedance, computer analysis, 607–612, 690–694impedance, problems, 613–625, 655–661, 695–701independent sources, 628independent sources, Norton’s theorem, 673–678independent sources, superposition theorem, 664–667independent sources, Thévenin’s theorem, 669–673inductive load, power to, 546–547instantaneous power, 544loop analysis, 632–637low-pass filters, 766–772maximum power transfer theorem, 686–689mesh analysis, 632–637

multimeters, 497–499nodal analysis, 637–643Norton’s theorem, 673–686Ohm’s law, 574–579overview, 462parallel, 588–595parallel resonant, 725–733parallel, current divider rule, 593–596parallel, Kirchhoff’s current law, 593–596parallel, resonant, series, 719–725peak value, 470peak-to-peak voltage, 470period, 468–469phase shifts, 477–479phasors, 479–487Pi, 643–646power factor, 555power triangle, 552–555power, complex circuits, 549–551power, computer analysis, 563–564power, problems, 564–569problems, 501–507radian measure, 473–474reactive power, 545resistive load, power to, 545–546resonant, problems, 737–745RMS values, 492–497series, 579–585series resonant, bandwidth, 712–719series resonant, impedance, 711–712series resonant, overview, 707–708series resonant, parallel, 719–725series resonant, power, 712–719series resonant, quality factor, 708–711series resonant, selectivity, 712–719series, Kirchhoff’s voltage law, 586–588series, voltage divider rule, 586–588series-parallel, 596–599source conversion, 629–632superimposed dc, 491–492superposition theorem, 664–669Tee, 643–646Thévenin’s theorem, 669–673, 678–686three-phase voltage generation, balanced system,

power, 856–861three-phase voltage generation, computer analysis, 867–869

37

Index

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