1. Electrical Engineering

2. Newnes Know It All SeriesPIC Microcontrollers: Know It AllLucio Di Jasio, Tim Wilmshurst, Dogan Ibrahim, John Morton, Martin Bates, Jack Smith, D.W. Smith, andChuck HellebuyckISBN: 978-0-7506-8615-0Embedded Software: Know It AllJean Labrosse, Jack Ganssle, Tammy Noergaard, Robert Oshana, Colin Walls, Keith Curtis, Jason Andrews,David J. Katz, Rick Gentile, Kamal Hyder, and Bob PerrinISBN: 978-0-7506-8583-2Embedded Hardware: Know It AllJack Ganssle, Tammy Noergaard, Fred Eady, Lewin Edwards, David J. Katz, Rick Gentile, Ken Arnold,Kamal Hyder, and Bob PerrinISBN: 978-0-7506-8584-9Wireless Networking: Know It AllPraphul Chandra, Daniel M. Dobkin, Alan Bensky, Ron Olexa, David Lide, and Farid DowlaISBN: 978-0-7506-8582-5RF & Wireless Technologies: Know It AllBruce Fette, Roberto Aiello, Praphul Chandra, Daniel Dobkin, Alan Bensky, Douglas Miron, David Lide,Farid Dowla, and Ron OlexaISBN: 978-0-7506-8581-8Electrical Engineering: Know It AllClive Maxeld, Alan Bensky, John Bird, W. Bolton, Izzat Darwazeh, Walt Kester, M.A. Laughton, AndrewLeven, Luis Moura, Ron Schmitt, Keith Sueker, Mike Tooley, DF Warne, Tim WilliamsISBN: 978-1-85617-528-9Audio Engineering: Know It AllDouglas Self, Richard Brice, Don Davis, Ben Duncan, John Linsely Hood, Morgan Jones, Eugene Patronis,Ian Sinclair, Andrew Singmin, John WatkinsonISBN: 978-1-85617-526-5Circuit Design: Know It AllDarren Ashby, Bonnie Baker, Stuart Ball, John Crowe, Barrie Hayes-Gill, Ian Grout, Ian Hickman, WaltKester, Ron Mancini, Robert A. Pease, Mike Tooley, Tim Williams, Peter Wilson, Bob ZeidmanISBN: 978-1-85617-527-2Test and Measurement: Know It AllJon Wilson, Stuart Ball, GMS de Silva, Tony Fischer-Cripps, Dogan Ibrahim, Kevin James, Walt Kester,M A Laughton, Chris Nadovich, Alex Porter, Edward Ramsden, Stephen Scheiber, Mike Tooley, D. F. Warne,Tim WilliamsISBN: 978-1-85617-530-2Mobile Wireless Security: Know It AllPraphul Chandra, Alan Bensky, Tony Bradley, Chris Hurley, Steve Rackley, John Rittinghouse, JamesRansome, Timothy Stapko, George Stefanek, Frank Thornton, Chris Lanthem, John WilsonISBN: 978-1-85617-529-6For more information on these and other Newnes titles visit: www.newnespress.com 3. Electrical Engineering Clive MaxeldJohn Bird M. A.Laughton W. Bolton Andrew LevenRon SchmittKeith Sueker Tim Williams Mike TooleyLuis Moura Izzat DarwazehWalt Kester Alan Bensky DF WarneAMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGOSAN FRANCISCO SINGAPORE SYDNEY TOKYONewnes is an imprint of Elsevier 4. Newnes is an imprint of Elsevier30 Corporate Drive, Suite 400, Burlington, MA 01803, USALinacre House, Jordan Hill, Oxford OX2 8DP, UKCopyright 2008, Elsevier Inc. All rights reserved.No part of this publication may be reproduced, stored in a retrieval system, or transmitted inany form or by any means, electronic, mechanical, photocopying, recording, or otherwise,without the prior written permission of the publisher.Permissions may be sought directly from Elseviers Science & Technology RightsDepartment in Oxford, UK: phone: (44) 1865 843830, fax: (44) 1865 853333,E-mail: permissions@elsevier.com. You may also complete your request onlinevia the Elsevier homepage (http://elsevier.com), by selecting Support & Contactthen Copyright and Permission and then Obtaining Permissions.Library of Congress Cataloging-in-Publication DataApplication submittedBritish Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library.ISBN: 978-1-85617-528-9 For information on all Newnes publications visit our Web site at www.elsevierdirect.comTypeset by Charon Tec Ltd., A Macmillan Company. (www.macmillansolutions.com)Printed in the United States of America08 09 10 10 9 8 7 6 5 4 3 2 1 5. ContentsAbout the Authors .............................................................................................................xvChapter 1: An Introduction to Electric Circuits ................................................................11.1 SI Units .......................................................................................................................11.2 Charge .........................................................................................................................21.3 Force ...........................................................................................................................21.4 Work ............................................................................................................................31.5 Power ..........................................................................................................................41.6 Electrical Potential and e.m.f. .....................................................................................51.7 Resistance and Conductance .......................................................................................51.8 Electrical Power and Energy .......................................................................................61.9 Summary of Terms, Units and Their Symbols............................................................71.10 Standard Symbols for Electrical Components ............................................................81.11 Electric Current and Quantity of Electricity ...............................................................81.12 Potential Difference and Resistance .........................................................................101.13 Basic Electrical Measuring Instruments ...................................................................111.14 Linear and Nonlinear Devices ..................................................................................111.15 Ohms Law ................................................................................................................121.16 Multiples and Submultiples ......................................................................................131.17 Conductors and Insulators ........................................................................................161.18 Electrical Power and Energy .....................................................................................161.19 Main Effects of Electric Current ...............................................................................20Chapter 2: Resistance and Resistivity ..............................................................................212.1 Resistance and Resistivity.........................................................................................212.2 Temperature Coefcient of Resistance .....................................................................25Chapter 3: Series and Parallel Networks .........................................................................313.1 Series Circuits ...........................................................................................................313.2 Potential Divider .......................................................................................................34 w w w.ne w nespress.com 6. viContents3.3 Parallel Networks ......................................................................................................373.4 Current Division........................................................................................................433.5 Relative and Absolute Voltages ................................................................................48Chapter 4: Capacitors and Inductors ...............................................................................534.1 Introduction to Capacitors ........................................................................................534.2 Electrostatic Field .....................................................................................................534.3 Electric Field Strength ..............................................................................................554.4 Capacitance ...............................................................................................................564.5 Capacitors .................................................................................................................564.6 Electric Flux Density ................................................................................................584.7 Permittivity ...............................................................................................................594.8 The Parallel Plate Capacitor......................................................................................614.9 Capacitors Connected in Parallel and Series ............................................................644.10 Dielectric Strength ....................................................................................................704.11 Energy Stored............................................................................................................714.12 Practical Types of Capacitors....................................................................................724.13 Inductance .................................................................................................................764.14 Inductors ...................................................................................................................784.15 Energy Stored............................................................................................................80Chapter 5: DC Circuit Theory ..........................................................................................815.1 Introduction ...............................................................................................................815.2 Kirchhoffs Laws ......................................................................................................815.3 The Superposition Theorem......................................................................................895.4 General DC Circuit Theory.......................................................................................955.5 Thvenins Theorem .................................................................................................995.6 Constant-Current Source.........................................................................................1065.7 Nortons Theorem ...................................................................................................1075.8 Thvenin and Norton Equivalent Networks............................................................1115.9 Maximum Power Transfer Theorem .......................................................................117Chapter 6: Alternating Voltages and Currents ..............................................................1236.1 The AC Generator ...................................................................................................1236.2 Waveforms ..............................................................................................................124w ww. n e w n e s p r e s s .c o m 7. Contents vii6.3 AC Values ...............................................................................................................1266.4 The Equation of a Sinusoidal Waveform ................................................................1336.5 Combination of Waveforms ....................................................................................1396.6 Rectication ............................................................................................................146Chapter 7: Complex Numbers ........................................................................................1497.1 Introduction .............................................................................................................1497.2 Operations involving Cartesian Complex Numbers ...............................................1527.3 Complex Equations .................................................................................................1557.4 The polar Form of a Complex Number...................................................................1577.5 Applying Complex Numbers to Series AC Circuits ...............................................1587.6 Applying Complex Numbers to Parallel AC Circuits .............................................171Chapter 8: Transients and Laplace Transforms ............................................................1858.1 Introduction .............................................................................................................1858.2 Response of R-C Series Circuit to a Step Input ......................................................1858.3 Response of R-L Series Circuit to a Step Input ......................................................1928.4 L-R-C Series Circuit Response ...............................................................................1998.5 Introduction to Laplace Transforms........................................................................2058.6 Inverse Laplace Transforms and the Solution of Differential Equations ................215Chapter 9: Frequency Domain Circuit Analysis ...........................................................2299.1 Introduction .............................................................................................................2299.2 Sinusoidal AC Electrical Analysis ..........................................................................2299.3 Generalized Frequency Domain Analysis ..............................................................257References ...............................................................................................................315Chapter 10: Digital Electronics ......................................................................................31710.1 Semiconductors .......................................................................................................31710.2 Semiconductor Diodes ............................................................................................31810.3 Bipolar Junction Transistors ...................................................................................31910.4 Metal-oxide Semiconductor Field-effect Transistors .............................................32110.5 The transistor as a Switch .......................................................................................32210.6 Gallium Arsenide Semiconductors .........................................................................32410.7 Light-emitting Diodes .............................................................................................32410.8 BUF and NOT Functions ........................................................................................327 w w w.ne w nespress.com 8. viii Contents10.9AND, OR, and XOR Functions ............................................................................32910.10 NAND, NOR, and XNOR Functions ....................................................................32910.11 Not a Lot ...............................................................................................................33110.12 Functions Versus Gates .........................................................................................33210.13 NOT and BUF Gates .............................................................................................33310.14 NAND and AND Gates ........................................................................................33510.15 NOR and OR Gates...............................................................................................33610.16 XNOR and XOR Gates .........................................................................................33710.17 Pass-Transistor Logic............................................................................................33910.18 Combining a Single Variable With Logic 0 or Logic 1 ........................................34210.19 The Idempotent Rules ...........................................................................................34210.20 The Complementary Rules ...................................................................................34310.21 The Involution Rules .............................................................................................34410.22 The Commutative Rules .......................................................................................34410.23 The Associative Rules...........................................................................................34410.24 Precedence of Operators .......................................................................................34510.25 The First Distributive Rule ...................................................................................34610.26 The Second Distributive Rule ...............................................................................34610.27 The Simplication Rules ......................................................................................34810.28 DeMorgan Transformations ..................................................................................34910.29 Minterms and Maxterms .......................................................................................35110.30 Sum-of-Products and Product-of-sums .................................................................35110.31 Canonical Forms ...................................................................................................35210.32 Karnaugh Maps .....................................................................................................35310.33 Minimization Using Karnaugh Maps ...................................................................35410.34 Grouping Minterms...............................................................................................35510.35 Incompletely Specied Functions .........................................................................35610.36 Populating Maps Using 0s versus 1s.....................................................................35910.37 Scalar Versus Vector Notation ..............................................................................36010.38 Equality Comparators ...........................................................................................36110.39 Multiplexers ..........................................................................................................36310.40 Decoders ...............................................................................................................36410.41 Tri-State Functions................................................................................................36510.42 Combinational Versus Sequential Functions ........................................................36710.43 RS Latches ............................................................................................................367w ww. n e w n e s p r e s s .c o m 9. Contents ix10.44D-Type Latches .....................................................................................................37310.45D-Type Flip-Flops.................................................................................................37410.46JK and T Flip-Flops ..............................................................................................37710.47Shift Registers .......................................................................................................37810.48Counters ................................................................................................................38110.49Setup and Hold Times ...........................................................................................38310.50Brick by Brick .......................................................................................................38410.51State Diagrams ......................................................................................................38610.52State Tables ...........................................................................................................38710.53State Machines ......................................................................................................38810.54State Assignment ..................................................................................................38910.55Dont Care States, Unused States, and Latch-Up Conditions...............................392Chapter 11: Analog Electronics .....................................................................................39511.1 Operational Ampliers Dened ............................................................................39511.2 Symbols and Connections .....................................................................................39511.3 Operational Amplier Parameters ........................................................................39711.4 Operational Amplier Characteristics ..................................................................40211.5 Operational Amplier Applications......................................................................40311.6 Gain and Bandwidth .............................................................................................40511.7 Inverting Amplier With Feedback ......................................................................40611.8 Operational Amplier Congurations ..................................................................40811.9 Operational Amplier Circuits .............................................................................41211.10 The Ideal Op-Amp ................................................................................................41811.11 The Practical Op-Amp ..........................................................................................42011.12 Comparators ..........................................................................................................45011.13 Voltage References................................................................................................459Chapter 12: Circuit Simulation ......................................................................................46512.1 Types of Analysis ..................................................................................................46612.2 Netlists and Component Models ...........................................................................47612.3 Logic Simulation...................................................................................................479Chapter 13: Interfacing ..................................................................................................48113.1 Mixing Analog and Digital ...................................................................................48113.2 Generating Digital Levels From Analog Inputs....................................................484w w w.ne w nespress.com 10. xContents13.3Classic Data Interface Standards ..........................................................................48713.4High Performance Data Interface Standards.........................................................493Chapter 14: Microcontrollers and Microprocessors......................................................49914.1 Microprocessor Systems .......................................................................................49914.2 Single-Chip Microcomputers ................................................................................49914.3 Microcontrollers....................................................................................................50014.4 PIC Microcontrollers ............................................................................................50014.5 Programmed Logic Devices ..................................................................................50014.6 Programmable Logic Controllers..........................................................................50114.7 Microprocessor Systems .......................................................................................50114.8 Data Representation ..............................................................................................50314.9 Data Types ............................................................................................................50514.10 Data Storage ..........................................................................................................50514.11 The Microprocessor ..............................................................................................50614.12 Microprocessor Operation ....................................................................................51214.13 A Microcontroller System ....................................................................................51814.14 Symbols Introduced in this Chapter......................................................................523Chapter 15: Power Electronics .......................................................................................52515.1 Switchgear ............................................................................................................52515.2 Surge Suppression.................................................................................................52815.3 Conductors ............................................................................................................53015.4 Capacitors .............................................................................................................53315.5 Resistors ................................................................................................................53615.6 Fuses .....................................................................................................................53815.7 Supply Voltages ....................................................................................................53915.8 Enclosures .............................................................................................................53915.9 Hipot, Corona, and BIL ........................................................................................54015.10 Spacings ................................................................................................................54115.11 Metal Oxide Varistors ...........................................................................................54215.12 Protective Relays ..................................................................................................54315.13 Symmetrical Components .....................................................................................54415.14 Per Unit Constants ................................................................................................54615.15 Circuit Simulation .................................................................................................547w ww. n e w n e s p r e s s .c o m 11. Contentsxi15.16 Simulation Software .............................................................................................55115.17 Feedback Control Systems....................................................................................55215.18 Power Supplies......................................................................................................559Chapter 16: Signals and Signal Processing ...................................................................60916.1 Origins of Real-World Signals and their Units of Measurement ..........................60916.2 Reasons for Processing Real-World Signals .........................................................61016.3 Generation of Real-World Signals ........................................................................61216.4 Methods and Technologies Available for Processing Real-World Signals ...........61216.5 Analog Versus Digital Signal Processing .............................................................61316.6 A Practical Example .............................................................................................614References .............................................................................................................617Chapter 17: Filter Design ...............................................................................................61917.1 Introduction ...........................................................................................................61917.2 Passive Filters .......................................................................................................62117.3 Active Filters .........................................................................................................62217.4 First-Order Filters .................................................................................................62817.5 Design of First-Order Filters.................................................................................63017.6 Second-Order Filters .............................................................................................63217.7 Using the Transfer Function .................................................................................63617.8 Using Normalized Tables ......................................................................................64117.9 Using Identical Components .................................................................................64117.10 Second-Order High-Pass Filters ...........................................................................64217.11 Bandpass Filters ....................................................................................................65017.12 Switched Capacitor Filter .....................................................................................65417.13 Monolithic Switched Capacitor Filter...................................................................65717.14 The Notch Filter ....................................................................................................65917.15 Choosing Components for Filters .........................................................................66317.16 Testing Filter Response .........................................................................................66517.17 Fast Fourier Transforms ........................................................................................66617.18 Digital Filters ........................................................................................................694References .............................................................................................................732Chapter 18: Control and Instrumentation Systems .......................................................73518.1 Introduction ...........................................................................................................735 w w w.ne w nespress.com 12. xii Contents18.2 Systems .................................................................................................................73718.3 Control Systems Models .......................................................................................74118.4 Measurement Elements .........................................................................................74718.5 Signal Processing ..................................................................................................76118.6 Correction Elements .............................................................................................76918.7 Control Systems ....................................................................................................78018.8 System Models ......................................................................................................79118.9 Gain .......................................................................................................................79318.10Dynamic Systems .................................................................................................79718.11Differential Equations ...........................................................................................81218.12Transfer Function ..................................................................................................81618.13System Transfer Functions ...................................................................................82218.14Sensitivity .............................................................................................................82618.15Block Manipulation ..............................................................................................83018.16Multiple Inputs ......................................................................................................835Chapter 19: Communications Systems...........................................................................83719.1 Introduction ...........................................................................................................83719.2 Analog Modulation Techniques ............................................................................83919.3 The Balanced Modulator/Demodulator ................................................................84819.4 Frequency Modulation and Demodulation ...........................................................85019.5 FM Modulators .....................................................................................................86019.6 FM Demodulators .................................................................................................86219.7 Digital Modulation Techniques.............................................................................86519.8 Information Theory ...............................................................................................87319.9 Applications and Technologies .............................................................................899References .............................................................................................................951Chapter 20: Principles of Electromagnetics ..................................................................95320.1 The Need for Electromagnetics ............................................................................95320.2 The Electromagnetic Spectrum .............................................................................95520.3 Electrical Length ...................................................................................................96020.4 The Finite Speed of Light .....................................................................................96020.5 Electronics ............................................................................................................96120.6 Analog and Digital Signals ...................................................................................96420.7 RF Techniques ......................................................................................................964w ww. n e w n e s p r e s s .c o m 13. Contents xiii20.8Microwave Techniques .........................................................................................96720.9Infrared and the Electronic Speed Limit ...............................................................96820.10 Visible Light and Beyond .....................................................................................96920.11 Lasers and Photonics ............................................................................................97120.12 Summary of General Principles ............................................................................97220.13 The Electric Force Field........................................................................................97320.14 Other Types of Fields ............................................................................................97520.15 Voltage and Potential Energy ................................................................................97620.16 Charges in Metals .................................................................................................97820.17 The Denition of Resistance.................................................................................98020.18 Electrons and Holes ..............................................................................................98020.19 Electrostatic Induction and Capacitance ...............................................................98220.20 Insulators (dielectrics)...........................................................................................98620.21 Static Electricity and Lightning ............................................................................98820.22 The Battery Revisited ...........................................................................................99220.23 Electric Field Examples ........................................................................................99320.24 Conductivity and Permittivity of Common Materials...........................................994References .............................................................................................................995Chapter 21: Magnetic Fields ........................................................................................100321.1 Moving Charges: Source of All Magnetic Fields ...............................................100321.2 Magnetic Dipoles ................................................................................................100521.3 Effects of the Magnetic Field ..............................................................................100821.4 The Vector Magnetic Potential and Potential Momentum ..................................101821.5 Magnetic Materials .............................................................................................101921.6 Magnetism and Quantum Physics.......................................................................1022References ...........................................................................................................1024Chapter 22: Electromagnetic Transients and EMI .....................................................102722.1 Line Disturbances ...............................................................................................102722.2 Circuit Transients ................................................................................................102822.3 Electromagnetic Interference ..............................................................................1030Chapter 23: Traveling Wave Effects .............................................................................103323.1 Basics ..................................................................................................................103323.2 Transient Effects .................................................................................................103523.3 Mitigating Measures ...........................................................................................1038w w w.ne w nespress.com 14. xiv ContentsChapter 24: Transformers ............................................................................................103924.1 Voltage and Turns Ratio ......................................................................................1040Chapter 25: Electromagnetic Compatibility (EMC) ....................................................104725.1 Introduction .........................................................................................................104725.2 Common Terms...................................................................................................104825.3 The EMC Model .................................................................................................104925.4 EMC Requirements.............................................................................................105225.5 Product design.....................................................................................................105425.6 Device Selection .................................................................................................105625.7 Printed Circuit Boards ........................................................................................105625.8 Interfaces .............................................................................................................105725.9 Power Supplies and Power-Line Filters ..............................................................105825.10 Signal Line Filters ...............................................................................................105925.11 Enclosure Design ................................................................................................106125.12 Interface Cable Connections ...............................................................................106325.13 Golden Rules for Effective Design for EMC ......................................................106525.14 System Design ....................................................................................................106625.15 Buildings .............................................................................................................106925.16 Conformity Assessment ......................................................................................107025.17 EMC Testing and Measurements ........................................................................107225.18 Management Plans ..............................................................................................1075References ...........................................................................................................1076Appendix A: General Reference ...................................................................................1077A.1 Standard Electrical QuantitiesTheir Symbols and Units ................................1077Appendix B: ...................................................................................................................1081B.1 Differential Equations .........................................................................................1081Index ..............................................................................................................................1091Note from the Publisher: The authors of this book are from around the world and as suchsymbols vary between US and UK styles.ww w. n e w n e s p r e s s .c o m 15. About the AuthorsAlan Bensky MScEE (Chapter 19) is an electronics engineering consultant with over25 years of experience in analog and digital design, management, and marketing.Specializing in wireless circuits and systems, Bensky has carried out projects forvaried military and consumer applications. He is the author of Short-range WirelessCommunication, Second Edition, published by Elsevier, 2004, and has written severalarticles in international and local publications. He has taught courses and gives lectureson radio engineering topics. Bensky is a senior member of IEEE.John Bird BSc (Hons), CEng, CMath, CSci, FIET, MIEE, FIIE, FIMA, FCollT RoyalNaval School of Marine Engineering, HMS Sultan, Gosport; formerly University ofPortsmouth and Highbury College, Portsmouth, U.K., (Chapters 1, 2, 3, 4, 5, 6, 7, 8,Appendix A) is the author of Electrical Circuit Theory and Technology, and over 120textbooks on engineering and mathematical subjects, is the former Head of AppliedElectronics in the Faculty of Technology at Highbury College, Portsmouth, U.K.More recently, he has combined freelance lecturing at the University of Portsmouth,with technical writing and Chief Examiner responsibilities for City and GuildsTelecommunication Principles and Mathematics, and examining for the InternationalBaccalaureate Organisation.John Bird is currently a Senior Training Provider at the Royal Naval School of MarineEngineering in the Defence College of Marine and Air Engineering at H.M.S. Sultan,Gosport, Hampshire, U.K. The school, which serves the Royal Navy, is one of Europeslargest engineering training establishments.Bill Bolton (Chapter 18, Appendix B.) is the author of Control Systems, and manyengineering textbooks, including the best-selling books Programmable Logic Controllers(Newnes) and Mechatronics (PearsonPrentice-Hall), and has formerly been a seniorlecturer in a College of Technology, Head of Research, Development and Monitoringat the Business and Technician Education Council, a member of the Nufeld AdvancedPhysics Project, and a consultant on a British Government Technician Education Projectin Brazil and on Unesco projects in Argentina and Thailand.w w w.ne w nespress.com 16. xvi About the AuthorsIzzat Darwazeh (Chapter 9) is the author of Introduction to Linear Circuit Analysis andModelling. He holds the University of London Chair of Communications Engineeringin the Department of Electronic and Electrical at UCL. He obtained his rst degreein Electrical Engineering from the University of Jordan in 1984 and the MSc andPhD degrees, from the University of Manchester Institute of Science and Technology(UMIST), in 1986 and 1991, respectively. He worked as a research Fellow at theUniversity of Wales-BangorU.K. from 1990 till 1993, researching very high speedoptical systems and circuits. He was a Senior Lecturer in Optoelectronic Circuits andSystems in the Department at Electrical Engineering and Electronics at UMIST. Hemoved to UCL in October 2001 where he is currently the Head of Communicationsand Information System (CIS) group and the Director of UCL Telecommunications forIndustry Programme. He is a Fellow of the IET and a Senior Member of the IEEE.His teaching covers aspects of wireless and optical bre communications,telecommunication networks, electronic circuits and high speed integrated circuitsand MMICs. He lectures widely in the U.K. and overseas. His research interests aremainly in the areas of wireless system design and implementation, high speed opticalcommunication systems and networks, microwave circuits and MMICs for optical breapplications and in mobile and wireless communication circuits and systems. He hasauthored/co-authored more than 120 research papers. He has co-authored (with LuisMoura) a book on Linear Circuit Analysis and Modelling (Elsevier 2005) and is theco-editor of the IEE book on Analogue Optical Communications (IEE 1995). Hecollaborates with various telecommunications and electronic industries in the U.K. andoverseas and has acted as a consultant to various academic, industrial, nancial andgovernment organisations.Walt Kester (Chapters 16, 17) is the author of Mixed-Signal and DSP Design Techniques.He is a corporate staff applications engineer at Analog Devices. For over 35 years atAnalog Devices, he has designed, developed, and given applications support for high-speed ADCs, DACs, SHAs, op amps, and analog multiplexers. Besides writing manypapers and articles, he prepared and edited eleven major applications books which form thebasis for the Analog Devices world-wide technical seminar series including the topics ofop amps, data conversion, power management, sensor signal conditioning, mixed-signal,and practical analog design techniques. He also is the editor of The Data ConversionHandbook, a 900 page comprehensive book on data conversion published in 2005 byElsevier. Walt has a BSEE from NC State University and MSEE from Duke University.w ww. n e w n e s p r e s s .c o m 17. About the AuthorsxviiMichael Laughton BASc, (Toronto), PhD (London), DSc (Eng.) (London), FREng,FIEE, CEng (Chapters 25) is the editor of Electrical Engineers Reference Book, 16thEdition. He is the Emeritus Professor of Electrical Engineering of the University ofLondon and former Dean of Engineering of the University and Pro-Principal of QueenMary and Westeld College, and is currently the U.K. representative on the EnergyCommittee of the European National Academies of Engineering, a member of energy andenvironment policy advisory groups of the Royal Academy of Engineering, the RoyalSociety and the Institution of Electrical Engineers as well as the Power Industry DivisionBoard of the Institution of Mechanical Engineers. He has acted as Specialist Adviserto U.K. Parliamentary Committees in both upper and lower Houses on alternative andrenewable energy technologies and on energy efciency. He was awarded The Institutionof Electrical Engineers Achievement Medal in 2002 for sustained contributions toelectrical power engineering.Andrew Leven (Chapter 17, 19) is the author of Telecommunications Circuits andTechnology. He holds a diploma in Radio Technology, HNC, BSc (Hons) Electronics,MSc Astronomy, C. Eng M.I.E.E, Teaching Diploma, M.I.P., International Education andTraining Consultant (Formerly Senior Lecturer in Telecommunications, Electronics andFibre Optics at James Watt College of Higher Education, U.K.)A. Maddocks (Chapter 25) was a contributor to Electrical Engineers Reference Book,16th Edition.Clive Max Maxeld (Chapter 10) is the author of Bebop to the Boolean Boogie. Heis six feet tall, outrageously handsome, English and proud of it. In addition to being ahero, trendsetter, and leader of fashion, he is widely regarded as an expert in all aspects ofelectronics and computing (at least by his mother).After receiving his B.Sc. in Control Engineering in 1980 from Shefeld Polytechnic (nowShefeld Hallam University), England, Max began his career as a designer of centralprocessing units for mainframe computers. During his career, he has designed everythingfrom ASICs to PCBs and has meandered his way through most aspects of ElectronicsDesign Automation (EDA). To cut a long story short, Max now nds himself Presidentof TechBites Interactive (www.techbites.com). A marketing consultancy, TechBitesspecializes in communicating the value of its clients technical products and servicesto non-technical audiences through a variety of media, including websites, advertising,technical documents, brochures, collaterals, books, and multimedia. w w w.ne w nespress.com 18. xviii About the AuthorsIn addition to numerous technical articles and papers appearing in magazines andat conferences around the world, Max is also the author and co-author of a numberof books, including Bebop to the Boolean Boogie (An Unconventional Guide toElectronics), Designus Maximus Unleashed (Banned in Alabama), Bebop BYTES Back(An Unconventional Guide to Computers), EDA: Where Electronics Begins, The DesignWarriors Guide to FPGAs, and How Computers Do Math (www.diycalculator.com).In his spare time (Ha!), Max is co-editor and co-publisher of the web-deliveredelectronics and computing hobbyist magazine EPE Online (www.epemag.com). Maxalso acts as editor for the Programmable Logic DesignLine website (www.pldesignline.com) and for the iDESIGN section of the Chip Design Magazine website (www.chipdesignmag.com).On the off-chance that youre still not impressed, Max was once referred to as anindustry notable and a semiconductor design expert by someone famous who wasntprompted, coerced, or remunerated in any way!Luis Moura (Chapter 9) is the author of Introduction to Linear Circuit Analysis andModelling. He received the diploma degree in electronics and telecommunications fromthe University of Aveiro, Portugal, in 1991, and the PhD degree in electronic engineeringfrom the University of North Wales, Bangor, U.K. in 1995. From 1995 to 1997 he workedas a research Fellow in the Telecommunications Research Group at University CollegeLondon, U.K. He is currently a Lecturer in Electronics at the University of Algarve,Portugal. In 2007 he took one year leave of absence to work in the company LimeMicrosystems U.K. as Senior Design Engineer. He was designing frequency synthesisersfor multi-mode/multi-standard wireless transceivers.Ron Schmitt (Chapters 20, 21) is the author of Electromagnetics Explained. He is theformer Director of Electrical Engineering, Sensor Research and Development Corp.Orono, Maine.Keith H. Sueker (Chapters 15, 22, 23) is the author of Power Electronics Design. Suekerreceived his BEE with High Distinction from the University of Minnesota, he continuedhis education at Illinois Institute of Technology where he received his MSEE, he alsocompleted his course work for his PhD. He spent many years working for WestinghouseElectric Corporation in various positions. He then moved on to Robicon Corporationas a consulting engineer, he retired in 1993. His responsibilities included analyticalw ww. n e w n e s p r e s s .c o m 19. About the Authorsxixtechniques and equipment design for power factor correction and harmonic mitigation.Sueker has written a number of IEEE papers and several articles for trade publications.Also, he has prepared a monograph and 90 minute video tape on these subjects. He andMr. R. P. Stratford have presented tutorial sessions on power factor and harmonics atIEEE-IAS annual meetings, and he has presented additional tutorials in other cities. Healso presented a tutorial on transformers for the local IEEE-IAS in the spring of 1999and repeated it in the fall of 2003. Sueker delivered a tutorial on power electronics forthe local IEEE-IAS/PES in the spring of 2005. He was also pleased to serve on the IEEEcommittee for awarding the IEEE Medal for Engineering Excellence for four years.He is currently a Life Senior Member of the IEEE and also a registered ProfessionalEngineer in the Commonwealth of Pennsylvania.Mike Tooley (Chapters 11, 12, 14, 24) is the author of Electronics Circuits. He is theformer Director of Learning Technology at Brooklands College, Surrey, U.K.Douglas Warne (Chapters 25) is the editor of Electrical Engineers Reference book,16th Edition. Warne graduated from Imperial College London in 1967 with a 1st classhonours degree in electrical engineering, during this time he had a student apprenticeshipwith AEI Heavy Plant Division, Rugby, 19631968. He is currently self-employed,and has taken on such projects as Co-ordinated LINK PEDDS programme for DTI,and the electrical engineering, electrical machines and drives and ERCOS programmesfor EPSRC. Initiated and manage the NETCORDE university-industry network foridentifying and launching new R&D projects. He has acted as co-ordinator for theindustry-academic funded ESR Network, held the part-time position of Research ContractCo-ordinator for the High Voltage and Energy Systems group at University of Cardiff andmonitored several projects funded through the DTI Technology Programme.Tim Williams (Chapters 11, 13, 15) is the author of The Circuit Designers Companion.He is employed with Elmac Services, Chichester, U.K. w w w.ne w nespress.com 20. This page intentionally left blank 21. CHAPTE R 1 An Introduction to Electric CircuitsJohn Bird1.1 SI UnitsThe system of units used in engineering and science is the Systme International dUnits(International system of units), usually abbreviated to SI units, and is based on the metricsystem. This was introduced in 1960 and is now adopted by the majority of countries asthe ofcial system of measurement.The basic units in the SI system are listed with their symbols, in Table 1.1.Derived SI units use combinations of basic units and there are many of them. Twoexamples are: Velocitymeters per second (m/s) Accelerationmeters per second squared (m/s2)Table 1.1: Basic SI units Quantity Unit length meter, m mass kilogram, kg time second, s electric current ampere, A thermodynamic temperaturekelvin, K luminous intensity candela, cd amount of substancemole, molw w w.ne w nespress.com 22. 2Chapter 1Table 1.2: Six most common multiples Prex NameMeaning M megamultiply by 1,000,000 (i.e., 106) k kilomultiply by 1,000 (i.e., 103) m milli divide by 1,000 (i.e., 103) micro divide by 1,000,000 (i.e., 106) n nanodivide by 1,000,000,000 (i.e., 109) p picodivide by 1,000,000,000,000 (i.e., 1012)SI units may be made larger or smaller by using prexes that denote multiplication ordivision by a particular amount. The six most common multiples, with their meaning, arelisted in Table 1.2.1.2 ChargeThe unit of charge is the coulomb (C) where one coulomb is one ampere second.(1 coulomb 6.24 1018 electrons). The coulomb is dened as the quantity ofelectricity that ows past a given point in an electric circuit when a current of one ampereis maintained for one second. Thus,charge, in coulombs Q Itwhere I is the current in amperes and t is the time in seconds.Example 1.1If a current of 5 A ows for 2 minutes, nd the quantity of electricity transferred.SolutionQuantity of electricity Q It coulombsI 5 A, t 2 60 120 sHence, Q 5 120 600 C1.3 ForceThe unit of force is the newton (N) where one newton is one kilogram meter persecond squared. The newton is dened as the force which, when applied tow ww. n e w n e s p r e s s .c o m 23. An Introduction to Electric Circuits3a mass of one kilogram, gives it an acceleration of one meter per second squared.Thus,force, in newtons F mawhere m is the mass in kilograms and a is the acceleration in meters per second squared.Gravitational force, or weight, is mg, where g 9.81 m/s2.Example 1.2A mass of 5000 g is accelerated at 2 m/s2 by a force. Determine the force needed.SolutionForce mass accelerationkg m 5 kg 2 m/s2 10 10 N s2Example 1.3Find the force acting vertically downwards on a mass of 200 g attached to a wire.SolutionMass 200 g 0.2 kg and acceleration due to gravity, g 9.81 m/s2Force acting downwards weight mass acceleration 0.2 kg 9.81 m/s2 1.962 N1.4 WorkThe unit of work or energy is the joule (J) where one joule is one Newton meter.The joule is dened as the work done or energy transferred when a force ofone newton is exerted through a distance of one meter in the direction of the force.Thus,work done on a body, in joules W Fswhere F is the force in Newtons and s is the distance in meters moved by the body in thedirection of the force. Energy is the capacity for doing work. w w w.ne w nespress.com 24. 4Chapter 11.5 PowerThe unit of power is the watt (W) where one watt is one joule per second. Power isdened as the rate of doing work or transferring energy. Thus,Wpower in watts, P twhere W is the work done or energy transferred in joules and t is the time in seconds. Thus,energy, in joules, W PtExample 1.4A portable machine requires a force of 200 N to move it. How much work is done if themachine is moved 20 m and what average power is utilized if the movement takes 25 s?SolutionWork done force distance 200 N 20 m 4000 Nm or 4 kJwork donePower time taken4000 J 160 J/s 160 W25 sExample 1.5A mass of 1000 kg is raised through a height of 10 m in 20 s. What is (a) the work doneand (b) the power developed?Solution(a) Work done force distance and force mass accelerationHence, work done (1000 kg 9.81 m/s2 ) (10 m ) 98100 Nm 98.1 kNm or 98.1 kJ8 work done98100 J(b) Power 4905 J/s time taken 20 s 4905 W or 4.905 kWw ww. n e w n e s p r e s s .c o m 25. An Introduction to Electric Circuits51.6 Electrical Potential and e.m.f.The unit of electric potential is the volt (V) where one volt is one joule per coulomb. Onevolt is dened as the difference in potential between two points in a conductor which,when carrying a current of one ampere, dissipates a power of one watt, i.e.,wattsjoules/secondvolts amperes amperesjoulesjoules ampere seconds coulombsA change in electric potential between two points in an electric circuit is called apotential difference. The electromotive force (e.m.f.) provided by a source of energy suchas a battery or a generator is measured in volts.1.7 Resistance and ConductanceThe unit of electric resistance is the ohm () where one ohm is one volt per ampere. Itis dened as the resistance between two points in a conductor when a constant electricpotential of one volt applied at the two points produces a current ow of one ampere inthe conductor. Thus, Vresistance, in ohms R Iwhere V is the potential difference across the two points in volts and I is the currentowing between the two points in amperes.The reciprocal of resistance is called conductance and is measured in siemens (S). Thus,1conductance, in siemens G Rwhere R is the resistance in ohms.Example 1.6Find the conductance of a conductor of resistance (a) 10 , (b) 5 k and (c) 100 m.Solution 1 1(a) Conductance G siemen 0.1 S R 10 w w w.ne w nespress.com 26. 6Chapter 1 11(b) G S 0.2 103 S 0.2 mS R 5 103 11103(c) G S S 10 S R 100 1031001.8 Electrical Power and EnergyWhen a direct current of I amperes is owing in an electric circuit and the voltage acrossthe circuit is V volts, then,power, in watts P VIElectrical energy Power time VIt joulesAlthough the unit of energy is the joule, when dealing with large amounts of energy, theunit used is the kilowatt hour (kWh) where1 kWh 1000 watt hour 1000 3600 watt seconds or joules 3,600,000 JExample 1.7A source e.m.f. of 5 V supplies a current of 3 A for 10 minutes. How much energy isprovided in this time?SolutionEnergy power time and power voltage current.Hence,Energy VIt 5 3(10 60) 9000 Ws or J 9 kJExample 1.8An electric heater consumes 1.8 MJ when connected to a 250 V supply for 30 minutes.Find the power rating of the heater and the current taken from the supply.w ww. n e w n e s p r e s s .c o m 27. An Introduction to Electric Circuits 7SolutionEnergy power time, energypower time 1.8 106 J 1000 J/s 1000 W30 60 si.e., Power rating of heater 1 kWP 1000Power P VI , thus, I 4AV 250Hence, the current taken from the supply is 4 A.1.9 Summary of Terms, Units and Their SymbolsTable 1.3: Electrical terms, units, and symbolsQuantity Quantity Symbol Unit Unit symbolLength lmeter mMass mkilogramkgTime tsecondsVelocity vmeters per second m/s or m s1Acceleration ameters per second squared m/s2 or m s2ForceFnewtonNElectrical charge or quantityQcoulomb CElectric current IampereAResistance Rohm ConductanceGsiemenSElectromotive forceEvoltVPotential difference VvoltVWork Wjoule JEnergy E (or W) joule JPowerPwattW w w w.ne w nespress.com 28. 8Chapter 1 Conductor Two conductors Two conductors crossing but not joined together joined Fixed resister Alternative symbolfor fixed resisterVariable resistorCell Battery of 3 cells Alternative symbolfor battery SwitchFilament lamp FuseA V Ammeter Voltmeter Alternative fuse symbolFigure 1.1: Common electrical component symbols1.10 Standard Symbols for Electrical ComponentsSymbols are used for components in electrical circuit diagrams and some of the morecommon ones are shown in Figure 1.1.1.11 Electric Current and Quantity of ElectricityAll atoms consist of protons, neutrons and electrons. The protons, which havepositive electrical charges, and the neutrons, which have no electrical charge, arecontained within the nucleus. Removed from the nucleus are minute negatively chargedparticles called electrons. Atoms of different materials differ from one another by havingdifferent numbers of protons, neutrons and electrons. An equal number of protons andelectrons exist within an atom and it is said to be electrically balanced, as the positive andw ww. n e w n e s p r e s s .c o m 29. An Introduction to Electric Circuits 9negative charges cancel each other out. When there are more than two electronsin an atom the electrons are arranged into shells at various distances from thenucleus.All atoms are bound together by powerful forces of attraction existing betweenthe nucleus and its electrons. Electrons in the outer shell of an atom, however, areattracted to their nucleus less powerfully than are electrons whose shells are nearer thenucleus.It is possible for an atom to lose an electron; the atom, which is now called an ion,is not now electrically balanced, but is positively charged and is thus able to attractan electron to itself from another atom. Electrons that move from one atom to anotherare called free electrons and such random motion can continue indenitely. However,if an electric pressure or voltage is applied across any material there is a tendencyfor electrons to move in a particular direction. This movement of free electrons,known as drift, constitutes an electric current ow. Thus current is the rate of movementof charge.Conductors are materials that contain electrons that are loosely connected to the nucleusand can easily move through the material from one atom to another.Insulators are materials whose electrons are held rmly to their nucleus.The unit used to measure the quantity of electrical charge Q is called the coulomb C(where 1 coulomb 6.24 1018 electrons).If the drift of electrons in a conductor takes place at the rate of one coulomb per secondthe resulting current is said to be a current of one ampere.Thus, 1 ampere 1 coulomb per second or 1 A 1 C/s. Hence, 1 coulomb 1 amperesecond or 1 C 1 As. Generally, if I is the current in amperes and t the time in secondsduring which the current ows, then I t represents the quantity of electrical charge incoulombs, i.e., quantity of electrical charge transferred, Q I t coulombsExample 1.9What current must ow if 0.24 coulombs is to be transferred in 15 ms?w w w.ne w nespress.com 30. 10 Chapter 1SolutionSince the quantity of electricity, Q It, then Q0.240.24 103 240I 3 16 A t 15 1015 15Example 1.10If a current of 10 A ows for 4 minutes, nd the quantity of electricity transferred.SolutionQuantity of electricity, Q It coulombsI 10 A; t 4 60 240 sHence, Q 10 240 2400 C1.12 Potential Difference and ResistanceFor a continuous current to ow between two points in a circuit a potential differenceor voltage, V, is required between them; a complete conducting path is necessary to andfrom the source of electrical energy. The unit of voltage is the volt, V.Figure 1.2 shows a cell connected across a lament lamp. Current ow, by convention,is considered as owing from the positive terminal of the cell, around the circuit to thenegative terminal.The ow of electric current is subject to friction. This friction, or opposition, is calledresistance R and is the property of a conductor that limits current. The unit of resistance Figure 1.2: Current oww ww. n e w n e s p r e s s .c o m 31. An Introduction to Electric Circuits 11is the ohm; 1 ohm is dened as the resistance which will have a current of 1 ampereowing through it when 1 volt is connected across it, i.e., potential differenceresistance R current1.13 Basic Electrical Measuring InstrumentsAn ammeter is an instrument used to measure current and must be connected in serieswith the circuit. Figure 1.2 shows an ammeter connected in series with the lamp tomeasure the current owing through it. Since all the current in the circuit passes throughthe ammeter it must have a very low resistance.A voltmeter is an instrument used to measure voltage and must be connected in parallelwith the part of the circuit whose voltage is required. In Figure 1.2, a voltmeter isconnected in parallel with the lamp to measure the voltage across it. To avoid a signicantcurrent owing through it, a voltmeter must have a very high resistance.An ohmmeter is an instrument for measuring resistance.A multimeter, or universal instrument, may be used to measure voltage, current andresistance. The oscilloscope may be used to observe waveforms and to measure voltagesand currents. The display of an oscilloscope involves a spot of light moving across ascreen. The amount by which the spot is deected from its initial position depends onthe voltage applied to the terminals of the oscilloscope and the range selected. Thedisplacement is calibrated in volts per cm. For example, if the spot is deected 3 cm andthe volts/cm switch is on 10 V/cm, then the magnitude of the voltage is 3 cm 10 V/cm,i.e., 30 V.1.14 Linear and Nonlinear DevicesFigure 1.3 shows a circuit in which current I can be varied by the variable resistor R2.For various settings of R2, the current owing in resistor R1, displayed on the ammeter,and the p.d. across R1, displayed on the voltmeter, are noted and a graph is plotted of p.d.against current. The result is shown in Figure 1.4(a) where the straight line graph passingthrough the origin indicates that current is directly proportional to the voltage. Since thew w w.ne w nespress.com 32. 12 Chapter 1 Figure 1.3: Circuit in which current can be varied Figure 1.4: Graphs of voltage vs. current: (a) linear device (b) nonlinear devicegradient, i.e., (voltage/current), is constant, resistance R1 is constant. A resistor is thus anexample of a linear device.If the resistor R1 in Figure 1.3 is replaced by a component such as a lamp, then the graphshown in Figure 1.4(b) results when values of voltage are noted for various currentreadings. Since the gradient is changing, the lamp is an example of a nonlinear device.1.15 Ohms LawOhms law states that the current I owing in a circuit is directly proportional to theapplied voltage V and inversely proportional to the resistance R, provided the temperatureremains constant. Thus, VV Ior V IRor R RIw ww. n e w n e s p r e s s .c o m 33. An Introduction to Electric Circuits 13Example 1.11The current owing through a resistor is 0.8 A when a voltage of 20 V is applied.Determine the value of the resistance.SolutionFrom Ohms law, V 20200resistance R 25 I 0.881.16 Multiples and SubmultiplesCurrents, voltages and resistances can often be very large or very small. Thus multiplesand submultiples of units are often used. The most common ones, with an example ofeach, are listed in Table 1.4.Example 1.12Determine the voltage which must be applied to a 2 k resistor in order that a current of10 mA may ow.SolutionResistance R 2 k 2 103 2000 Table 1.4: Common multiples and submultiples of units Prex NameMeaning Example M megamultiply by 1,000,000 (i.e., 106) 2 M 2,000,000 ohms k kilomultiply by 1000 (i.e., 103)10 kV 10,000 volts m milli divide by 1000 (i.e., 103) 2525 mA A 1000 0.025 amperes micro divide by 1,000,000 (i.e., 106) 5050 V V1000 000 0.00005 volts w w w.ne w nespress.com 34. 14 Chapter 1Current I 10 mA 1010 10 103 A or orA 1031000 0.01 AFrom Ohms law, potential difference,V IR (0.01) (2000) 20 VExample 1.13A coil has a current of 50 mA owing through it when the applied voltage is 12 V.What is the resistance of the coil?SolutionV12 12 103Resistance R I 50 1035012 000 240 50Example 1.14A 100 V battery is connected across a resistor and causes a current of 5 mA to ow.Determine the resistance of the resistor. If the voltage is now reduced to 25 V, what willbe the new value of the current owing?SolutionV 100100 103Resistance R I 5 103 5 20 103 20 kCurrent when voltage is reduced to 25 V, V25 25I 103 1.25 mA R 20 10 3 20w ww. n e w n e s p r e s s .c o m 35. An Introduction to Electric Circuits 15Example 1.15What is the resistance of a coil that draws a current of (a) 50 mA and (b) 200 A froma 120 V supply?Solution V120(a) Resistance R I 50 103 12012 000 2400 or 2.4 k 0.055 120 120(b) Resistance R 6 200 10 0.00021200 000 600 000 or 600 kr2 or 0.6 MExample 1.16The current/voltage relationship for two resistors A and B is as shown in Figure 1.5.Determine the value of the resistance of each resistor.SolutionFor resistor A, V20 A202000R 1000 or 1 k I 20 mA 0.02 2 Figure 1.5: Current/voltage for two resistors A and B w w w.ne w nespress.com 36. 16Chapter 1For resistor B,V 16 V16 16 000R 3200 or 3.2 kI 5 mA 0.00551.17 Conductors and InsulatorsA conductor is a material having a low resistance which allows electric current to owin it. All metals are conductors and some examples include copper, aluminium, brass,platinum, silver, gold and carbon.An insulator is a material having a high resistance which does not allow electric currentto ow in it. Some examples of insulators include plastic, rubber, glass, porcelain, air,paper, cork, mica, ceramics and certain oils.1.18 Electrical Power and Energy1.18.1 Electrical PowerPower P in an electrical circuit is given by the product of potential difference V andcurrent I. The unit of power is the watt, W. Hence, P V I wattsFrom Ohms law, V IR.Substituting for V in equation (1.1) gives:P (IR) Ii.e.,P I2R wattsVAlso, from Ohms law, I RSubstituting for I in the equation above gives:VPVRV2i.e., P watts RThere are three possible formulas that may be used for calculating power.w ww. n e w n e s p r e s s .c o m 37. An Introduction to Electric Circuits 17Example 1.17A 100 W electric light bulb is connected to a 250 V supply. Determine (a) the currentowing in the bulb, and (b) the resistance of the bulb.Solution PPower P V I , from which, current I V100 0 102(a) Current I 0.4 A250255 V2502500(b) Resistance R 625 I0.4 4Example 1.18Calculate the power dissipated when a current of 4 mA ows through a resistance of 5 k.SolutionPower P I2R (4 103)2(5 103) 16 106 5 103 80 103 0.08 W or 80 mWAlternatively, since I 4 103 and R 5 103 then from Ohms law,voltage V IR 4 103 5 103 20 VHence, power P V I 20 4 103 80 mWExample 1.19An electric kettle has a resistance of 30 . What current will ow when it is connected toa 240 V supply? Find also the power rating of the kettle.SolutionV 240Current, I 8AR30Power, P VI 240 8 1920 W 1.95 kW power rating of kettlew w w.ne w nespress.com 38. 18 Chapter 1Example 1.20A current of 5 A ows in the winding of an electric motor, the resistance of the windingbeing 100 . Determine (a) the voltage across the winding, and (b) the power dissipatedby the coil.SolutionPotential difference across winding, V IR 5 100 500 VPower dissipated by coil, P I2R 52 100 2500 W or 2.5 kW(Alternatively, P V I 500 5 2500 W or 2.5 kW)Example 1.21The hot resistance of a 240 V lament lamp is 960 . Find the current taken by the lampand its power rating.SolutionFrom Ohms law, V240241current I A or 0.25 AR 9609641Power rating P VI (240) 60 W 4 1.18.2 Electrical EnergyElectrical energy power timeIf the power is measured in watts and the time in seconds then the unit of energy iswatt-seconds or joules. If the power is measured in kilowatts and the time in hours thenthe unit of energy is kilowatt-hours, often called the unit of electricity. The electricitymeter in the home records the number of kilowatt-hours used and is thus an energy meter.Example 1.22A 12 V battery is connected across a load having a resistance of 40 . Determinethe current owing in the load, the power consumed and the energy dissipated in2 minutes.w ww. n e w n e s p r e s s .c o m 39. An Introduction to Electric Circuits19SolutionV 12Current I 0.3 AR 40Power consumed, P VI (12)(0.3) 3.6 WEnergy dissipated power time (3.6 W)(2 60 s) 432 J (since 1 J 1 Ws)Example 1.23A source of e.m.f. of 15 V supplies a current of 2 A for 6 minutes. How much energy isprovided in this time?SolutionEnergy power time, and power voltage currentHence, energy Vt 15 2 (6 60) 10 800 Ws or J 10.8 kJExample 1.24An electric heater consumes 3.6 MJ when connected to a 250 V supply for 40 minutes.Find the power rating of the heater and the current taken from the supply.Solution energy 3.6 106 JPower (or W ) 1500 Wtime 40 60 si.e., power rating of heater 1.5 kWP 1500Power P VI , thus I 6AV 250Hence, the current taken from the supply 6 Aw w w.ne w nespress.com 40. 20 Chapter 11.19 Main Effects of Electric CurrentThe three main effects of an electric current are:(a) magnetic effect (b) chemical effect(c) heating effectSome practical applications of the effects of an electric current include:Magnetic effect: bells, relays, motors, generators, transformers, telephones, car ignition, and lifting magnetsChemical effect: primary and secondary cells, and electroplatingHeating effect:cookers, water heaters, electric res, irons, furnaces, kettles, and soldering ironsw ww. n e w n e s p r e s s .c o m 41. CHAPTE R 2Resistance and ResistivityJohn Boyd2.1 Resistance and ResistivityThe resistance of an electrical conductor depends on four factors, these being: (a) thelength of the conductor, (b) the cross-sectional area of the conductor, (c) the type ofmaterial and (d) the temperature of the material.Resistance, R, is directly proportional to length, l, of a conductor. For example, if thelength of a piece of wire is doubled, then the resistance is doubled.Resistance, R, is inversely proportional to cross-sectional area, a, of a conductor, i.e.,R is proportional to 1/a. Thus, for example, if the cross-sectional area of a piece of wireis doubled, then the resistance is halved.Since R is proportional to l and R is proportional to 1/a, then R is proportional to l/a. Byinserting a constant of proportionality into this relationship, the type of material used maybe taken into account. The constant of proportionality is known as the resistivity of thematerial and is given the symbol (Greek rho). Thus, lresistance R ohms a is measured in ohm meters (m).The value of the resistivity is the resistance of a unit cube of the material measuredbetween opposite faces of the cube. w w w.ne w nespress.com 42. 22 Chapter 2Resistivity varies with temperature and some typical values of resistivities measured atabout room temperature are given in Table 2.1.Note that good conductors of electricity have a low value of resistivity and goodinsulators have a high value of resistivity.Example 2.1The resistance of a 5 m length of wire is 600 . Determine (a) the resistance of an 8 mlength of the same wire, and (b) the length of the same wire when the resistance is 420 .SolutionResistance, R, is directly proportional to length, l, i.e., R l. Hence, 600 5 m or600 (k)(5), where k is the coefcient of proportionality. Hence, 600k 1205When the length l is 8 m, then resistanceR kl (120)(8) 960 When the resistance is 420 , 420 kl, from which 420 420length l 3.5 mk120Example 2.2A piece of wire of cross-sectional area 2 mm2 has a resistance of 300 . Find (a) theresistance of a wire of the same length and material if the cross-sectional area is 5 mm2, and(b) the cross-sectional area of a wire of the same length and material of resistance 750 .Table 2.1: Typical resistivity values Copper 1.7 108 m (or 0.017 m)8 Aluminum 2.6 10 m (or 0.026 m) Carbon (graphite)10 108 m(or 0.10 m) Glass1 108 m(or 104 m) Mica 1 1013 m(or 107 m)w ww. n e w n e s p r e s s .c o m 43. Resistance and Resistivity 23SolutionResistance R is inversely proportional to cross-sectional area, a, i.e., R (1/a )So 300 (1/ 2 mm 2 ) or 300 (k )(1/2) from which the coefcient of proportionality,k 300 2 600(a) When the cross-sectional area a 5 mm2then R (k )(1/5) (600)(1/5) 120 (Note that resistance has decreased as the cross-sectional area is increased.)(b) When the resistance is 750 then 750 (k)(1/a), from which cross-sectional area, k600a 0.8 mm 2750 750Example 2.3A wire of length 8 m and cross-sectional area 3 mm2 has a resistance of 0.16 . If the wireis drawn out until its cross-sectional area is 1 mm2, determine the resistance of the wire.SolutionResistance R is directly proportional to length l, and inversely proportional to the cross-sectional area, a, i.e., R (l/a ) or R k (l/a ) , where k is the coefcient of proportionality.Since R 0.16, l 8 and a 3, then 0.16 (k )(8 / 3) from whichk 0.16 (3/8) 0.06If the cross-sectional area is reduced to {1/3} of its original area, then the length must betripled to 3 8, i.e., 24 m.New resistance R k (l/a ) 0.06 (24 /1) 1.44 Example 2.4Calculate the resistance of a 2 km length of aluminum overhead power cable if thecross-sectional area of the cable is 100 mm2. Take the resistivity of aluminum to be0.03 106 m.w w w.ne w nespress.com 44. 24 Chapter 2SolutionLength l 2 km 2000 m; area, a 100 mm2 100 106 m2; resistivity 0.03 106 ml (0.03 106 m)(2000 m)Resistance R a (100 106 m 2 ) 0.03 2000 100 0.6 Example 2.5Calculate the cross-sectional area, in mm2, of a piece of copper wire, 40 m in length andhaving a resistance of 0.25 . Take the resistivity of copper as 0.02 106 m.Solutionl lResistance R so cross-sectional area a aR(0.02 106 m)( 40 m) 0.25 3.2 106 m 2 (3.2 106 ) 106 mm 2 3.2 mm 2Example 2.6The resistance of 1.5 km of wire of cross-sectional area 0.17 mm2 is 150 . Determine theresistivity of the wire.SolutionlResistance R aRa (150 )(0.17 106 m 2 )so resistivity l (1500 m) 0.017 106 m or 0.017 mExample 2.7Determine the resistance of 1200 m of copper cable having a diameter of 12 mm if theresistivity of copper is 1.7 108 m.w ww. n e w n e s p r e s s .c o m 45. Resistance and Resistivity25SolutionCross-sectional area of cable, a r 2 ( 12 ) 36 mm 2 36 106 m 22 2l (1.7 108 m)(1200 m)Resistance R a (36 106 m 2 )1.7 1200 1061.7 128 36 1036 0.180 2.2 Temperature Coefcient of ResistanceIn general, as the temperature of a material increases, most conductors increase inresistance, insulators decrease in resistance, while the resistance of some special alloysremains almost constant.The temperature coefcient of resistance of a material is the increase in the resistanceof a 1 resistor of that material when it is subjected to a rise of temperature of 1C.The symbol used for the temperature coefcient of resistance is (Greek alpha).Thus, if some copper wire of resistance 1 is heated through 1C and its resistanceis then measured as 1.0043 12 then 0.0043 /C for copper. The units areusually expressed only as per C. So, 0.0043/C for copper. If the 1resistor of copper is heated through 100C then the resistance at 100C would be1 100 0.0043 1.43 .Some typical values of temperature coefcient of resistance measured at 0C are given inTable 2.2.(Note that the negative sign for carbon indicates that its resistance falls with increase oftemperature.)Table 2.2: Typical values of temperature coefcient of resistanceCopper 0.0043/CAluminum 0.0038/CNickel 0.0062/CCarbon 0.00048/CConstantan 0Eureka 0.00001/C w w w.ne w nespress.com 46. 26 Chapter 2If the resistance of a material at 0C is known, the resistance at any other temperature canbe determined from:R R0 (1 0 )where R resistance at 0C R resistance at temperature C 0 temperature coefcient of resistance at 0CExample 2.8A coil of copper wire has a resistance of 100 when its temperature is 0C. Determineits resistance at 70C if the temperature coefcient of resistance of copper at 0C is0.0043/C.SolutionResistance R R0 (1 0)So resistance at 70C, R70 100[1 (0.0043)(70)] 100[1 0.301] 100(1.301) 1.031 Example 2.9An aluminum cable has a resistance of 27 at a temperature of 35C. Determine itsresistance at 0C. Take the temperature coefcient of resistance at 0C to be 0.0038/C.SolutionResistance at C, R R0(1 0) RHence resistance at 0C, R0 (1 0 )27[1 (0.0038)(35)] 27 271 0.133 1.133 23.83 w ww. n e w n e s p r e s s .c o m 47. Resistance and Resistivity27Example 2.10A carbon resistor has a resistance of 1 k at 0C. Determine its resistance at 80C.Assume that the temperature coefcient of resistance for carbon at 0C is 0.0005/C.SolutionResistance at temperature C, R R0(1 0)i.e., R 1000[1 (0.0005)(80)] 1000[1 0.040] 1000(0.96) 960 If the resistance of a material at room temperature (approximately 20C), R20, and thetemperature coefcient of resistance at 20C, 20, are known then the resistance R attemperature C is given by:R R20 [1 20 ( 20)]Example 2.11A coil of copper wire has a resistance of 10 at 20C. If the temperature coefcient ofresistance of copper at 20C is 0.004/C, determine the resistance of the coil when thetemperature rises to 100C.SolutionResistance at temperature C, R R20[1 20( 20)]Hence resistance at 100C,R100 10[1 (0.004)(100 20)] 10[1 (0.004)(80)] 10[1 0.32] 10(1.32) 13.2 w w w.ne w nespress.com 48. 28 Chapter 2Example 2.12The resistance of a coil of aluminum wire at 18C is 200 . The temperature of the wireis increased and the resistance rises to 240 . If the temperature coefcient of resistanceof aluminum is 0.0039/C at 18C determine the temperature to which the coil has risen.SolutionLet the temperature rise to Resistance at C, R R18[1 18( 18)]i.e.,240 200[1 (0.0039)( 18)]240 200 (200)(0.0039)( 18) 240 200 0.78( 18)40 0.78( 18)40 18 0.7851.28 18, from which, 51.28 18 69.28CHence the temperature of the coil increases to 69.28C.If the resistance at 0C is not known, but is known at some other temperature 1, then theresistance at any temperature can be found as follows:R1 R0 (1 01) andR2 R0(1 02)Dividing one equation by the other gives:R1 1 0 1 R2 1 0 2where R2 resistance at temperature 2.Example 2.13Some copper wire has a resistance of 200 at 20C. A current is passed through thewire and the temperature rises to 90C. Determine the resistance of the wire at 90C,w ww. n e w n e s p r e s s .c o m 49. Resistance and Resistivity 29correct to the nearest ohm, assuming that the temperature coefcient of resistance is0.004/C at 0C.SolutionR20 200 , 0 0.004/CR20 [1 0 (20)]R90 [1 0 (90)]R20 [1 90 0 ]Hence, R90 [1 20 0 ]200[1 90(0.004)] [1 20(0.004)]200[1 0.36] [1 0.08]200(1.36) 251.85 (1.08)So, the resistance of the wire at 90C is 252 .w w w.ne w nespress.com 50. This page intentionally left blank 51. CHAPTE R 3 Series and Parallel NetworksJohn Bird3.1 Series CircuitsFigure 3.1 shows three resistors R1, R2 and R3 connected end to end, i.e., in series,with a battery source of V volts. Since the circuit is closed, a current I will owand the voltage across each resistor may be determined from the voltmeter readings V1,V2 and V3.In a series circuit: (a) the current I is the same in all parts of the circuit; therefore, the same reading is found on each of the two ammeters shown, and, (b) the sum of the voltages V1, V2 and V3 is equal to the total applied voltage, V, i.e.,V V1 V2 V3Figure 3.1: Series circuit w w w.ne w nespress.com 52. 32 Chapter 3From Ohms law:V1 IR1, V2 IR2, V3 IR3 and V IRwhere R is the total circuit resistance.Since V V1 V2 V3then IR IR1 IR2 IR3Dividing throughout by I gives: R R1 R2 R3So, for a series circuit, the total resistance is obtained by adding together the values of theseparate resistances.Example 3.1For the circuit shown in Figure 3.2, determine (a) the battery voltage V, (b) the totalresistance of the circuit, and (c) the values of resistance of resistors R1, R2 and R3, giventhat the voltages across R1, R2 and R3 are 5 V, 2 V and 6 V, respectively.Solution(a) Battery voltage V V1 V2 V3 5 2 6 13 V V 13(b) Total circuit resistance R 3.25 I4Figure 3.2: Circuit for Example 3.1w ww. n e w n e s p r e s s .c o m 53. Series and Parallel Networks 33 V1 5(c) Resistance R1 1.25 I 4 V22 Resistance R2 0.5 I4 V 6 Resistance R3 3 1.5 I4 (Check: R1 R2 R3 1.25 0.5 1.5 3.25 R)Example 3.2For the circuit shown in Figure 3.3, determine the voltage across resistor R3. If the totalresistance of the circuit is 100 , determine the current owing through resistor R1. Findalso the value of resistor R2.SolutionVoltage across R3, V3 25 10 4 11 VV 25Current I 0.25 A, which is the current owing in each resistorR 100V24Resistance R2 16 I 0.25Example 3.3A 12 V battery is connected in a circuit having three series-connected resistors havingresistances of 4 , 9 and 11 . Determine the current owing through, and the voltageacross the 9 resistor. Find also the power dissipated in the 11 resistor. Figure 3.3: Circuit for Example 3.2w w w.ne w nespress.com 54. 34 Chapter 3Figure 3.4: Circuit for Example 3.3SolutionThe circuit diagram is shown in Figure 3.4.Total resistance R 4 9 11 24 V12Current I 0.5 A , which is the current in the 9 resistor.R24Voltage across the 9 resistor, V1 I 9 0.5 9 4.5 VPower dissipated in the 11 resistor, P I2R 0.52(11) 0.25(11) 2.75 W3.2 Potential DividerThe voltage distribution for the circuit shown in Figure 3.5(a) is given by: R V1 1 R R V 1 2 R V2 2 R R V 1 1The circuit shown in Figure 3.5(b) is often referred to as a potential divider circuit. Sucha circuit can consist of a number of similar elements in series connected across a voltagesource, voltages being taken from connections between the elements. Frequently thedivider consists of two resistors as shown in Figure 3.5(b), where: R VOUT 2 R R VIN 1 2w ww. n e w n e s p r e s s .c o m 55. Series and Parallel Networks35Figure 3.5: Potential divider circuitA potential divider is the simplest way of producing a source of lower e.m.f. from asource of higher e.m.f., and is the basic operating mechanism of the potentiometer, ameasuring device for accurately measuring potential differences.Example 3.4Determine the value of voltage V shown in Figure 3.6.SolutionFigure 3.6 may be redrawn as shown in Figure 3.7, and voltage 6 (50) 30 VV 64 Example 3.5Two resistors are connected in series across a 24 V supply and a current of 3 A ows inthe circuit. If one of the resistors has a resistance of 2 determine (a) the value of theother resistor, and (b) the voltage across the 2 resistor. If the circuit is connected for 50hours, how much energy is used? w w w.ne w nespress.com 56. 36 Chapter 3SolutionThe circuit diagram is shown in Figure 3.8.(a) Total circuit resistance R V 24 8 I3Value of unknown resistance, Rx 8 2 6 (b) Voltage across 2 resistor, V1 IR1 3 2 6 V Alternatively, from above, R V 2 (24) 6 V V1 1 R1 Rx 26 Figure 3.6: Circuit for Example 3.4Figure 3.7: Redrawn version of Figure 3.6Figure 3.8: Circuit for Example 3.5w ww. n e w n e s p r e s s .c o m 57. Series and Parallel Networks37Energy used power time VIt (24 3 W) (50 h) 3600 Wh 3.6 kWh3.3 Parallel NetworksFigure 3.9 shows three resistors, R1, R2 and R3 connected across each other, i.e., inparallel, across a battery source of V volts.In a parallel circuit: (a) the sum of the currents I1, I2 and I3 is equal to the total circuit current, I, i.e., I I1 I2 I3, and (b) the sou