Solution Manual for Mathematics for Electricity and Electronics, 4th Edition

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Solutions Manualto AccompanyMATHEMATICS FORELECTRICITY ANDELECTRONICSFOURTH EDITIONArthur D. Kramer

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ContentsCHAPTER 1Basic Arithmetic1Exercise 1.1Arithmetic Operations1Exercise 1.2Multiplying and Dividing Fractions1Exercise 1.3Adding Fractions2Exercise 1.4Hand Calculator Operations2Review Exercises3CHAPTER 2Decimals and Percentages3Exercise 2.1Decimals3Exercise 2.2Percentages4Exercise 2.3Precision and Accuracy5Exercise 2.4Hand Calculator Operations5Review Exercises6CHAPTER 3Powers and Roots6Exercise 3.1Powers6Exercise 3.2Powers of Ten7Exercise 3.3Square Roots and Cube Roots8Exercise 3.4Hand Calculator Operations8Review Exercises9CHAPTER 4Systems of Measurement10Exercise 4.1Scientific and Engineering Notation10Exercise 4.2Metric System (SI)11Exercise 4.3The U.S. Customary System12Exercise 4.4Hand Calculator Operations13Review Exercises14CHAPTER 5Basic Algebra15Exercise 5.1Signed Numbers15Exercise 5.2Algebraic Terms15Exercise 5.3Rules for Exponents16Review Exercises17CHAPTER 6Linear Equations18Exercise 6.1Solution of First-Degree Equations18Exercise 6.2Equation Solving Methods19Review Exercises19CHAPTER 7Basics of DC Circuits20Exercise 7.1DC Circuits and Ohm’s Law20iii

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Exercise 7.2Electric Power21Review Exercises22CHAPTER 8Multiplying and Factoring Polynomials22Exercise 8.1Multiplying Polynomials22Exercise 8.2Monomial Factors23Exercise 8.3Binomial Factors24Exercise 8.4Second-Degree Equations24Review Exercises25CHAPTER 9Algebraic Fractions26Exercise 9.1Reducing Fractions26Exercise 9.2Multiplying and Dividing Fractions26Exercise 9.3Addition of Fractions27Exercise 9.4Equations with Fractions28Review Exercises29CHAPTER 10Formulas and Problem Solving31Exercise 10.1Formulas and Literal Equations31Exercise 10.2Problem Solving32Review Exercises33CHAPTER 11Series and Parallel DC Circuits34Exercise 11.1Series Circuits34Exercise 11.2Parallel Circuits35Exercise 11.3Series-Parallel Circuits36Review Exercises37CHAPTER 12Graphs39Exercise 12.1Rectangular Coordinate System39Exercise 12.2Linear Function42Exercise 12.3Nonlinear Graphs46Review Exercises50CHAPTER 13Linear Systems54Exercise 13.1Graphical Solution of Two Equations54Exercise 13.2Algebraic Solution of Two Equations56Exercise 13.3Solution by Determinants57Exercise 13.4Solution of Three Linear Equations58Review Exercises59CHAPTER 14Network Analysis60Exercise 14.1Voltage Division60Exercise 14.2Kirchhoff’s Laws61Exercise 14.3Solving Circuits61Review Exercises62iv•CONTENTS

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CHAPTER 15Network Theorems63Exercise 15.1Superposition Theorem63Exercise 15.2Thevenin’s Theorem64Exercise 15.3Norton’s Theorem66Review Exercises67CHAPTER 16Trigonometry of the Right Triangle69Exercise 16.1Angles and Triangles69Exercise 16.2Pythagorean Theorem70Exercise 16.3Trigonometric Ratios70Review Exercises71CHAPTER 17Trigonometry of the Circle72Exercise 17.1Trigonometric Functions72Exercise 17.2Reference Angles and Special Angles73Exercise 17.3Inverse Functions73Review Exercises74CHAPTER 18Alternating Current75Exercise 18.1Alternating Current Waves75Exercise 18.2Root Mean Square Values77Exercise 18.3Frequency and Period78Exercise 18.4Phase Angle79Review Exercises81CHAPTER 19Trigonometry of Vectors82Exercise 19.1Vectors and Phasors82Exercise 19.2Law of Sines83Exercise 19.3Law of Cosines83Review Exercises84CHAPTER 20Complex Numbers and Phasors85Exercise 20.1ThejOperator85Exercise 20.2Complex Numbers85Exercise 20.3Complex Phasors86Exercise 20.4Operations with Complex Phasors88Review Exercises89CHAPTER 21Series AC Circuits90Exercise 21.1Inductive Reactance andRLSeries Circuits90Exercise 21.2Capacitive Reactance andRCSeries Circuits91Exercise 21.3RLCSeries Circuits and Resonance92Review Exercises93CHAPTER 22Parallel AC Circuits94Exercise 22.1RLCircuits94Exercise 22.2RCCircuits94CONTENTS•v

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Exercise 22.3Susceptance and Admittance95Exercise 22.4RLCCircuits96Exercise 22.5AC Networks97Exercise 22.6Filters97Review Exercises98CHAPTER 23Exponents and Logarithms99Exercise 23.1Fractional Exponents99Exercise 23.2Exponential Functions100Exercise 23.3Common and Natural Logarithms102Review Exercises103CHAPTER 24Applications of Logarithms104Exercise 24.1Exponential Equations104Exercise 24.2RC and RL Circuits105Exercise 24.3Power and Gain106Exercise 24.4Bode Plots107Review Exercises116CHAPTER 25Computer Number Systems119Exercise 25.1Binary Number System119Exercise 25.2Binary Arithmetic119Exercise 25.3Octal Number System120Exercise 25.4Hexadecimal Number System121Exercise 25.5Hexadecimal Arithmetic121Exercise 25.6Computer Codes122Review Exercises122CHAPTER 26Boolean Algebra124Exercise 26.1Boolean Algebra124Exercise 26.2Logic Circuits125Exercise 26.3Karnaugh Maps126Review Exercises127CHAPTER 27Statistics128Exercise 27.1Mean, Median, and Mode128Exercise 27.2Standard Deviation129Exercise 27.3Histograms and the Normal Curve130Review Exercises132vi•CONTENTS

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Detailed solutions are shown for more difficult problems. For a group of similarproblems, procedures are shown for the first one in the group and for any othersthat differ significantly.CHAPTER 1Basic ArithmeticExercise 1.1Arithmetic Operations1.162.153.44.205.1206.1607.48.579.3610.711.4012.513.5014.215.2616.1417.7718.919.4520.20021.1022.25023.224.3025.12026.4027.528.529.2530.931.132.133.1034.1935.5536.15037.150038.51039.140.541.342.543.18090=20 mi/gal;21010=21 mi/gal44.tech $64040=$16/hr;teacher$57030=$19/hr45.(6000)(9000)=54,000,000 mi46.442kmh=22 km/h47.1 A48.2 A49.16 V50.12 V51.752.122Exercise 1.2Multiplying and Dividing Fractions1.352.133.454.125.346.237.158.1209.2910.3711.21112.61313.93514.1715.21516.12417.41518.116019.4320.621.222.523.2524.11225.284526.101127.228.14529.51630.111231.5632.52133.22134.1835.636.337.1338.1539.1240.2541.842.51443.644.321

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45.146.447.1550310=ft48.34 100()=75 ft49.()10003512  =$30050.(,)$40 00012145000  =51.27 V52.60 V53.116A54.150A55.925W56.120WExercise 1.3Adding Fractions1.77=12.453.584.565.13206.11147.19248.11129.141510.2511.316012.313613.5720014.417515.1416.11017.1618.16019.91020.7821.112022.12023.852424.693525.526.3427.338028.3710029.12720030.4912031.72032.710033.6310034.15435.316036.72437.2338.5639.71240.62541.18042.5910043.131244.32045.141546.3847.4110048.15049.112050.3451.3852.1453.334054.2555.1 lb56.up58lb57.1458.1859.134in60.()( )5361251ftininft− ÷=61.10Ω62.25Ω63.20Ω64.300Ω65.203Ω66.403Ω67.110312203÷  =468.710910920720 =Exercise 1.4Hand Calculator Operations1.42.1973.474.19005.1306.127.4128.49.22•CHAPTER 1Basic Arithmetic

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10.311.14712.3213.6014.315.4016.20017.118.219.120.121.422.223.1224.125.710 (OIL)26.14285727.666.7Ω28.57.1ΩReview Exercises1.222.473.124.4005.216.1357.1548.129.3210.2511.15212.1913.414.1015.5216.4517.111618.15019.1520.17621.222.223.72424.134025.53626.2527.2710028.12829.8730.71631.20032.5833.14734.235.236.337.25 mi/h38.$16039.12500=()250 ft40.500−400−25=$7541.1000+250=$125042.715 45121638− ÷ ÷=ft43.12A44.116A45.10 V46.245V47.185W48.24 W49.27 V50.25A51.20Ω52.60Ω53.20Ω54.37Ω55.1553553259÷  =56.eje j72012910736=CHAPTER 2Decimals and PercentagesExercise 2.1Decimals1.10.092.65.1293.0.914.69.3845.22.716.7.397.4.058.1.2029.0.006210.10.0111.1212.0.069Exercise 2.1Decimals•3

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13.6.2514.0.0280415.0.0000116.0.0000617.3018.21019.0.1220.33.0121.1022.0.123.0.0824.2.825.3226.5027.0.828.1.61229.12.330.0.8731.0.0232.0.1533.434.0.12135.1036.100037.4038.0.5539.740.0.341.0.0842.0.443.0.2083 mm44.3.12 cm45.0.5555 cm246.0.08 in, 0.0004 in247.8.4 ft48.109.72 m49.40.1 V50.1.50 A51.17.0 cm52.4.4 mm, 1.21 mm2Exercise 2.2Percentages1.0.75, 75%2.0.5, 50%3.0.4, 40%4.0.3, 30%5.0.375, 37.5%6.0.875, 87.5%7.0.04, 4%8.0.09, 9%9.0.5625, 56.25%10.0.15, 15%11.15%,32012.25%,1413.10%,11014.60%,3515.12%,32516.16%,42517.28%,72518.36%,92519.15, 0.220.45, 0.821.320, 0.1522.720, 0.3523.4350, 0.8624.1120, 0.5525.99100, 0.9926.49100, 0.4927.0.05, 5%28.0.12, 12%29.1.25, 125%30.2.4, 240%31.120, 5%32.225, 8%33.32, 150%34.11, 100%35.65, 1.236.21, 2.037.7125, 0.05638.101200, 0.50539.33%, 0.3340.0.0625, 6.25%41.316, 18.75%42.78, 87.5%43.17200, 0.08544.116, 0.062545.11000, 0.1%46.0.002, 0.2%47.348.1649.1550.3051.1.3552.1.1953.7554.12.555.8156.1257.1.6558.0.487559.2.560.3.62561.$13.2062.$150.0063.0.95 ft364.30 g65.85%66.0.025%67.$38.00, $42.7568.$44.0069.$64.00, $68.8070.$20.00, $21.6571.$42.00, $44.1072.$64273.12%74.20%75.110%,11201000,98, 116, 1.1976.0.03,140,0 525., 0.50%77.165Ω78.532Ω79.0.11 A, 1.21 A80.0.22 A, 0.88 A81.40% decrease82.50% increase83.20% increase84.25% decrease4•CHAPTER 2Decimals and Percentages

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Exercise 2.3Precision and Accuracy1.32.33.24.25.36.47.38.19.410.111.412.313.414.115.416.317.418.219.220.421.422.323.5, 5.2, 5.1524.3, 3.1, 3.1025.300, 320, 31826.100, 120, 12127.0.4, 0.44, 0.44528.0.4, 0.44, 0.44029.10,000, 9900, 991030.10,000, 11,000, 10,90031.80,000, 82,000, 81,90032.1000, 1100, 107033.100 100 101,,34.30, 29, 29.035.20, 19, 18.936.0.09, 0.090, 0.089937.20 20 20 0,,.38.40, 39, 39.139.300, 340, 33640.500, 450, 45441.300 260 260,,42.700, 680, 67843.1000 1000 999,,44.9000, 8900, 889045.461 m246.5,570,000 m347.152 lb48.27.1 ft/s, 18.5 mi/h49.18 V50.30 mA51.203 in252.0.046 cm353.120 V54.0.11 A55.1480 W56. (a)1.3Ω(b)1.28Ω57. (a)$43(b)$4658. (a)$170(b)$172Exercise 2.4Hand Calculator Operations1.22.82803.21.14.9505.2.06.37.0.58.2.59.14710.48.411.2.412.0.2013.0.6814.0.0084415.0.14316.0.7517.0.86018.2.6919.35.520.12421.1.9022.167,00023.11024.50525.8.2726.0.027027.0.0048228.0.00090029.0.0026630.20.731.197,000,000 mi232.14.9 cm33. (a)4.67%(b)19.1%34.(,)( .)( ,)( .)$,.87 000 01537 850 0 02913 538 65+=35.33.0 V36.295 V37.0.415 A38.0.338 AExercise 2.4Hand Calculator Operations•5

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Review Exercises1.31.262.0.00113.4.044.8.4645.220.16.307.0.258.49.0.00610.0.14411.2012.0.02513.4414.0.0115.0.8, 80%16.0.125, 12.5%17.0.15, 15%18.310, 30%19.425, 16%20.2, 200%21.720, 0.3522.18, 0.12523.11200, 0.05524.91000, 0.9%25.0.005, 0.5%26.32, 1.527.128.829.8.430.24.531.3932.0.933.82.534.8.5535.0.536.5137.3338.3.439.0.9540.0.05841.31.042.0.86743.66.944.14945.25.3 in, 26.7 in246.$1317.50, $1240.0047.(40,000)(0.4)e j34=$12,00048.(317)(10)(0.75)=2380 Btu/h49.$59.84, $64.3350.$11051.7652.0.0048 s53. (a)0.41 A(b)2.5 A54.210Ω55.10%56.33%57.(4700)e j13(0.75) = 1175≈1200Ω58.0.41 A59.21 mA60. (a)515100(%)=33%(b)2 516723../e j=≈1.7ΩCHAPTER 3Powers and RootsExercise 3.1Powers1.812.643.1284.1255.100,0006.6257.1218.80009.116, 0.062510.271000, 0.02711.925, 0.3612.1125, 0.00813.110 000,, 0.000114.49100, 0.4915.2516, 1.562516.81625, 0.129617.0.36,92518.0.008,112519.2.25,9420.3625, 1.4421.8125, 0.06422.18, 0.12523.0.0001,110 000,24.1625, 0.001625.0.000008,1125 000,26.0.027,27100027.19, 0.111 …28.5029.130.75, 1.431.140, 0.0256•CHAPTER 3Powers and Roots

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32.125, 2.433.6125, 0.04834.14, 0.2535.18, 0.12536.671000, 0.06737.120, 0.0538.11100, 0.1139.258, 3.12540.14425, 5.7641.950, 0.1842.729100, 7.2943.1500, 0.00244.825, 0.3245.564=0.07812546.3125, 0.02447.17250, 0.06848.2120, 1.0549.754, 18.7550.2094, 52.2551.19, 0.111 …52.116, 0.062553.0.512 cm354.8100 ft255.$26,62056.$140.2657.2.25 mm258.0.396 ft359.20Ω60.125Ω61.17 W62.50.7 W63.0.06 W64.18 WExercise 3.2Powers of Ten1.1032.1063.1004.1095.106−6.103−7.104−8.101−9.102−10.105−11.101−12.103−13.103−14.104−15.100,00016.100,000,00017.1,000,00018.119.0.01,110020.0.0001,110 000,21.0.1,11022.0.001,1100023.0.000001,11 000 000,,24.0.000000001,11 000 000 000,,,25.1026.100027.10628.10929.105−30.1010−31.106−32.101−33.10934.10635.109−36.10037.10338.10439.10−240.10−541.101=1042.10243.10−244.10−645.10246.106−47.101−48.104−49.10450.10751.10252.100=153.103−54.101° =55.10956.10−657.101−58.108−59.12×10260.49×100=4961.24×101=24×1062.72×10263.6×10−1264.45×104−65.12×101−66.4×10667.3×10368.5×103−Exercise 3.2Powers of Ten•7

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69.2.5×10770.5107×71.2.5×102−72.4.5×10573.0.75×10674.1×10575.16×103, 16,00076.40×106−, 0.00004077.7×109−, 0.00000000778.5×1012,5,000,000,000,00079.6.5×104, 65×103,65,00080.6×103=60×102=600081.29×104−=2.9×103−,0.002982.43×10−2=4.3×101−,0.4383.4.5×10=4584.085.480 W86.3.8 W87.45.5 A88.100 A89.3.0 V90.0.0099 V91.0.05 A92.0.11 A93.2000Ω94.300,000ΩExercise 3.3Square Roots and Cube Roots1.42.113.524.3105.236.297.0.88.0.69.0.110.0.311.20012.5013.3014.4015.0.0916.0.1217.1.318.1.519.320.521.1222.2523.0.124.0.225.1026.0.127.1428.1829.2830.2431.1.432.2.233.2.134.1.835.1236.1837.0.6=3538.0.04=12539.240.15=0.241.0.1=11042.12=0.543.64×10944.36×10445.16×10846.27×101247.0.64×101048.0.01×10249.0.001×10950.0 0081018.×51.9×101152.32×101053.150×10654.0 21014.×55.4×10356.5×10257.12×1058.7×10659.0.5×10260.0.8×10361.2×10362.3×1063.6×10364.5×10465.0.2×10166.0.5×101−67.1.5×105−68.0.32×102−69.0.75×10570.4×10271.70 ft72.100 mm, 10 cm73.3%74.4%75.2.576.0.1 ft77.20Ω78.25Ω79.60 V80.0.02 A81.0.2 A82.48 V83.6.4 W84.7.2 W85.0.05 A86.400 V87.169292+=88.4(9)−11=25Exercise 3.4Hand Calculator Operations1.58.12.0.8853.0.01014.56.65.0.6556.0.03647.79.78.8.958•CHAPTER 3Powers and Roots

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9.0.24210.2.9511.57.012.0.20213.15.014.0.94015.10.116.0.60617.57.418.2.1919.97.920.2.7421.148 cm322.341 m/s23.0.794 W24.1320 W25.4830Ω26.9 66103.×ΩReview Exercises1.3432.1213.116, 0.06254.8125, 0.0645.0.216,271256.0.064,81257.1.21,1211008.0.001,110009.0.01,110010.0.625,5811.25, 0.412.0.004,125013.114.18, 0.12515.0.29,2910016.0.0625,11617.718.65, 1.219.25, 0.420.221.0.3,31022.0.11,1110023.424.0.3,31025.126.1327.0.06,35028.0.9,91029.730.1131.75, 1.432.0.9,91033.100,000,00034.0.00001,1100 000,35.110 000,, 0.000136.103=100037.102=10038.106−=0.000001,11 000 000,,39.104=10,00040.104−=0.0001,110 000,41.105−=0.00001,1100 000,42.101−=0.1,11043.109=1,000,000,00044.10011110−=. ,45.106=1,000,00046.106−=0.000001,11 000 000,,47.14×10248.24×108−49.2×103−50.4.5×101−51.010101010910..×=×−−52.2.5×100=2.553.1×10854.1055.16×10556.1×106−57.6.5×103=65×10258.12×106−=120×107−59.81×10860.6.75×10661.9×10362.0.6×1063.4×10364.0.2×10265.7×10366.9×10267.0.1×10768.0.8×10269.0.014070.0.030171.27772.0.30873.51.774.0.13675.9.4876.0.32677.56 ft78.$102.5079.50 mm=5 cm80.0.216 m381.50ΩReview Exercises•9

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82.256 W83.0.04 A84.20×102=2000Ω85.6.5Ω86.22 V87.0.075×103=75 W88.0.013 A89.0.0031Ω90.0.15CHAPTER 4Systems of MeasurementExercise 4.1Scientific and Engineering Notation1.4.26×1010, 42.6×1092.1.17×107, 11.7×1063.9.30×104−, 930×106−4.3.01×105−, 30.1×106−5.1.05×107, 10.5×1066.4.49×104, 44.9×1037.4.56×101, 45.6×1008.2.70×101, 27.0×1009.2.35×10010.8.73×10011.1.17×103−12.9.81×10−2, 98.1×103−13.3.34×102, 334×10014.6.99×104, 69.9×10315.1.12×101−, 112×103−16.4.09×101−, 409×103−17.1×10318.1×10119.1.62×105, 162×10320.7.76×10321.56,400,000, 5.64×107,56.4×10622.336 3 36103361020,.,××23.1,200,000, 1.2×10624.14 000 000 1 410141076,,, .,××25.0.000000114, 1.14×10−7, 114×10−926.0 345 3 451034 51023.,.,.××−−27.52.8, 5.28×101, 52.8×10028.0 384 384103841013.,.,××−−29.0.00569, 5.69×10−330.1560 1560100., .×31.5,660,000, 5.66×10632.9 900 000 000 9 90109,,,,.×33.0.000552, 5.52×10−4, 552×10−634.0 0891 8 91108911023.,.,.××−−35.26,400,000, 2.64×107, 26.4×10636.433 000 4 33104331053,,.,××37.0.00000390, 3.90×10−638.0 0000931 9 31109311056.,.,.××−−39.1.45, 1.45×10040.46 7 46 7100. ,.×41.0.0101, 1.01×10−2, 10.1×10−342.0 0634 6 341063 41023.,.,.××−−43.112,000, 1.12×105, 112×10344.87 000 8 701087 01043,,.,.××45.0.0000105, 1.05×10−5, 10.5×10−646.0 717 717107171013.,.,××−−47.871,000,000, 8.71×108, 871×10648.4 440 000 4 44106,,,.×49.1.23, 1.23×10050.0 000001005 1005106., .×−51.125,000, 1.25×105, 125×10352.0 0000101 101101011056., .,.××−−53.0.503, 5.03×10−1, 503×10−354.0 0550 5 501055 01023.,.,.××−−55.1.29×107, 12.9×106, 12,900,00056.5 68105 680 0006.,,,×10•CHAPTER 4Systems of Measurement

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