Grob’s Basic Electronics sch10858_fm_i-xxvi_1.indd i 3/17/10 12:14:36 PM This page intentionally left blank Grob’s Basic Electronics 11th Edition Mitchel E Schultz Western Technical College TM sch10858_fm_i-xxvi_1.indd iii 3/17/10 12:14:36 PM TM GROB’S BASIC ELECTRONICS Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY, 10020 Copyright © 2011 by The McGraw-Hill Companies, Inc All rights reserved Previous editions © 2007, 2003, 1997, 1992, and 1989 No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning Some ancillaries, including electronic and print components, may not be available to customers outside the United States This book is printed on acid-free paper DOW/DOW ISBN 978-0-07-351085-9 MHID 0-07-351085-8 Vice president/Editor in chief: Elizabeth Haefele Vice president/Director of marketing: John E Biernat Director of Development: Sarah Wood Editorial coordinator: Vincent Bradshaw Marketing manager: Kelly Curran Lead digital product manager: Damian Moshak Digital development editor: Kevin White Director, Editing/Design/Production: Jess Ann Kosic Project manager: Jean R Starr Manager, Digital production: Janean A Utley Senior designer: Srdjan Savanovic Senior photo research coordinator: Jeremy Cheshareck Photo researcher: Allison Grimes Cover design: George Kokkonas Interior design: PV Design Inc Typeface: 10/12 Times Roman Compositor: MPS Limited, A Macmillan Company Printer: R R Donnelley Cover credit: © Nicemonkey/Dreamstime.com Credits: The credits section for this book begins on page 1196 and is considered an extension of the copyright page Library of Congress Cataloging-in-Publication Data Schultz, Mitchel E Grob’s basic electronics / Mitchel E Schultz.—11th ed p cm Includes index ISBN-13: 978-0-07-351085-9 (alk paper) ISBN-10: 0-07-351085-8 (alk paper) Electronics—Textbooks I Grob, Bernard Basic electronics II Title III Title: Basic electronics TK7816.G75 2011 621.381—dc22 2010008273 The Internet addresses listed in the text were accurate at the time of publication The inclusion of a Web site does not indicate an endorsement by the authors or McGraw-Hill, and McGraw-Hill does not guarantee the accuracy of the information presented at these sites www.mhhe.com sch10858_fm_i-xxvi_1.indd iv 3/17/10 10:11:27 PM Dedication This textbook is dedicated to all of my students, both past and present sch10858_fm_i-xxvi_1.indd v 3/17/10 12:14:36 PM This page intentionally left blank Brief Contents I Introduction to Powers of 10 Chapter Electricity 22 Chapter Resistors 54 Chapter Ohm’s Law 76 Chapter Series Circuits 106 Chapter Parallel Circuits 138 Chapter Series-Parallel Circuits 168 Chapter Voltage Dividers and Current Dividers 202 Chapter Analog and Digital Multimeters 226 Chapter Kirchhoff ’s Laws 258 Chapter 10 Network Theorems 282 Chapter 11 Conductors and Insulators 314 Chapter 12 Batteries 342 Chapter 13 Magnetism 376 Chapter 14 Electromagnetism 396 Chapter 15 Alternating Voltage and Current 428 Chapter 16 Capacitance 470 Chapter 17 Capacitive Reactance 510 Chapter 18 Capacitive Circuits 532 Chapter 19 Inductance 558 Chapter 20 Inductive Reactance 602 Chapter 21 Inductive Circuits 624 Chapter 22 RC and L/R Time Constants 652 Chapter 23 Alternating Current Circuits Chapter 24 Complex Numbers for AC Circuits 714 Chapter 25 Resonance 744 Chapter 26 Filters 780 Chapter 27 Diodes and Diode Applications 824 686 vii sch10858_fm_i-xxvi_1.indd vii 3/17/10 12:14:36 PM viii sch10858_fm_i-xxvi_1.indd viii Chapter 28 Bipolar Junction Transistors 872 Chapter 29 Transistor Amplifiers 906 Chapter 30 Field Effect Transistors 948 Chapter 31 Power Amplifiers 988 Chapter 32 Thyristors 1020 Chapter 33 Operational Amplifiers 1038 Appendix A Electrical Symbols and Abbreviations 1090 Appendix B Solder and the Soldering Process 1093 Appendix C Listing of Preferred Resistance Values 1100 Appendix D Component Schematic Symbols 1101 Appendix E Using the Oscilloscope 1107 Appendix F Introduction to MultiSim 1122 Glossary 1159 Answers Self-Tests 1168 Answers Odd-Numbered Problems and Critical Thinking Problems 1174 Credits 1196 Index 1197 Brief Contents 3/17/10 12:14:36 PM Contents Preface xviii I Introduction to Powers of 10 I–1 I–2 I–3 I–4 I–5 Scientific Notation Engineering Notation and Metric Prefixes Converting between Metric Prefixes 10 Addition and Subtraction Involving Powers of 10 Notation 11 Multiplication and Division Involving Powers of 10 Notation 12 I–6 Reciprocals with Powers of 10 13 I–7 Squaring Numbers Expressed in Powers of 10 Notation 13 I–8 Square Roots of Numbers Expressed in Powers of 10 Notation 14 I–9 The Scientific Calculator 15 Summary 17 Chapter Electricity 22 1–1 1–2 1–3 1–4 1–5 1–6 Negative and Positive Polarities 24 Electrons and Protons in the Atom 24 Structure of the Atom 27 The Coulomb Unit of Electric Charge 30 The Volt Unit of Potential Difference 33 Charge in Motion Is Current 35 1–7 Resistance Is Opposition to Current 38 1–8 The Closed Circuit 40 1–9 The Direction of Current 42 1–10 Direct Current (DC) and Alternating Current (AC) 45 1–11 Sources of Electricity 46 1–12 The Digital Multimeter 47 Summary 49 Chapter Resistors 54 2–1 2–2 2–3 2–4 Types of Resistors 56 Resistor Color Coding 59 Variable Resistors 63 Rheostats and Potentiometers 64 2–5 Power Rating of Resistors 2–6 Resistor Troubles 68 Summary 70 66 Chapter Ohm’s Law 76 3–1 3–2 3–3 3–4 The Current I ϭ V/ R 78 The Voltage V ϭ IR 80 The Resistance R ϭ V/I 81 Practical Units 82 3–5 3–6 Multiple and Submultiple Units 82 The Linear Proportion between V and I 83 ix sch10858_fm_i-xxvi_1.indd ix 3/17/10 12:14:37 PM Summary ■ There is only one voltage VA across all components in parallel ■ The current in each branch Ib equals the voltage VA across the branch divided by the branch resistance Rb, or Ib ϭ VA /Rb ■ Kirchhoff’s current law states that the total current IT in a parallel circuit equals the sum of the individual branch currents Expressed as an equation, Kirchhoff’s current law is IT ϭ I1 ϩ I2 ϩ I3 ϩ · · · ϩ etc ■ The equivalent resistance REQ of parallel branches is less than the smallest branch resistance, since all the branches must take more current from the source than any one branch ■ For only two parallel resistances of any value, REQ ϭ R1R2 /(R1 ϩ R2) ■ For any number of equal parallel resistances, REQ is the value of Table 5–1 results in no current for any of the branches one resistance divided by the number of resistances ■ For the general case of any number of branches, calculate REQ as VA / IT or use the reciprocal resistance formula: ■ A short circuit has zero resistance, resulting in excessive current When one branch is short-circuited, all parallel paths are also short-circuited The entire current is in the short circuit and no current is in the shortcircuited branches ■ The voltage across a good fuse and the voltage across a closed switch are approximately V When the fuse in the main line of a parallel circuit opens, the voltage across the fuse equals the full applied voltage Likewise, when the switch in the main line of a parallel circuit opens, the voltage across the open switch equals the full applied voltage ■ Table 5–1 compares series and parallel circuits REQ ϭ ⁄R ϩ 1⁄R ϩ 1⁄R ϩ · · · ϩ etc ■ For any number of conductances in parallel, their values are added for GT, in the same way as parallel branch currents are added ■ The sum of the individual values of power dissipated in parallel resistances equals the total power produced by the source ■ An open circuit in one branch results in no current through that branch, but the other branches can have their normal current However, an open circuit in the main line Comparison of Series and Parallel Circuits Series Circuit Parallel Circuit Current the same in all components Voltage the same across all branches V across each series R is I ϫ R I in each branch R is V͞R VT ϭ V1 ϩ V2 ϩ V3 ϩ · · · ϩ etc IT ϭ I1 ϩ I2 ϩ I3 ϩ · · · ϩ etc RT ϭ R1 ϩ R2 ϩ R3 ϩ · · · ϩ etc G T ϭ G1 ϩ G2 ϩ G3 ϩ · · · ϩ etc R T must be more than the largest individual R REQ must be less than the smallest branch R P1 ϭ P1 ϩ P2 ϩ P3 ϩ · · · ϩ etc PT ϭ P1 ϩ P2 ϩ P3 ϩ · · · ϩ etc Applied voltage is divided into IR voltage drops Main-line current is divided into branch currents The largest IR drop is across the largest series R The largest branch I is in the smallest parallel R Open in one component causes entire circuit to be open Open in one branch does not prevent I in other branches Important Terms Equivalent resistance, REQ in a parallel circuit, this refers to a single resistance that would draw the same amount of current as all of the parallel connected branches Parallel Circuits sch10858_ch05_138-167.indd 159 Kirchhoff’s current law (KCL) a law stating that the sum of the individual branch currents in a parallel circuit must equal the total current, I T Main line the pair of leads connecting all individual branches in a parallel circuit to the terminals of the applied voltage, VA The main line carries the total current, I T, 159 3/15/10 10:22:16 AM flowing to and from the terminals of the voltage source Parallel bank a combination of parallel-connected branches Reciprocal resistance formula a formula stating that the equivalent resistance, REQ, of a parallel circuit equals the reciprocal of the sum of the reciprocals of the individual branch resistances Related Formulas V V V I1 ϭ A , I2 ϭ A , I3 ϭ A R1 R2 R3 IT ϭ I1 ϩ I2 ϩ I3 ϩ · · · ϩ etc V REQ ϭ A IT REQ ϭ _ ⁄R ϩ 1⁄R ϩ 1⁄R ϩ · · · ϩ etc R (R for equal branch resistances) REQ ϭ n EQ R1 ϫ R2 REQ ϭ (R for only two branch resistances) R1 ϩ R2 EQ R ϫ REQ RX ϭ _ R Ϫ REQ GT ϭ G1 ϩ G2 ϩ G3 ϩ · · · ϩ etc PT ϭ P1 ϩ P2 ϩ P3 ϩ · · · ϩ etc Self-Test Answers at back of book A 120-k⍀ resistor, R1, and a 180-k⍀ resistor, R2, are in parallel How much is the equivalent resistance, REQ? a 72 k⍀ b 300 k⍀ c 360 k⍀ d 90 k⍀ A 100-⍀ resistor, R1, and a 300-⍀ resistor, R2, are in parallel across a dc voltage source Which resistor dissipates more power? a The 300-⍀ resistor b Both resistors dissipate the same amount of power c The 100-⍀ resistor d It cannot be determined Three 18-⍀ resistors are in parallel How much is the equivalent resistance, REQ? a 54 ⍀ b ⍀ c ⍀ d none of the above Which of the following statements about parallel circuits is false? a The voltage is the same across all branches in a parallel circuit b The equivalent resistance, REQ, of a parallel circuit is always smaller than the smallest branch resistance 160 sch10858_ch05_138-167.indd 160 c In a parallel circuit the total current, IT , in the main line equals the sum of the individual branch currents d The equivalent resistance, REQ, of a parallel circuit decreases when one or more parallel branches are removed from the circuit Two resistors, R1 and R2, are in parallel with each other and a dc voltage source If the total current, IT , in the main line equals A and I2 through R2 is A, how much is I1 through R1? a A b A c A d It cannot be determined How much resistance must be connected in parallel with a 360-⍀ resistor to obtain an equivalent resistance, REQ, of 120 ⍀? a 360 ⍀ b 480 ⍀ c 1.8 k⍀ d 180 ⍀ If one branch of a parallel circuit becomes open, a all remaining branch currents increase b the voltage across the open branch will be V c the remaining branch currents not change in value d the equivalent resistance of the circuit decreases If a 10-⍀ R1, 40-⍀ R2, and 8-⍀ R3 are in parallel, calculate the total conductance, G T , of the circuit a 250 mS b 58 S c ⍀ d 0.25 S Which of the following formulas can be used to determine the total power, PT, dissipated by a parallel circuit a PT ϭ VA ϫ IT b PT ϭ P1 ϩ P2 ϩ P3 ϩ · · · ϩ etc V A2 c PT ϭ _ REQ d all of the above 10 A 20-⍀ R1, 50-⍀ R2, and 100-⍀ R3 are connected in parallel If R2 is short-circuited, what is the equivalent resistance, REQ, of the circuit? a approximately ⍀ b infinite (ϱ) ⍀ c 12.5 ⍀ d It cannot be determined 11 If the fuse in the main line of a parallel circuit opens, a the voltage across each branch will be V Chapter 3/15/10 10:22:17 AM b the current in each branch will be zero c the current in each branch will increase to offset the decrease in total current d both a and b 12 A 100-⍀ R1 and a 150-⍀ R2 are in parallel If the current, I1, through R1 is 24 mA, how much is the total current, IT? a 16 mA b 40 mA c 9.6 mA d It cannot be determined 13 A 2.2-k⍀ R1 is in parallel with a 3.3-k⍀ R2 If these two resistors carry a total current of 7.5 mA, how much is the applied voltage, VA? a 16.5 V b 24.75 V c 9.9 V d 41.25 V 14 How many 120-⍀ resistors must be connected in parallel to obtain an equivalent resistance, REQ, of 15 ⍀? a 15 b c 12 d 15 A 220-⍀ R1, 2.2-k⍀ R2, and 200-⍀ R3 are connected across 15 V of applied voltage What happens to REQ if the applied voltage is doubled to 30 V? a REQ doubles b REQ cuts in half c REQ does not change d REQ increases but is not double its original value 16 If one branch of a parallel circuit opens, the total current, IT , a does not change b decreases c increases d goes to zero 17 In a normally operating parallel circuit, the individual branch currents are a independent of each other b not affected by the value of the applied voltage c larger than the total current, I T d none of the above 18 If the total conductance, G T , of a parallel circuit is 200 S, how much is REQ? a 500 ⍀ b 200 k⍀ c k⍀ d 500 k⍀ 19 If one branch of a parallel circuit is short-circuited, a the fuse in the main line will blow b the voltage across the shortcircuited branch will measure the full value of applied voltage c all the remaining branches are effectively short-circuited as well d both a and c 20 Two lightbulbs in parallel with the 120-V power line are rated at 60 W and 100 W, respectively What is the equivalent resistance, REQ, of the bulbs when they are lit? a 144 ⍀ b 90 ⍀ c 213.3 ⍀ d It cannot be determined Essay Questions Draw a wiring diagram showing three resistances connected in parallel across a battery Indicate each branch and the main line Redraw Fig 5–17 with five parallel resistors R1 to R5 and explain why they all would be shorted out with a short circuit across R3 State two rules for the voltage and current values in a parallel circuit State briefly why the total power equals the sum of the individual values of power, whether a series circuit or a parallel circuit is used Explain briefly why the current is the same in both sides of the main line that connects the voltage source to the parallel branches 10 Explain why an open in the main line disables all the branches, but an open in one branch affects only that branch current 11 Give two differences between an open circuit and a short circuit 12 List as many differences as you can in comparing series circuits with parallel circuits Why can the current in parallel branches be different when they all have the same applied voltage? 13 Why are household appliances connected to the 120-V power line in parallel instead of in series? Why does the current increase in the voltage source as more parallel branches are added to the circuit? 14 Give one advantage and one disadvantage of parallel connections 15 A 5-⍀ and a 10-⍀ resistor are in parallel across a dc voltage source Which resistor will dissipate more power? Provide proof with your answer (a) Show how to connect three equal resistances for a combined equivalent resistance one-third the value of one resistance (b) Show how to connect three equal resistances for a combined equivalent resistance three times the value of one resistance Show how the formula REQ ϭ R1R2/(R1 ϩ R2) is derived from the reciprocal formula ϭ ϩ _ REQ R1 Parallel Circuits sch10858_ch05_138-167.indd 161 R2 161 3/15/10 10:22:17 AM Problems SECTION 5–1 THE APPLIED VOLTAGE VA IS THE SAME ACROSS PARALLEL BRANCHES 5–1 MultiSim In Fig 5–19, how much voltage is across points a A and B? b C and D? c E and F? d G and H? Figure 5–21 ϩ VA ϭ 102 V Ϫ Figure 5–19 A VA ϭ 12 V 5–9 In Fig 5–21, solve for the branch currents I1, I2, I3, and I4 C ϩ R1 ϭ 120 ⍀ Ϫ B E D R1 ϭ 510 ⍀ R2 ϭ 6.8 k⍀ R3 ϭ 1.2 k⍀ R4 ϭ 5.1 k⍀ G 5–10 Recalculate the values for I1, I2, I3, and I4 in Fig 5–21 if the applied voltage, VA, is reduced to 51V R2 ϭ 60 ⍀ F H 5–2 In Fig 5–19, how much voltage is across a the terminals of the voltage source? b R1? c R2? 5–3 In Fig 5–19, how much voltage will be measured across points C and D if R1 is removed from the circuit? SECTION 5–3 KIRCHHOFF’S CURRENT LAW (KCL) 5–11 MultiSim In Fig 5–19, solve for the total current, I T 5–12 MultiSim In Fig 5–19 re-solve for the total current, I T , if a 10-⍀ resistor, R3, is added across points G and H 5–13 In Fig 5–20, solve for the total current, I T 5–14 In Fig 5–20, re-solve for the total current, I T , if R2 is removed from the circuit 5–15 In Fig 5–21, solve for the total current, I T VA SECTION 5–2 EACH BRANCH I EQUALS _ R 5–4 In Fig 5–19, solve for the branch currents, I1 and I2 5–5 In Fig 5–19, explain why I2 is double the value of I1 5–6 In Fig 5–19, assume a 10-⍀ resistor, R3, is added across points G and H a Calculate the branch current, I3 b Explain how the branch currents, I1 and I2 are affected by the addition of R3 5–16 In Fig 5–21, re-solve for the total current, I T , if VA is reduced to 51 V 5–17 In Fig 5–22, solve for I1, I2, I3, and I T Figure 5–22 H 5–7 In Fig 5–20, solve for the branch currents I1, I2, and I3 G ϩ VA ϭ 24 V F R1 ϭ k⍀ Ϫ E R2 ϭ 1.2 k⍀ R3 ϭ 1.5 k⍀ Figure 5–20 A ϩ VA ϭ 18 V Ϫ R1 ϭ 30 ⍀ R2 ϭ 20 ⍀ R3 ϭ 60 ⍀ 5–8 In Fig 5–20, the branch currents I1 and I3 remain the same if R2 is removed from the circuit? Explain your answer 162 sch10858_ch05_138-167.indd 162 B C D 5–18 In Fig 5–22, how much is the current in the wire between points a A and B? b B and C? c C and D? d E and F? e F and G? f G and H? Chapter 3/15/10 10:22:17 AM 5–19 In Fig 5–22 assume that a 100-⍀ resistor, R4, is added to the right of resistor, R3 How much is the current in the wire between points a A and B? b B and C? c C and D? d E and F? e F and G? f G and H? 5–20 In Fig 5–23, solve for I1, I2 I3, and IT 5–27 In Fig 5–20, re-solve for REQ if R2 is removed from the circuit 5–28 In Fig 5–21, solve for REQ 5–29 In Fig 5–21, re-solve for REQ if VA is reduced to 51 V 5–30 In Fig 5–22, solve for REQ 5–31 In Fig 5–23, solve for REQ 5–32 In Fig 5–24, solve for REQ 5–33 Figure 5–23 I G F ϩ In Fig 5–25, how much is REQ if R1 ϭ 100 ⍀ and Figure 5–25 VA ϭ 66 V Ϫ MultiSim R2 ϭ 25 ⍀? E H R3 ϭ 33 ⍀ 5–26 In Fig 5–20, solve for REQ R1 ϭ 330 ⍀ R2 ϭ 220 ⍀ A J B C REQ D 5–21 In Fig 5–23, how much is the current in the wire between points a A and B? b B and C? c C and D? d E and F? e F and G? f G and H? g G and I? h B and J? 5–22 In Fig 5–24, apply Kirchhoff’s current law to solve for the unknown current, I3 R1 IT ϭ 160 mA R2 5–34 MultiSim In Fig 5–25, how much is REQ if R1 ϭ 1.5 M⍀ and R2 ϭ M⍀? 5–35 MultiSim In Fig 5–25, how much is REQ if R1 ϭ 2.2 k⍀ and R2 ϭ 220 ⍀? 5–36 In Fig 5–25, how much is REQ if R1 ϭ R2 ϭ 10 k⍀? 5–37 In Fig 5–25, how much resistance, R2, must be connected in parallel with a 750 ⍀ R1 to obtain an REQ of 500 ⍀? 5–38 In Fig 5–25, how much resistance, R1, must be connected in parallel with a 6.8 k⍀ R2 to obtain an REQ of 1.02 k⍀? 5–39 How much is REQ in Fig 5–26 if R1 ϭ k⍀, R2 ϭ k⍀, R3 ϭ 200 ⍀, and R4 ϭ 240 ⍀? Figure 5–24 ϩ VA ϭ 120 V Ϫ R1 I1 ϭ mA R2 I2 ϭ 12 mA R3 I3 ϭ ? R4 Figure 5–26 I4 ϭ 60 mA REQ R1 R2 R3 R4 5–23 Two resistors R1 and R2 are in parallel with each other and a dc voltage source How much is I2 through R2 if I T ϭ 150 mA and I1 through R1 is 60 mA? SECTION 5–4 RESISTANCES IN PARALLEL 5–24 In Fig 5–19, solve for REQ 5–40 How much is REQ in Fig 5–26 if R1 ϭ 5.6 k⍀, R2 ϭ 4.7 k⍀, R3 ϭ 8.2 k⍀, and R4 ϭ 2.7 k⍀? 5–25 In Fig 5–19, re-solve for REQ if a 10-⍀ resistor, R3 is added across points G and H 5–41 Parallel Circuits sch10858_ch05_138-167.indd 163 MultiSim How much is REQ in Fig 5–26 if R1 ϭ 1.5 k⍀, R2 ϭ k⍀, R3 ϭ 1.8 k⍀, and R4 ϭ 150 ⍀? 163 3/15/10 10:22:18 AM 5–42 How much is REQ in Fig 5–26 if R1 ϭ R2 ϭ R3 ϭ R4 ϭ 2.2 k⍀? 5–43 A technician is using an ohmmeter to measure a variety of different resistor values Assume the technician has a body resistance of 750 k⍀ How much resistance will the ohmmeter read if the fingers of the technician touch the leads of the ohmmeter when measuring the following resistors: a 270 ⍀ b 390 k⍀ c 2.2 M⍀ d 1.5 k⍀ e 10 k⍀ SECTION 5–5 CONDUCTANCES IN PARALLEL 5–44 In Fig 5–27, solve for G1, G2, G3, G T, and REQ SECTION 5–7 ANALYZING PARALLEL CIRCUITS WITH RANDOM UNKNOWNS 5–53 In Fig 5–29, solve for VA, R1, I2, REQ, P1, P2, and PT Figure 5–29 ϩ VA IT ϭ 200 mA Figure 5–30 VA REQ ϭ 75 ⍀ R1 ϭ k⍀ G1 R2 ϭ k⍀ G2 I1 ϭ 50 mA 5–54 In Fig 5–30, solve for VA, I1, I2, R2, IT, P2, and PT Figure 5–27 GT REQ R2 ϭ 120 ⍀ R1 Ϫ ϩ P1 ϭ 2.25 W Ϫ R1 ϭ 100 ⍀ R3 ϭ 200 ⍀ G3 R2 5–55 In Fig 5–31, solve for R3, VA, I1, I2, IT, P1, P2, P3, and PT Figure 5–31 5–45 In Fig 5–28, solve for G1, G2,G3, G4, G T, and REQ Figure 5–28 VA ϩ REQ ϭ Ϫ 125 ⍀ GT REQ R1 ϭ 500 ⍀ G1 R2 ϭ k⍀ G2 R3 ϭ 1.2 k⍀ G3 R4 ϭ 100 ⍀ G4 R1 ϭ 500 ⍀ R2 ϭ 250 ⍀ R3 I3 ϭ 150 mA 5–56 In Fig 5–32, solve for IT, I1, I2, R1, R2, R3, P2, P3, and PT Figure 5–32 5–46 Find the total conductance, GT for the following branch conductances; G1 ϭ mS, G2 ϭ 200 S, and G3 ϭ 1.8 mS How much is REQ? 5–47 Find the total conductance, GT for the following branch conductances; G1 ϭ 100 mS, G2 ϭ 66.67 mS, G3 ϭ 250 mS, and G4 ϭ 83.33 mS How much is REQ? SECTION 5–6 TOTAL POWER IN PARALLEL CIRCUITS 5–48 In Fig 5–20, solve for P1, P2, P3, and PT ϩ VA ϭ 108 V REQ ϭ 90 ⍀ Ϫ R1 P1 ϭ 10.8 W R3 R2 I3 ϭ 200 mA 5–57 In Fig 5–33, solve for IT, I1, I2, I4, R3, R4, P1, P2, P3, P4, and PT Figure 5–33 5–49 In Fig 5–21, solve for P1, P2, P3, P4, and PT 5–50 In Fig 5–22, solve for P1, P2, P3, and PT 5–51 In Fig 5–23, solve for P1, P2, P3, and PT 5–52 In Fig 5–24, solve for P1, P2, P3, P4, and PT 164 sch10858_ch05_138-167.indd 164 VA ϭ 36 V ϩ REQ ϭ Ϫ 360 ⍀ R1 ϭ 1.2 k⍀ R2 ϭ 1.8 k⍀ R3 I3 ϭ 15 mA R4 Chapter 3/15/10 10:22:19 AM 5–58 In Fig 5–34, solve for VA, I1, I2, R2, R3, I4, and REQ SECTION 5–8 TROUBLESHOOTING: OPENS AND SHORTS IN PARALLEL CIRCUITS 5–60 Figure 5–36 shows a parallel circuit with its normal operating voltages and currents Notice that the fuse in the main line has a 25-A rating What happens to the circuit components and their voltages and currents if a the appliance in Branch shorts? b the motor in Branch burns out and becomes an R4 ϭ open? 1.5 k⍀ c the wire between points C and E develops an open? d the motor in Branch develops a problem and begins drawing 16 A of current? Figure 5–34 M1 150 mA ϩ VA R1 ϭ 240 ⍀ Ϫ R3 I3 ϭ 24 mA R2 40 mA M2 5–59 In Fig 5–35, solve for VA, I1, I2, I4, R1, R3, and REQ Figure 5–35 Figure 5–36 M2 ϩ VA R1 Ϫ R2 ϭ 800 ⍀ Fuse, F1 A 30 mA C 25 A R3 I3 ϭ mA R4 ϭ k⍀ 80 mA 120 V ac Power-line voltage B E Branch Branch 120 V Motor 120 V 100-W lightbulb I1 ϭ 0.833 A D G Branch Household 120 V appliance I2 ϭ 8.33 A F I3 ϭ 10 A H M1 Critical Thinking 5–61 A 180-⍀,¼-W resistor is in parallel with 1-k⍀, ½-W and 12-k⍀, 2-W resistors What is the maximum total current, I T, that this parallel combination can have before the wattage rating of any resistor is exceeded? 5–62 A 470-⍀,1/8-W resistor is in parallel with 1-k ẳ-W and 1.5-k, ẵ-W resistors What is the maximum voltage, V, that can be applied to this circuit without exceeding the wattage rating of any resistor? 5–63 Three resistors in parallel have a combined equivalent resistance REQ of k⍀ If R2 is twice the value of R3 and three times the value of R1, what are the values for R1, R2, and R3? 5–64 Three resistors in parallel have a combined equivalent resistance REQ of ⍀ If the conductance, G1, is onefourth that of G2 and one-fifth that of G3, what are the values of R1, R2, and R3? 5–65 A voltage source is connected in parallel across four resistors R1, R2, R3, and R4 The currents are labeled I1, I2, I3, and I4, respectively If I2 ϭ 2I1, I3 ϭ 2I2, and I4 ϭ 2I3, calculate the values for R1, R2, R3, and R4 if REQ ϭ k⍀ Troubleshooting Challenge Figure 5–37 shows a parallel circuit with its normal operating voltages and currents Notice the placement of the meters M1, M2, and M3 in the circuit M1 measures the total current IT, M2 measures the applied voltage VA, and M3 measures the current between points C and D The following problems deal with troubleshooting the parallel circuit in Fig 5–37 5–66 If M1 measures 2.8 A, M2 measures 36 V, and M3 measures 1.8 A, which component has most likely failed? How is the component defective? 5–67 If M1 measures 2.5 A, M2 measures 36 V, and M3 measures A, what is most likely wrong? How could you isolate the trouble by making voltage measurements? 5–69 If the fuse F1 is blown, (a) How much current will be measured by M1 and M3? (b) How much voltage will be measured by M2? (c) How much voltage will be measured across the blown fuse? (d) What is most likely to have caused the blown fuse? (e) Using resistance measurements, outline a procedure for finding the defective component 5–68 If M1 measures 3.3 A, M2 measures 36 V, and M3 measures 1.8 A, which component has most likely failed? How is the component defective? 5–70 If M1 and M3 measure A but M2 measures 36 V, what is most likely wrong? How could you isolate the trouble by making voltage measurements? Parallel Circuits sch10858_ch05_138-167.indd 165 165 3/18/10 9:31:24 PM Figure 5–37 Circuit diagram for troubleshooting challenge Normal values for I1, I2, I3, and I4 are shown on schematic M3 F1, A B C D E 1.8 A M2 ϩ VA ϭ 36 V A S1 R1 ϭ 24 ⍀ I1 ϭ 1.5 A 36 V Ϫ R2 ϭ 36 ⍀ I2 ϭ A R3 ϭ 60 ⍀ I3 ϭ 600 mA R4 ϭ 30 ⍀ I4 ϭ 1.2 A 4.3 A J I H G F M1 5–71 If the fuse F1 has blown because of a shorted branch, how much resistance would be measured across points B and I? Without using resistance measurements, how could the shorted branch be identified? 5–72 If the wire connecting points F and G opens, (a) How much current will M3 show? (b) How much voltage would be measured across R4? (c) How much voltage would be measured across points D and E? (d) How much voltage would be measured across points F and G? Answers to Self-Reviews 5–73 Assuming that the circuit is operating normally, how much voltage would be measured across, (a) the fuse F1; (b) the switch S1? 5–74 If the branch resistor R3 opens, (a) How much voltage would be measured across R3? (b) How much current would be indicated by M1 and M3? 5–75 If the wire between points B and C breaks open, (a) How much current will be measured by M1 and M3? (b) How much voltage would be measured across points B and C? (c) How much voltage will be measured across points C and H? 5–1 a 1.5 V b 120 V c two each 5–5 a S b 0.75 S, 1.33 M⍀ c 0.25 M⍀ 5–2 a b c d 5–6 a 480 W b 660 W c 30 W 10 V 1A 10 V 2A 5–3 a A b A c 1.2 A 5–4 a 1.57 M⍀ b 1.2 M⍀ c ⍀ 5–7 a 120 V b A c A 5–8 a b c d e 120 V 0⍀ 6A V, 120 V 120 V Laboratory Application Assignment In this lab application assignment you will examine the characteristics of a simple parallel circuit You will also determine the required resistance values in a parallel circuit having random unknowns Equipment: Obtain the following items from your instructor • Variable dc power supply 166 sch10858_ch05_138-167.indd 166 • Assortment of carbon-film resistors • DMM Parallel Circuit Characteristics Examine the parallel circuit in Fig 5–38 Calculate and record the following values: I1ϭ , I2 ϭ , I3 ϭ , IT ϭ , REQ ϭ Chapter 3/15/10 10:22:21 AM Remove the voltage source connections in Fig 5–38, and add another 1.2 k⍀ resistor to the right of resistor R3 Measure and record the equivalent resistance, REQ: REQ ϭ How did adding another branch resistance affect the equivalent resistance, REQ? Figure 5–38 ϩ VA ϭ 12 V R1 ϭ k⍀ Ϫ R2 ϭ 1.5 k⍀ R3 ϭ 1.2 k⍀ Explain why REQ changed as it did. _ Design Challenge Construct the parallel circuit in Fig 5–38 Measure and record the following values (Note that the power supply connections must be removed to measure REQ.) I1 ϭ , I2 ϭ , I3 ϭ , IT ϭ , REQ ϭ How does the ratio I1 / l2 compare to the ratio R2 / R1? _ What is unique about comparing these ratios? Add the measured branch currents I1, I2, and I3 Record your answer _ How does this value compare to the measured value of IT? _ Does the sum of these individual branch currents satisfy KCL? _ In Fig 5–38, which branch resistance dissipates the most power? Which branch resistance dissipates the least amount of power? Examine the parallel circuit in Fig 5–39 Determine the values for R1, R 2, R 3, and R4 that will provide the division of currents represented in the figure The equivalent resistance, REQ, must equal 450 ⍀ The applied voltage, VA, can have any value Recommended Procedure Make sure you understand the problem before you begin Draw a workable schematic on a separate sheet of paper Show all known circuit values on your hand-drawn schematic Show all your calculations in solving for R1, R 2, R 3, and R4 Select standard values for R1, R 2, R 3, and R4 that are within Ϯ10% of your calculated values Construct the circuit using the standard values from step If your results are way off from what you expect, seek help from your instructor If your results are close to the specified design criteria, adjust the values of R1, R 2, R 3, or R4 for best results You must show all calculations! 10 Have an instructor check your results, and receive your just reward Figure 5–39 REQ ϭ 450 ⍀ ϩ VA Parallel Circuits sch10858_ch05_138-167.indd 167 Ϫ R1 I1 ϭ R2 IT I2 ϭ R3 IT I3 ϭ R4 IT I4 ϭ 10 IT 167 3/15/10 10:22:21 AM chapter Series-Parallel Circuits A series-parallel circuit, also called a combination circuit, is any circuit that combines both series and parallel connections Although many applications exist for series or parallel circuits alone, most electronic circuits are actually a combination of the two In general, series-parallel or combination circuits are used when it is necessary to obtain different voltage and current values from a single supply voltage, VT When analyzing combination circuits, the individual laws of series and parallel circuits can be applied to produce a much simpler overall circuit In this chapter you will be presented with several different series-parallel combinations For each type of combination circuit shown, you will learn how to solve for the unknown values of voltage, current, and resistance You will also learn about a special circuit called the Wheatstone bridge As you will see, this circuit has several very interesting applications in electronics And finally, you will learn how to troubleshoot a series-parallel circuit containing both open and shorted components sch10858_ch06_168-201.indd 168 3/18/10 8:27:28 AM Chapter Objectives After studying this chapter you should be able to ■ ■ Chapter Outline 6–1 Finding RT for Series-Parallel Resistances ■ 6–2 Resistance Strings in Parallel ■ 6–3 Resistance Banks in Series 6–4 Resistance Banks and Strings in Series-Parallel 6–5 Analyzing Series-Parallel Circuits with Random Unknowns ■ ■ 6–6 The Wheatstone Bridge 6–7 Troubleshooting: Opens and Shorts in Series-Parallel Circuits ■ Determine the total resistance of a series-parallel circuit Calculate the voltage, current, resistance, and power in a series-parallel circuit Calculate the voltage, current, resistance, and power in a series-parallel circuit having random unknowns Explain how a Wheatstone bridge can be used to determine the value of an unknown resistor List other applications of balanced bridge circuits Describe the effects of opens and shorts in series-parallel circuits Troubleshoot series-parallel circuits containing opens and shorts Important Terms balanced bridge banks in series ratio arm standard resistor strings in parallel Wheatstone bridge Online Learning Center Additional study aids for this chapter are available at the Online Learning Center: www.mhhe.com/grob11e Series-Parallel Circuits sch10858_ch06_168-201.indd 169 169 3/15/10 10:24:13 AM 6–1 Finding R T for Series-Parallel Resistances In Fig 6–1, R1 is in series with R2 Also, R3 is in parallel with R4 However, R2 is not in series with either R3 or R4 The reason is that the current through R2 is equal to the sum of the branch currents I3 and I4 flowing into and away from point A (see Fig 6–1b) As a result, the current through R3 must be less than the current through R2 Therefore, R2 and R3 cannot be in series because they not have the same current For the same reason, R4 also cannot be in series with R2 However, because the current in R1 and R2 is the same as the current flowing to and from the terminals of the voltage source, R1, R2, and VT are in series The wiring is shown in Fig 6–1a and the schematic diagram in Fig 6–1b To find RT, we add the series resistances and combine the parallel resistances In Fig 6–1c, the 0.5-k⍀ R1 and 0.5-k⍀ R2 in series total k⍀ for R1–2 The calculations are GOOD TO KNOW Most electronic circuitry consists of a combination of series and 0.5 k⍀ ϩ 0.5 k⍀ ϭ k⍀ parallel connections Also, the 1-k⍀ R3 in parallel with the 1-k⍀ R4 can be combined, for an equivalent resistance of 0.5 k⍀ for R3–4, as in Fig 6–1d The calculations are k⍀ ϭ 0.5 k⍀ _ MultiSim Figure 6–1 Example of a series-parallel circuit (a) Wiring of a series-parallel circuit (b) Schematic diagram of a series-parallel circuit (c) Schematic with R1 and R2 in series added for R1–2 (d ) Schematic with R3 and R4 in parallel combined for R3–4 (e) Axial-lead resistors assembled on a lab prototype board to form the series-parallel circuit shown in part c R1 ϭ 0.5 k⍀ R2 R1 R4 R3 R2 ϭ 0.5 k⍀ A I T ϭI1 ϭI ϭ I3 ϩ I4 ϩ Ϫ R3 ϭ k⍀ VT ϭ 1.5 V R4 ϭ k⍀ IT (a ) I3 I4 B (b ) R1–2 ϭ k⍀ ϩ Ϫ VT ϭ 1.5 V R1–2 ϭ k⍀ A R3 ϭ k⍀ R4 ϭ k⍀ ϩ Ϫ A R3–4 ϭ 500 ⍀ VT ϭ 1.5 V B B (c ) 170 sch10858_ch06_168-201.indd 170 (d ) (e) Chapter 3/15/10 10:24:15 AM This parallel R3–4 combination of 0.5 k⍀ is then added to the series R1–2 combination for the final RT value of 1.5 k⍀ The calculations are 0.5 k⍀ ϩ k⍀ ϭ 1.5 k⍀ The 1.5 k⍀ is the RT of the entire circuit connected across the VT of 1.5 V With RT known to be 1.5 k⍀, we can find IT in the main line produced by 1.5 V Then V 1.5 V ϭ mA IT ϭ _T ϭ RT 1.5 k⍀ This 1-mA IT is the current through resistors R1 and R2 in Fig 6–1a and b or R1–2 in Fig 6–1c At branch point B, at the bottom of the diagram in Fig 6–1b, the mA of electron flow for IT divides into two branch currents for R3 and R4 Since these two branch resistances are equal, IT divides into two equal parts of 0.5 mA each At branch point A at the top of the diagram, the two 0.5-mA branch currents combine to equal the 1-mA IT in the main line, returning to the source VT Figure 6–1e shows axial-lead resistors assembled on a lab prototype board to form the series-parallel circuit shown in part c ■ 6–1 Self-Review Answers at end of chapter Refer to Fig 6–1b a Calculate the series R of R1 and R2 b Calculate the parallel R of R3 and R4 c Calculate RT across the source VT 6–2 Resistance Strings in Parallel More details about the voltages and currents in a series-parallel circuit are illustrated in Fig 6–2, which shows two identical series strings in parallel Suppose that four 120-V, 100-W lightbulbs are to be wired with a voltage source that produces 240 V Each bulb needs 120 V for normal brilliance If the bulbs were connected directly across the source, each would have the applied voltage of 240 V This would cause excessive current in all the bulbs that could result in burned-out filaments If the four bulbs were connected in series, each would have a potential difference of 60 V, or one-fourth the applied voltage With too low a voltage, there would be insufficient current for normal operation, and the bulbs would not operate at normal brilliance Figure 6–2 Two identical series strings in parallel All bulbs have a 120-V, 100-W rating (a) Wiring diagram (b) Schematic diagram R1 R3 R4 R2 String (a ) sch10858_ch06_168-201.indd 171 R3 V3 ϭ 120 V R2 V2 ϭ 120 V R4 V4 ϭ 120 V VA ϭ 240 V VA ϭ 240 V Series-Parallel Circuits R1 V1 ϭ 120 V String String String (b ) 171 3/15/10 10:24:17 AM Figure 6–3 Series string in parallel with another branch (a) Schematic diagram (b) Equivalent circuit Branch Branch R1 ϭ 8⍀ 8V ϩ V ϭ 12 V Ϫ ⌱T ϭ 3A Branch Branch 12 V R3 ϭ 6⍀ R2 ϭ 4⍀ 4V ⌱1 ϭ A ⌱2 ϭ A ϩ ⌱T ϭ 3A When a parallel branch contains series resistors, both resistors have the same current but the individual resistor voltage drops ⌱1 ϭ A R3 ϭ 6⍀ ⌱2 ϭ A (b ) (a ) GOOD TO KNOW R1-2 ϭ 12 ⍀ V ϭ 12 V Ϫ However, two bulbs in series across the 240-V line provide 120 V for each filament, which is the normal operating voltage Therefore, the four bulbs are wired in strings of two in series, with the two strings in parallel across the 240-V source Both strings have 240 V applied In each string, two series bulbs divide the 240 V equally to provide the required 120 V for normal operation Another example is illustrated in Fig 6–3 This circuit has just two parallel branches One branch includes R1 in series with R2 The other branch has just the one resistance R3 Ohm’s law can be applied to each branch will be less than the voltage applied across the entire branch The individual resistor voltage drops add, however, to equal the voltage applied across the branch Branch Currents I1 and I2 In Fig 6–3a, each branch current equals the voltage applied across the branch divided by the total resistance in the branch In branch 1, R1 and R2 total ϩ ϭ 12 ⍀ With 12 V applied, this branch current I1 is 12͞12 ϭ A Branch has only the 6-⍀ R3 Then I2 in this branch is 12͞6 ϭ A Series Voltage Drops in a Branch For any one resistance in a string, the current in the string multiplied by the resistance equals the IR voltage drop across that particular resistance Also, the sum of the series IR drops in the string equals the voltage across the entire string Branch is a string with R1 and R2 in series The I1R1 drop equals V, whereas the I1R2 drop is V These drops of and V add to equal the 12 V applied The voltage across the R3 branch is also the same 12 V Calculating IT The total line current equals the sum of the branch currents for all parallel strings Here IT is A, equal to the sum of A in branch and A in branch Calculating RT The resistance of the total series-parallel circuit across the voltage source equals the applied voltage divided by the total line current In Fig 6–3a, RT ϭ 12 V͞3 A, or ⍀ This resistance can also be calculated as 12 ⍀ in parallel with ⍀ Fig 6–3b shows the equivalent circuit Using the product divided by the sum formula, 72͞18 ϭ ⍀ for the equivalent combined RT Applying Ohm’s Law There can be any number of parallel strings and more than two series resistances in a string Still, Ohm’s law can be used in the same way for the series and parallel parts 172 sch10858_ch06_168-201.indd 172 Chapter 3/15/10 10:24:17 AM of the circuit The series parts have the same current The parallel parts have the same voltage Remember that for V͞R the R must include all the resistance across the two terminals of V ■ 6–2 Self-Review Answers at end of chapter Refer to Fig 6–3a a How much is the voltage across R3? b If I in R2 were A, what would I in R1 be? c If the source voltage were 18 V, what would V3 be across R3? 6–3 Resistance Banks in Series In Fig 6–4a, the group of parallel resistances R2 and R3 is a bank This is in series with R1 because the total current of the bank must go through R1 The circuit here has R2 and R3 in parallel in one bank so that these two resistances will have the same potential difference of 20 V across them The source applies 24 V, but there is a 4-V drop across R1 The two series voltage drops of V across R1 and 20 V across the bank add to equal the applied voltage of 24 V The purpose of a circuit like this is to provide the same voltage for two or more resistances in a bank, where the bank voltage must be less than the applied voltage by the amount of the IR drop across any series resistance To find the resistance of the entire circuit, combine the parallel resistances in each bank and add the series resistance As shown in Fig 6–4b, the two 10-⍀ resistances, R2 and R3 in parallel, are equivalent to ⍀ Since the bank resistance of ⍀ is in series with ⍀ for R1, the total resistance is ⍀ across the 24-V source Therefore, the main-line current is 24 V͞6 ⍀, which equals A The total line current of A divides into two parts of A each in the parallel resistances R2 and R3 Note that each branch current equals the bank voltage divided by the branch resistance For this bank, 20͞10 ϭ A for each branch The branch currents, I2 and I3, are combined in the main line to provide the total A in R1 This is the same total current flowing in the main line, in the source, into the bank, and out of the bank There can be more than two parallel resistances in a bank and any number of banks in series Still, Ohm’s law can be applied in the same way to the series and parallel parts of the circuit The general procedure for circuits of this type is to find the equivalent resistance of each bank and then add all series resistances GOOD TO KNOW When a parallel bank exists in a series path, both resistors have the same voltage but the individual branch currents are less than the series current The branch currents add, however, to equal the series current entering and leaving the parallel bank Figure 6–4 Parallel bank of R2 and R3 in series with R1 (a) Original circuit (b) Equivalent circuit V1 ϭ V R1 ϭ ⍀ IT ϭ A ϩ ϩ Ϫ IT ϭ A ϩ R2 ϭ 10 ⍀ VT ϭ 24 V Ϫ I2 ϭ 20 V I3 ϭ 2A 2A Ϫ Y (a) Series-Parallel Circuits IT ϭ A X Parallel bank R3 ϭ 10 ⍀ X ϩ VT ϭ 24 V Ϫ R2– ϭ ⍀ Y IT ϭ A sch10858_ch06_168-201.indd 173 R1 ϭ ⍀ IT ϭ A (b) 173 3/15/10 10:24:18 AM ... 10 6) Ϫ (0.5 ϫ 10 8) I–98 (20 ϫ 10 Ϫ3) Ϫ (5000 ϫ 10 Ϫ6) sch10858_intro_002-0 21. indd 20 10 4 I? ?11 6 10 Ϫ4 I? ?11 7 10 1 I? ?11 8 10 Ϫ8 I? ?11 9 10 Ϫ7 I? ?12 0 10 ? ?13 I? ?12 1 10 15 I? ?12 2 10 18 Ϫ9 Subtract the following numbers... I? ?1 Powers of 10 1, 000,000,000 ϭ 10 9 10 ϭ 10 1 0.0000 01 ϭ 10 Ϫ6 10 0,000,000 ϭ 10 8 ϭ 10 0 0.00000 01 ϭ 10 Ϫ7 10 ,000,000 ϭ 10 7 0 .1 ϭ 10 ? ?1 0.000000 01 ϭ 10 Ϫ8 1, 000,000 ϭ 10 6 0. 01 ϭ 10 Ϫ2 0.0000000 01 ϭ 10 Ϫ9... ϭ 10 Ϫ9 10 0,000 ϭ 10 5 0.0 01 ϭ 10 Ϫ3 0.00000000 01 ϭ 10 ? ?10 10 ,000 ϭ 10 4 0.00 01 ϭ 10 Ϫ4 0.000000000 01 ϭ 10 ? ?11 1, 000 ϭ 10 3 0.000 01 ϭ 10 Ϫ5 0.0000000000 01 ϭ 10 ? ?12 10 0 ϭ 10 2 sch10858_intro_002-0 21. indd