Introductory Circuit Analysis

Instructor s Resource Manual to accompany Introductory Circuit Analysis Eleventh Edition Robert L. Boylestad Upper Saddle River, New Jersey Columbus, Ohio

Contents CHAPTER CHAPTER 9 CHAPTER 3 3 CHAPTER 4 CHAPTER 5 9 CHAPTER 6 39 CHAPTER 7 5 CHAPTER 8 65 CHAPTER 9 86 CHAPTER 0 06 CHAPTER 4 CHAPTER 43 CHAPTER 3 50 CHAPTER 4 57 CHAPTER 5 70 CHAPTER 6 95 CHAPTER 7 0 CHAPTER 8 CHAPTER 9 53 CHAPTER 0 66 CHAPTER 80 CHAPTER 3 CHAPTER 3 38 CHAPTER 4 333 CHAPTER 5 34 TEST ITEM FILE 353 iii

Chapter.. 3. d 0,000 ft mi 60 s 60 min 4. υ t 0 s 5,80 ft min h 363.64 mph 5. h 4 min 0.067 h 60 min d 3mi υ t.067 h 9.05 mph 6. a. 95 mi 5,80 ft h min 39.33 ft/s h mi 60 min 60 s b. d 60 ft t υ 39.33 ft/s 0.43 s c. d 60 ft 60 s 60min mi υ 40.9 mph t s min h 5,80 ft 7. 8. 9. 0. 5 5 5 MKS, CGS, C ( F 3) (68 3) (36) 0 9 9 9 SI: K 73.5 + C 73.5 + 0 93.5. 0.7378 ft - lb 000 J 737.8 ft-lbs J 3 ft in..54 cm. 0.5 yd yd ft in. 45.7 cm 3. a. 0 4 b. 0 6 c. 0 3 d. 0 3 e. 0 0 f. 0 4. a. 5 0 3 b. 30 0 3 c..4 0 6 d. 50 0 3 e. 4.0 0 4 f. 0 0 Chapter

5. a. 4. 0 3 + 48.0 0 3 5. 0 3 5. 0 4 b. 90 0 3 + 360 0 3 450 0 3 4.50 0 5 c. 50 0 5 6 0 5 44 0 5 4.4 0 4 d.. 0 3 + 0.05 0 3 0.6 0 3 0.65 0 3 6.5 0 6. a. (0 )(0 3 ) 0 5 00 0 3 b. (0 )(0 3 ) 0 0 c. (0 3 )(0 6 ) 0 9 d. (0 )(0 5 ) 0 3 e. (0 6 )(0 0 6 ) 0 f. (0 4 )(0 8 )(0 8 ) 0 4 7. a. (50 0 3 )(3 0 4 ) 50 0.5 0 b. (. 0 3 )( 0 3 ) 4.4 0 0 4.4 c. (8 0 6 )(.8 0 6 ) 9.6.96 0 d. (30 0 4 )(4 0 3 )(7 0 8 ) 840 0 8.40 0 3 8. a. 0 /0 4 0 0 0 3 b. 0 /0 3 0 5 0 0 6 c. 0 4 /0 3 0 7 0 0 6 d. 0 7 /0.0 0 9 e. 0 38 /0 4.0 0 4 f. 00 /0 0 /0 0 3 9. a. ( 0 3 )/(8 0 5 ) 0.5 0 8.50 0 7 b. (4 0 3 )/(60 0 4 ) 4/60 0 7 0.667 0 7 6.67 0 8 c. ( 0 5 )/(5 0 5 ) /5 0 0 4.4 d. (78 0 8 )/(4 0 6 ).95 0 5 0. a. (0 ) 3.0 0 6 b. (0 4 ) / 0.0 0 3 c. (0 4 ) 8 00.0 0 30 d. (0 7 ) 9.0 0 63. a. (4 0 ) 6 0 4.6 0 5 b. (6 0 3 ) 3 6 0 9.6 0 7 c. (4 0 3 )(6 0 ) (4 0 3 )(36 0 4 ) 44 0.44 0 3 d. (( 0 3 )(0.8 0 4 )(0.003 0 5 )) 3 (4.8 0 3 ) 3 (4.8) 3 (0 3 ) 3 0.6 0 9. 0. a. ( 0 3 ).0 0 6 b. c. d. 4 (0 )(0 ) 0 /0 3.0 0 5 3 0 3 6 4 (0 ) (0 ) (0 )(0 ) 0.0 0 8 4 4 4 0 0 0 3 4 (0 )(0 ) 0 7 /0 4.0 0 4 0 Chapter

e. ( 0 4 ) 3 (0 )/0 6 (0 )(0 )/0 6 0 0 /0 6.0 0 6 3 [(0 )(0 )] f. 4 3 3 [(0 ) ][ 0 ] (0 )(0 ) 0.0 0 3. a. (3 0 ) (0 ) (9 0 4 )(0 )/(3 0 4 ) (9 0 6 )/(3 0 4 ) 3 0 300 4 3 0 b. 4 8 (4 0 ) 6 0 3 3 (0) 8 0 0 5 00.0 0 3 c. 4 8 (6 0 ) 36 0 4 ( 0 ) 4 0 9.0 0 d. (7 0 0 6 / 3 5 ) 3 0 0 5.5 0 7 50.0 0 9 e. 3 (4 0 ) (3 0 ) (6 0 )(3 0 ) 48 0 4 4 4 0 0 0 6 8 4.0 0 f. (6 0 6 ) / (0 5 ) 5 ( 0 ) (4 0 3 )(0 5 )( 0 ) 8 0 0 800.0 0 8 g. 3 3 4 / (3 0 ).60 0 ( 0 )(8 0 ) 5 (7 0 ) 9 4 / (7 0 )(.56 0 )(6 0 ) 0 49 0 5 6 (69. 0 )(4 0 ) 76.48 0 0 0 49 0 49 0 5.64 0 4 56.4 0 3 +3 4. a. 6 0 3 0.006 0 +6 3 3 b. 4 0 3 4000 0 6 +3 +3 +3 c. 50 0 5 5000 0 3 5 0 6 0.005 0 9 + 3 3 Chapter 3

+5 3 3 d. 30 0 8 0.0003 0 3 0.3 0 6 300 0 9 5 +3 +3 3 5. a. 0.05 0 0 s 50 0 3 s 50 ms +3 +3 b. 000 0 6 s 0 3 s ms 3 3 c. 0.04 0 3 s 40 0 6 s 40 μs +3 +6 d. 8400 0 s 0.0084 0 6 s 0.0084 μs 6 3 e. 4 0 3 0 3 m 4 0 0 m 4000 0 3 m 4000 mm +3 0 0 increase by 3 f. 60 0 3 0 3 m 0.6 0 3 m 0.6 km 3 6. a. 60 s.5 min 90 s min b. 60 min 60 s 0.04 h h min 44 s c. μs 0.05 s 0.05 0 6 μs 50 0 3 μs 0 6 s d. mm 0.6 m 0.6 0 3 mm 60 mm 0 3 m 4 Chapter

e.. 0 7 ns s 0 9 s. 0 ns 0 ns f. 3.6 0 6 min h day s 60 s 60 min 4 h 4.90 days 6 0 F pf 7. a. 0. μf μf 0 F 0. 0 6 0 pf 0 5 pf b. 80 0 3 00 cm m m 8000 0 3 cm 8 cm m km c. 60 cm 00 cm 000 m 60 0 5 km 60 min 60 s ms d. 3. h.5 0 6 ms h min 0 3 s 3 0 m μ m e. 0.06 mm 6 mm 0 m 0.06 0 3 μm 6 μm f. 60 cm m m 00 cm 00 cm 60 0 4 m m 8. a. 00 in. 39.37 in..54 m in. m b. 4 ft ft 39.37 in.. m 4.45 N c. 6 lb lb 6.7 N d. 60 0 3 N lb dynes 5 0 dynes 4.45 N 0.3 lb in. ft e. 50,000 cm.54 cm in. 49.6 ft 580 ft in. m f. 0.00 mi 3. m mi ft 39.37 in. Chapter 5

yd 9. 580 ft, 580 ft 760 yds 3 ft in. m 580 ft 609.35 m,.6 km ft 39.37 in. m 39.37 in. ft mi 60 s 60 min 30. 99,79,458 s m in. 580 ft min h 670,65,88. mph 670.6 0 6 mph 3 ft mi 3. 00 yds yd 5,80 ft 60 mi h min h 60 min 60 s 0.0568 mi 0.067 mi/s 3. d 0.0568 mi t υ 0.067 mi/s 3.40 s 30 mi 580 ft in. m h min h mi ft 39.37 in. 60 min 60 s 3.4 m/s 50 yd 60 min 3 ft mi 33..705 mi/h min h yd 5,80 ft d 3000 mi day t 760 h 73.33 days υ.705 mi/h 4 h 000 m 39.37 in. ft mi 34. 0 km km m in. 580 ft mi d 6.4 mi υ, t 40.39 min 6.5 min υ mi 6.5 min 6.4 mi 3 ft in. 35. 00 yds yd ft 3600 in 3600 quarters 36. 60 mph: d 00 mi t.67 h h:40. min υ 60 mi/h 75 mph: d 00 mi t.33 h h:9.98 min υ 75 mi/h difference 0. minutes 6 Chapter

cm 60 min 60 s m 600 0.06 h 345.6 m s h min 00 cm 37. d υt [ ] 4 ft step 38. d 86 stories 605 steps story 9 ft d d 605 steps minute υ t 80.5 seconds t υ steps 60 seconds second 3.38 minutes 4 ft mile 39. d (86 stories) 04 ft story 5,80 ft min 0.7833 min 47.30 min/mile mile 0.8 miles 0.8 miles 40. 5 min mile υ d t mile 5,80 ft 056 ft 4 ft 5 min mile, distance 86 stories minute story d 04 ft t.4 minutes υ ft 056 min 04 ft 4. a. Btu 5 J 4.74 0 3 Btu 054.35 J b. 3 gallon m 4 ounces 8 ounces 64.7 gallons 7. 0 4 m 3 c. 86,400 s.4 days. 0 5 s day d. m 3 64.7 gallons 8 pints 3.38 pints 3 m gallon 4. 6(4 + 8) 7 43. (0 + 3)/4 3 44. (8 + ) 4.4 45. MODE DEGREES: cos 50 0.64 46. MODE DEGREES: tan (3/4) 36.87 Chapter 7

47. ( 400/(6 0) ) +.95 48. 05 0 6 49..0 0 50. 6.667 0 6 + 0.5 0 6 7.7 0 6 8 Chapter

Chapter. QQ. a. F ( 9 0 )(C)( C) k 8 0 9 N r (m) 9 QQ b. F k r 9 ( 9 0 )(C) (3 m) ( C) 0 9 N 9 QQ c. F ( 9 0 )(C)( C) k 0.8 0 9 N r (0 m) 9 r3 0 m d. Exponentially, r m 0 while F 8 0 N 9 F 0.8 0 N 00 3. a. r mi: 580 ft in. m mi 609.35 m mi ft 39.37 in. kqq (9 0 )(8 0 C)(40 0 C) 880 0 F r (609.35 m).59 0 9 6-6 3 6. μn b. r 0 ft: in. m 0 ft ft 39.37 in. 3.05 m F 3 3 880 0 880 0 kq Q r 0.3 N (3.05 m) 9.30 in. m c..59 mm 6 39.37 in. 3 3 kqq 880 0 880 0 F 38.34 0 3 6 r (.59 0 m).53 0 38.34 kn 3 N 4. kqq kqq (9 0 )(0 0 5. F r 4 r F 3.6 0 9 6 ) 0 mm Chapter 9

kqq kqq 6. F.8 kq Q 4(.8) 7. r ( m) kqq 7. a. F 7 mn r (0) b. Q /Q / Q Q 7. kq Q (9 0 9 )(Q )(Q ) 9 0 9 ( Q ) 7. 7. Q 9 Q 0 μc 9 8 0 8 0 Q Q ( 0 5 C) 40 μc 7. W. J Q 0.4 mc 3 k 8. W Q (60 )(8 mc) 0.48 J 9. Q W 96 J 6 6 C 0. Q W 7 J 9 8 C. I. I Q t Q t mc 4.9 ma.8 s 3 C.60 A ()(60 s) 3. Q It (40 ma)(0.8)(60 s).9 C 4. Q It (50 ma)(.)(60 s) 8.0 C 5. t Q I 6 mc ma 3 s 6..847 0 8 C electrons 3.5 C 8 6.4 0 electrons Q 3.5 C I 0.9 A t s 7. Q It (4 ma)(90 s) 360 mc 8 6.4 0 electrons 360 mc.5 0 8 electrons C 0 Chapter

8. I Q t 86 C (.)(60 s).94 A > A (yes) 9. 0.84 0 6 C electrons.346 mc 8 6.4 0 electrons Q.346 mc I.43 ma t 60 ms 0. a. Q It ( ma)(0.0 μs) 0 C 0 8 6.4 0 electrons C C electron.5 0 8 $.5 0 6.5 million b. Q It (00 μa)(.5 ns).5 0 3 C.5 0 3 8 6.4 0 electrons $ C C electron (a) > (b) 0.94 million. Q It (00 0 3 A)(30 s) 6 C W 40 J 6.67 Q 6 C 40 C. Q It (0.5 min) min W 74 J 3.53 Q 0 C 0 C W 0.4 J 3. Q 0.067 C 4 Q 0.067 C I 3.34 A 3 t 5 0 s 4. I Ah rating 00 Ah t(hours) 40 h 5 A 5. Ah (0.8 A)(75 h) 60.0 Ah 6. t(hours) Ah rating I 3 Ah.8 A 5 h Chapter

60 min 60 s 7. 40 Ah(for h): W Q I t ( )(40 A)( h).78 0 6 J h min 60 min 60 s 60 Ah(for h): W ( )(60 A)( h).59 0 6 J h min Ratio W /W.5 or 50% more energy available with 60 Ah rating. min h For 60 s discharge: 40 Ah It I [ 60 s] I(6.67 0 3 h) 60 s 60 min 40 Ah and I 400 A -3 6.67 0 h min h 60 Ah It I [ 60 s] I(6.67 0 3 h) 60 s 60 min 60 Ah and I 3600 A -3 6.67 0 h I /I.5 or 50 % more starting current available at 60 Ah 8. I 3 Ah 500 ma 6.0 h 60 min 60 s Q It (500 ma)(6 h) h min W Q (0.8 kc)( ) 9.6 kj 0.80 kc 9. 30. 3. 3. 33. 34. 60 s 35. 4 min 40 s min Q It (.5 A)(40 s) 600 C 36. Q It (0 0 3 A)(0 s) 00 mc W Q (.5 )(00 0 3 C).5 J Chapter

Chapter 3. a. 0.5 in. 500 mils 000 mils b. 0.0 in. in. 0 mils c. 000 mils in. 0.5 in. 4 in. 50 mils d. in. 000 mils e. 3 in. 0 mils 0.0 ft 40 mils ft in. in. 000 mils f. 0. cm.54 cm in. 39.37 mils. a. A CM (30 mils) 900 CM b. 0.06 in. 6 mils, A CM (6 mils) 56 CM c. " 8 0.5" 5 mils, A CM (5 mils) 5.63 0 3 CM in. 000 mils d. cm.54 cm in. 393.7 mils, A CM (393.7 mils) 55 0 3 CM in. 000 mils e. 0.0 ft ft in. 40 mils, A CM (40 mils) 57.60 0 3 CM 39.37 in. f. 0.004 m m 0.654 in. 65.4 mils, A CM (65.4 mils) 7.36 0 3 CM 3. A CM (d mils ) d mils A CM a. d 600 CM 40 mils 0.04 in. b. d 80 CM 8.64 mils 0.09 in. c. d 40,000 CM 00 mils 0. in. Chapter 3 3

d. d 65 CM 5 mils 0.05 in. e. d 6.5 CM.5 mils 0.005 in. f. d 00 CM 0 mils 0.0 in. 4. 0.0 in. 0 mils, A CM (0 mils) 00 CM l (00 ) R ρ (0.37) 0.74 Ω A 00 CM 5. A CM (4 mils) l 6 CM, R ρ A l 80 6. a. A ρ 7 544 CM R.5 Ω (50 ft) ( 9.9) 9.8 Ω 6 CM b. d A 544 CM 3.3 mils 3.3 0 3 in. CM 7. " 3 R 0.035" 3.5 mils, A CM (3.5 mils) 976.56 CM l ρ l R RA ρ (. Ω)(976.56 CM) 3.58 ft 600 l 8. a. A CM ρ (0.37)(300 ) 94.73 CM A 3.3 Ω d 94.73 CM 30.70 mils 30.7 0 3 in. b. larger c. smaller 9. a. R silver > R copper > R aluminum l (9.9)(0 ft) b. Silver: R ρ A CM 99 Ω { A CM ( mil) CM l (0.37)(50 ft) Copper: R ρ A 00 CM 5.9 Ω { A CM (0 mils) 00 CM Aluminum: R l ρ A (7)(00 ft) 500 CM.36 Ω { A CM (50 mils) 500 CM 0. ρ RA (500 Ω)(94 CM) l 000 47 nickel 4 Chapter 3

. a. 3" 3000 mils, /" 0.5 in. 500 mils Area (3 0 3 mils)(5 0 mils) 5 0 5 sq. mils 5 0 5 4/ π CM sq mils 9.08 0 5 CM sq mil l (0.37)(4 ) R ρ.7 μω 5 A 9.08 0 CM l (7)(4 ) b. R ρ 35.59 μω 5 A 9.08 0 CM Aluminum bus-bar has almost 64% higher resistance. c. increases d. decreases. l l, A A /4, ρ ρ ρl R A ρla l A 8 R ρ l ρl A l A / 4 A and R 8R 8(0. Ω).6 Ω ΔR.6 Ω 0. Ω.4 Ω 3. πd 4A 4(0.04 in. ) A d 4 π π 0.57 in. d mils 5.7 mils A CM (5.7 mils) 50,940.49 CM l ρ R A ρl A l A R l ρ ρla la A (ρ ρ ) and R R l A l A Ω (800 m )(300 ft)(40,000 CM) 94.8 mω (00 ft)(50,940.49 CM) 4. a..60 Ω #: 450 ft 000 ft.55 Ω #4: 450 ft 000 ft 0.567 Ω.36 Ω b. Resistance: #4:#.36 Ω:0.567 Ω : c. Area: #4:# 406.8 CM:834.0 CM : Chapter 3 5

0.68 Ω 5. a. #8: R 800 ft 000 ft.3 Ω 6.385 Ω #8: R 800 ft.49 Ω 000 ft b. #8:#8.49 Ω:.3 Ω 0.7: 0: c. #8:#8 64.3 CM:6,509 CM :0.6 :0 6. a. l (0.37)(30 ) 3.CM A ρ 5,850 CM #3 3 R 6 mω 6 0 but 0 A # b. l (0.37)(30 ) 3.CM A ρ 03,700 CM #0 3 R 3 mω 3 0 7. a. A/CM 30 A/,600 CM.09 ma/cm b..09 ma CM 000 mils 000 mils CM π sq mils in. in..39 ka/in. 4 in. c. 5 ka.39 ka 3.6 in. 8. in. 0.083 in..54 cm in. 0. cm π d (3.4)(0. cm) A 4 4 0.035 cm RA ( Ω)(0.035 cm ) l 6 ρ.74 0 40,603 cm 406.03 m 9. a. ".54 cm ".7 cm, 3 in..54 cm in. 7.6 cm in..54 cm 4 ft ft in..9 cm -6 l (.74 x 0 )(.9 cm) R ρ.7 μω A (.7 cm)(7.6 cm) b. R 6 (.85 0 )(.9 cm) ρ A (.7 cm)(7.6 cm) 35.59 μω 6 Chapter 3

c. increases d. decreases 6 ρ ρ 50 0 0. R s 00 d d 00 00. R R s l w w s l R R (50 Ω)(/ in.) 500 Ω.5 μcm 0.5 in.. a. d in. 000 mils A CM (0 3 mils) 0 6 CM 6 RA ( m Ω)(0 CM) ρ CM-Ω/ft 3 l 0 ft b. in..54 cm πd π(.54 cm) A 5.067 cm 4 4 in..54 cm l 000 ft ft in. 30,480 cm RA ( m Ω)(5.067 cm ) ρ.66 0 7 Ω-cm l 30,480 cm c. k 7 ρ.66 0 Ω-cm ρ CM- Ω / ft.66 0 7 3. 4. 34.5 + 0 34.5 + 80 Ω R 36 + 0 36 + 00 0.0 Ω R R (0.0 Ω)(336) 36, R (34.5)( Ω ) 44.5 0.08 Ω.57 Ω 5 5 5. C ( F 3) (3 3) 0 (3 F) 9 9 5 C (70 3). (70 F) 9 34.5 +. 34.5 + 0 4 Ω R ( 34.5)(4 Ω ) R 3.67 Ω 55.6 Chapter 3 7

6. 7. 34.5 + 30 34.5 40 0.76 Ω R R ( 94.5)(0.76 Ω ) 0.56 Ω 64.5 43 + ( 30) 43 + 0 0.04 Ω R R (43)(40 m Ω ) 3 46 mω 8. a. 68 F 0 C, 3 F 0 C 34.5 + 0 34.5 + 0 0.00 R R (34.5)( m Ω ) 54.5.84 mω F 00 C 34.5 + 0 34.5 + 00 m Ω R R (334.5)( m Ω ) 54.5.63 mω b. ΔR.63 m Ω mω 0.63 mω Δ T 00 C 0 C 80 C 7.88 μω/ C or 7.88 0-5 Ω/0 C 9. a. 34.5 + 4 34.5 + t, Ω. Ω t 7.85 C 34.5 + 4 34.5 + t b. Ω 0.Ω, t 0.65 C 30. a. K 73.5 + C 50 73.5 + C C 3.5 34.5 + 0 34.5 3.5 0 Ω R R c. F.35 (0 Ω) 0.446 Ω 54.5 9 9 C + 3 ( 73.5 ) + 3 459.67 5 5 b. K 73.5 + C 38.65 73.5 + C C 34.5 34.5 + 0 34.5 0 Ω R 34.5 ( 0)0 Ω R 0 Ω 54.5 Recall: 34.5 Inferred absolute zero R 0 Ω 8 Chapter 3

3. a. α 0 T i + 0 C 34.5 + 0 54.5 0.00399 0.00393 b. R R 0 [ + α 0 (t 0 C)] Ω 0.8 Ω[ + 0.00393(t 0 )].5 + 0.00393t 0.0786.5 0.94 0.00393t 0.386 0.00393t 0.386 t 0.00393 83.6 C 3. R R 0 [ + α 0 (t 0 C)] 0.4 Ω[ + 0.00393(6 0)] 0.4 Ω[ 0.057] 0.39 Ω 33. Table: 000 of # copper wire.588 Ω @ 0 C C 9 5 (F 3) 9 5 (5 3) 46. C R R 0 [ + α 0 (t 0 C)].588 Ω[ + 0.00393(46. 0)].75 Ω Rnominal Ω 34. ΔR (PPM)( ΔT) 6 6 (00)(65 0 ) 0.98 Ω 0 0 R R nominal + ΔR.98 Ω Rnominal 00 Ω 35. ΔR (PPM)( ΔT) 6 6 (00)(50 0 ) 0.30 Ω 0 0 R R nominal + ΔR 00 Ω + 0.30 Ω 00.30 Ω 36. 37. 38. #: Area 659 CM.54 cm d 659 CM 80.8 mils 0.0808 in. in. πd π (0.05 cm) A 0.033 cm 4 4 MA I [0.033 cm ] 33 ka >> 0 A cm 0.05 cm 39. 40. a. times larger b. 4 times larger 4. 0 kω 3.5 kω 6.5 kω Chapter 3 9

4. 6.5 kω and 8.75 kω 43. 44. a. 560 kω ± 5%, 560 kω ± 8 kω, 53 kω 588 kω b. 0 Ω ± 0%, 0 Ω ± Ω, 98 Ω 4 Ω c. 00 Ω ± 0%, 00 Ω ± 0 Ω, 80 Ω 0 Ω 45. a. 0 Ω Brown, Red, Brown, Silver b. 8. Ω Gray, Red, Gold, Silver c. 6.8 kω Blue, Gray, Red, Silver d. 3.3 MΩ Orange, Orange, Green, Silver 46. 0 Ω± 0% 8 Ω Ω no overlap, continuance 5 Ω± 0% Ω 8 Ω 47. 0 Ω± 0% 0 Ω± Ω 9 Ω Ω No overlap 5 Ω± 0% 5 Ω±.5 Ω 3.5 Ω 6.5 Ω 48. a. 6 6 0 Ω 60 Ω 0.6 kω b. 333 33 0 3 Ω 33 kω c. Q 3.9 0 Ω 390 Ω d. C6. 0 6 Ω. MΩ 49. a. G R 0 Ω 8.33 ms b. G 4 kω 0.5 ms c. G 0.46 μs. MΩ G a > G b > G c vs. R c > R b > R a 50. a. Table 3., Ω/000.588 Ω G R 69.7 ms.588 Ω or G A 659.9 CM (Table 3.) ρ l (0.37)(000 ) 69.69 ms (Cu) b. G c. G 659.9 CM (7)(000 ) 659.9 CM (74)(000 ) 384. ms (Al) 88.4 ms (Fe) 0 Chapter 3

5. A A 5 3 3 A l, l l 3, ρ ρ 3 A l ρ A G l ρla 3 G A ρla 5 ρ 5 l A l 3 5. 53. 54. G 5G 5(00 S) 500 S 55. a. 50 C specific resistance 0 5 Ω-cm 50 C specific resistance 500 Ω-cm 00 C specific resistance 7 Ω-cm b. negative c. No d. ρ ΔΩ cm 300 30 70 Ω cm ΔT 5 50 75 C 3.6 Ω-cm/ C 56. a. Log scale: 0 fc 3 kω 00 fc 0.4 kω b. negative c. no log scales imply linearity d. kω 30 fc 0 kω fc ΔR 0 k Ω k Ω Δfc 30 fc fc 57. a. @ 0.5 ma, 95 @ ma, 00 @ 5 ma, 5 b. Δ total 5 95 0 c. 5 ma:0.5 ma 0: compared to 5 : 00.08: and ΔR Δfc 3.43 Ω/fc 3.43 Ω/fc Chapter 3

Chapter 4. IR (.5 A)(47 Ω) 7.5. I R 6.8 Ω.76 A 3. R 6 I.5 ma 4 kω 4. I 3 R 40 0 Ω 300 A 5. IR (3.6 μa)(0.0 MΩ) 0.07 7 m 6. I 6 R 5 k Ω 4.3 ma 7. R 0 I. A 54.55 Ω 8. I 0 R 7.5 k Ω 6 ma 9. R 0 I 4. A 8.57 Ω 0. R 4.5 I 5 m A 36 Ω. R I 4 m 0 μ A. kω. IR (5 A)(0.5 Ω) 7.5 3. a. R 0 I 9.5 A.63 Ω 60 min 60 s b. t h h min 3600 s W Pt It (0 )(9.5 A)(3600 s) 4. 0 6 J 4. IR (.4 μa)(3.3 MΩ) 7.9 5. Chapter 4

6. b. (0.3 ma)(500 h) 65 mah 7. 8. 9. 0. P W t 40 J 40 J 60 s 40 s 4 min min.75 W. t. a. W 640 J P 40 J/s 6 s 60 min 60 s 8 h h min 8,800 s W Pt ( W)(8,000 s) 57.6 kj b. kwh ( W)(8 h) 000 6 0 3 kwh Q 300 C min 3. I t min 60 s 5 C/s 5 A P I R (5 A) 0 Ω 50 W 4. P I (3 )(.4 A) 4.0 W W J t P 4. W.86 s 48 C min 5. I min 60 s 0.8 A P EI (6 )(0.8 A) 4.8 W 6. P I R (7. ma) 4 kω 07.36 mw 7. P I R I P 40 mw R. kω 0.44 ma P W 8. I R 9.0 ma 0 Ω IR (9.0 ma)(0 Ω) 5.49 Chapter 4 3

E 9. I R.4 ma 5.6 kω P I R (.4 ma) 5.6 kω 5.65 mw 60 min 60 s W P t (5.65 mw) h h min 9.34 J 30. E P 34 W I.7 A 0 3. I no P R W 4.7 MΩ 46.7 μa 3. PR (4 mw)(. k Ω ) 9.40 9.6 33. P EI (9 )(45 ma) 405 mw P 00 W 34. P I, I 0 0.833 A 0 R I 0.833 A 44.06 Ω 35. R P 450 W I 3.75 A 0 0 I 3.75 A 3 Ω 36. a. P EI and I 37. I P E 3 0.4 0 W 0.3 ma 3 b. Ah rating (0.3 ma)(500 h) 66.5 mah P R 00 W 5 0 0 kω 3 70.7 ma PR (00 W)(0 k Ω ).4 k 38. a. W Pt t 60 s R 0 Ω 864 J b. Energy doubles, power the same 4 Chapter 4

39. 4 weeks h 3 [5 months] 60 h week month (30 W)(60 h) kwh 59.80 kwh 000 40. kwh Pt (000)(kWh) (000)( kwh) t 8 h 000 P 500 W (4 W)(3 h) 4. kwh 7 0 3 kwh 000 (7 0 3 kwh)(9 /kwh) 0.65 4. a. kwh Pt (000)(kWh) (000)(00 kwh) P 0 kw 000 P 0 h b. I 3 P 0 0 W 576.9 A E 08 c. P lost P i P o P i ηp i P i ( η) 0 kw( 0.8).6 kw Pt (.6 kw)(0 h) kwh lost 6 kwh 000 000 43. #kwh $.00. 9 Pt (kwh)(000) (.)(000) kwh t 44.44 h 000 P.50 t (kwh)(000) (.)(000).3 h P 4800 44. a. W Pt (60 W)( h) 60 Wh 60 min 60 s b. W Pt (60 W) h h min 6 kws c. kj Ws, 6 kj d. W Pt (60 W)( h) 60 0 3 kwh 000 000 Chapter 4 5

45. a. P EI (9 )(0.455 A) 4. W b. R E 9 I 0.455 A 9.78 Ω c. W Pt (4. W)(,600 s) 88.56 kj 60 min 60 s 6 h h min,600 s 46. a. P EI (0 )(00 A) kw b. P T 5 hp 746 W hp + 3000 W + 400 W + 000 W 0,30 <,000 W (Yes) c. W Pt (0.3 kw)( h) 0.6 kwh h (860 W)(6 h) + (4800 W)(/ h) + (900 W) 0 min + (0 W)(3.5 h) 60 min) 47. kwh 000 560 Wh +400 Wh + 300 Wh + 385 Wh 8.45 kwh 000 (8.45 kwh)(9 /kwh) 74. h h (00 W)(4 h) + (00 W) 0 min + (70 W)(.5 h) + (50 W) 30 min 60 min 60 min 48. kwh 000 800 Wh + 400 Wh + 05 Wh + 35 Wh.63 kwh 000 (.63 kwh)(9 /kwh) 4.67 49. η P o P i 746 W (0.5 hp) hp 373 00% 00% 00% 94.43% 395 W 395 50. η Po P, P P i o i P i P i EI, I (.8 hp)(746 W/hp) η 0.685 960.9 W 960.9 W E 0 6.34 A 5. η Po 746 W 746 00% 00% 00% P (4 A)(0 ) 880 84.77% i 6 Chapter 4

5. a. P i EI (0 )(.4 A) 88 W P i P o + P lost, P lost P i P o 88 W 50 W 38 W b. η% P o P i 00% 50 W 88 W 00% 7.36% Po 53. P i EI η I P o (3.6 hp)(746 W/hp) ηe (0.76)(0 ) 6.06 A 54. a. P i P o η ( hp)(746 W/hp) 0.9 657.78 W 55. P i b. P i EI 657.78 W (0 )I 657.78 W I 657.78 W 5.07 A 0 c. P o ( hp)(746 W/hp) P i η 0.7 3.43 W P i EI 3.43 W (0 )I 3.43 W I 3.43 W 0 9.38 A I P o η P i E (5 hp)(746 W/hp) 0.9,433.33 W 0 56.5 A,433.33 W 56. η T η η 0.75 0.85 η η 0.88 57. η T η η (0.87)(0.75) 0.655 65.5% 58. η η.08 η T (η )(η ) (0.8)(0.8) 0.64 Wo η T Wo W η T W i (0.64)(60 J) 38.4 J i 59. η T η η 0.7 0.9η η 0.7 0.8 80% 0.9 Chapter 4 7

60. a. η T η η η 3 (0.98)(0.87)(0.) 0.790 7.9% 6. η T b. η T η η η 3 (0.98)(0.87)(0.90) 0.7673 76.73% 76.73% 7.9% 00% 38.66% 7.9% P o P η η η η i Po η η P i η η (0.4) 0.8 η 40%, η 80% η Po 8 W P (400 W) 0.4 i 8 Chapter 4

Chapter 5. a. E and R b. R and R c. E and R d. E and R, R 3 and R 4. a. R T 0. kω + 0.39 kω +. kω.69 kω b. R T. Ω +.7 Ω + 8. Ω. Ω c. R T 8. kω + 0 kω + 9. kω +.8 kω +.7 kω 3.8 kω d. R T 47 Ω + 80 Ω + 9 Ω +. kω 58.0 Ω 3. a. R T. kω + kω +. kω + 3.3 kω 7.7 kω b. R T kω + kω + 3 kω + 4.7 kω + 6.8 kω 7.5 kω 4. a. MΩ b. 00 Ω, kω c. R T 00 Ω + kω + MΩ + 00 kω.0 MΩ vs.. MΩ for part b. 5. a. R T 05 Ω 0 Ω + 33 Ω + R, R 6 Ω b. R T 0 kω. kω + R +.7 kω + 3.3 kω, R.8 kω c. R T 38 kω R + 56 kω + kω + 33 kω, R 7 kω d. R T 9 kω 4 kω + R + 43 kω + R 67 kω + 3R, R 8 kω R 6 kω 6. a.. kω b. 3.3 kω + 4.3 kω 7.6 kω c. 0 Ω d. Ω 7. a. R T 0 Ω + Ω + 8 Ω 40 Ω E 0 b. I s 3 A R T 40 Ω c. I R (3 A)(0 Ω) 30, I R (3 A)( Ω) 36, 3 I 3 R 3 (3 A)(8 Ω) 54 8. a. the most: R 3, the least: R b. R 3, R T. kω + 6.8 kω + 8 kω 90 kω E 45 I s R T 90 kω 0.5 ma c. I R (0.5 ma)(. kω) 0.6, I R (0.5 ma)(6.8 kω) 3.4, 3 I 3 R 3 (0.5 ma)(8 kω) 4, results agree with part (a) 9. a. R T kω + 4 kω + 6 kω kω E IR T (4 ma)( kω) 88 b. R T 8 Ω + 4 Ω + 8 Ω + 40 Ω 80 Ω E IR T (50 ma)(80 Ω) 0 Chapter 5 9

0. a. a. I R 5..3 Ω 4 A b. E IR T (4 A)(9 Ω) 36 c. R T 9 Ω 4.7 Ω +.3 Ω + R, R 3 Ω d. 4.7 Ω (4 A)(4.7 Ω) 8.8.3 Ω (4 A)(.3 Ω) 5. 3 Ω (4 A)(3 Ω) b. a. 6.6 I 3 ma R. kω b. 3.3 kω (3 ma)(3.3 kω) 9.9 E 6.6 + 9 + 9.9 5.5 9 c. R 3 kω I 3 ma d.. kω 6.6, 3 kω 9, 3.3 kω 9.9. a. I E R T 36 4.4 kω 8.8 ma, E (36 ) 8 b. R T kω +.4 kω + 5.6 kω 9 kω E.5 I.5 ma,.5 ma(.4 kω + 5.6 kω) 0 9 kω R T c. R T 0 kω + kω + 33 kω + 0 MΩ 0.065 MΩ E 00 I 9.94 μa 0.065 MΩ R T (9.935 μa)(0 MΩ) 99.35. a. R T 3 kω + kω + kω 6 kω E 0 I s 0 ma R T 6 kω R (0 ma)(3 kω) 60 R (0 ma)( kω) 0 R 3 (0 ma)( kω) 40 b. P I R (0 ma) 3 kω. W R R P I R (0 ma) kω 0.4 W P I 3 R 3 (0 ma) kω 0.8 W R 3 c. P T P + P + P. W + 0.4 W + 0.8 W.4 W R R R3 d. P T EI s (0 )(0 ma).4 W 30 Chapter 5

e. the same f. R the largest g. dissipated h. R : W, R : / W, R 3 : W 3. a. R T Ω + 0 Ω + 47 Ω + 3 Ω 8.0 Ω E 0.5 I s R 50 ma 8.0 Ω T R I R (50 ma)( Ω) 5.50 R I R (50 ma)(0 Ω).50 R 3 I 3 R 3 (50 ma)(47 Ω).75 R 4 I 4 R 4 (50 ma)(3 Ω) 0.75 b. P R I R (50 ma) Ω.38 W P R I R (50 ma) 0 Ω 65.00 mw 3 3 P R I R (50 ma) 47 Ω.94 W 4 4 3 P R I R (50 ma) 3 Ω 87.50 mw 4 c. P T P + P + P + P.38 W + 65.00 mw +.94 W + 87.50 mw 5.3 W R R R3 R4 d. P EI s (0.5 )(50 ma) 5.3 W e. the same f. 47 Ω the largest g. dissipated h. R : W; R : / W, R 3 : 5 W, R 4 : / W 4. a. P W ( A) R, R Ω I R ( A)( Ω), I R ( A)( Ω) 3 I 3 R 3 ( A)( Ω) E + + 3 + + 4 b. P 4 W I Ω, I 4 A P 8 W I R ( A) R, R Ω R T 6 Ω Ω + R + Ω 3 Ω + R, E IR T ( A)(6 Ω) 3 R 3 Ω Chapter 5 3

5. a. R T NR 8 8 Ω 5 Ω 8 E 0 I 0.53 A R T 5 Ω b. P I 8 64 5 R A 8 Ω 5 8 5 8 8 W 8 5 c. IR A Ω 5 8 5 d. All go out! 6. P s P R + P R + P R3 E I I R + I R + 4 (R + R )I E I + 4 0 6I 4 I + 4 0 I 4 I + 4 0 I ( 4) ± ( 4) () 4()(4) 4 ± 6 6 4 A P 4 W ( A) R, R 4 Ω 6 Ω 4 7. a. ab 4 8 + 0 b. ab 4 8 + 6 6 c. ab 0 + 8 6 + 4 4 8. a. E T 6 4 8 4, I 388.35 ma (CCW) 0.3 Ω b. E T 8 4, I 73.9 ma (CW).5 Ω 9. a. P 8 mw I 8 mw 8 mw R, R I ( ma) kω E 0 E I ma (CW), R 3 kω+ kω E 0 T 6 b. I kω E I RT E 4 8 ma, R I E 4 0 E kω +.5 kω.5 kω 8 ma 4 8 ma (CCW) 3.5 kω 3 Chapter 5

0. a. +0 + 4 3 0 4 3 b. +30 + 0 8 0 50 8 4 c. +6 0 4 + 60 0 76 4 6. a. +60 0 0 60 3 8 b. +E 4 6 + 8 0 E 8 4. a. +0 0 0 +0 6 0 4 b. +4 0 0 4 +0 + 8 0 8 3. a. +0 0 0, 9 +0 0, 8 b. + 0 + 6 3 0, +0 3 0, 7 4. 50, R Ω R 00, R 3 Ω R 3 (50 )( Ω ) 00 Ω (00 )( Ω ) 00 Ω 5. a. 8. kω b. 3 : 8. kω: kω 8.: 3 : 8. kω:00 Ω 8: c. R3E (8. kω)(60 ) 3 0.kΩ + kω + 8. kω 5.90 d. R T ( R + R3 ) E R T (kω + 8. kω)(60 ) 59.35 9.3 kω Chapter 5 33

6. a. 40 Ω(30 ) 40 Ω + 0 Ω 0 b. ( kω+ 3 k Ω)(40 ) (5 k Ω)(40 ) 4 kω+ k Ω+ k Ω+ 3 kω 0 kω 0 c. (.5 Ω+ 0.6 Ω+ 0.9 Ω)(0.7 ) (3 Ω)(0.7 ) (.5 Ω+.5 Ω+ 0.6 Ω+ 0.9 Ω+ 0.5 Ω) 6 kω 0.36 7. a. 6 Ω 4 Ω 0, Ω 0, Ω (6 Ω)(0 ) Ω (4 Ω)(0 ) Ω 60 40 E + 0 + 60 + 0 + 40 0 b. 0 80 0, 40 80 0 3 0, 3 70 c. 000 Ω(000 ), 0 00 Ω Ω 00 Ω 000 Ω(000 ), 0 00 Ω Ω 00 Ω E + + 000 0 + 0 + 000 030 d. 6 6 0, 0 6 3 8., kω kω kω( ) kω 4 4, 4 kω 3 kω 3 kω( ) kω 6 I ma kω E + 4 + + 6 4 34 Chapter 5

9. a. 4 R(0 ), R.6 kω kω + 6 kω (6 Ω+ R)40 b. 00 3 Ω+ 6 Ω+ R 300 Ω + 600 Ω + 00R 840 Ω + 40 R 40R 00R 840 Ω + 900 Ω 40R 60 Ω R 60 Ω.5 Ω 40 30. a. 4 0 Ω(4 ) 0 Ω 0 Ω 0 Ω 8 b. 3 E 40 4 8 8 c. 4 8 (8 )(0 Ω) R3 70 Ω 0 Ω R 4 3 8 3. a. R bulb 60 Ω 50 ma Rbulb ( ) 60 Ω( ) bulb 8 R + R x 60 Ω + R x bulb, R x 80 Ω in series with the bulb b. R 8 4, P R (4 ) 80 Ω 0. W, /4 W okay 3. + 7 R R R + R 7 5 7 R + 7, R 60 5. R 60 R 7 60 R 5 kω, R I 4 ma I 4 ma R R 4 ma 3 kω 33. R T R + R + R 3 R 3 + 7R 3 + R 3 0R 3 R3 (60 ) R 3 6, R 0R R3 (6 ), R 7 R 7(6 ) 4 3 3 34. a. R 3 4 R 4(3 R ) R E + 3 + R T R + 3R + R 6R R R R 64 0 ma 6.4 kω R 400 Ω, R 3R. kω, R 3 R 4.8 kω 6 6.4 kω Chapter 5 35

64 6.4 MΩ b. R T 6.4 MΩ, R 400 kω, R. MΩ, R 3 4.8 MΩ 0 μa 6 I 0 ma 0 3 R 400 kω and I 0 μa R 400 Ω 03 also 35. a. a + 8 4 b 8 ab a b 4 ( 8 ) b. a 0 6 4 b +4 ab a b 4 4 0 c. a +0 + 3 3 b +6 ab a b 3 6 7 80 6 36. a. I(CW) 6 Ω+ 3 Ω 54 9 Ω 6 A IR (6 A)(3 Ω) 8 70 0 b. I(CW) 0 Ω+ 0 Ω+ 30 Ω 60 60 Ω A IR ( A)(0 Ω) 0 6 4 37. a. I 0.4 A (CW) 0 Ω+ 0 Ω 30 Ω a 6 I(0 Ω) 6 (0.4 A)(0 Ω) 6 4 IR (0.4 A)(0 Ω) 8 + 0 + 8 30 b. I 5.455 ma. k Ω+ 3.3 k Ω 5.5 k Ω a I(. kω) + 0 (5.455 ma)(. kω) + 0 + 0 0 I(. kω) (5.455 ma)(. kω) 47 0 7 38. I 3 ma (CCW) k Ω+ 3 k Ω+ 4 kω 9 kω kω 6, 3kΩ 9, 4kΩ a. a 0, b 0 + 6 6, c 0 + 6 + 9 35 d, e 0 b. ab 6, dc 47, cb 9 c. ac 5, db 47 + 9 38 36 Chapter 5

39. R I R 4 + 4 8 8 Ω 8 Ω A, R I R 3 R 3 8 4 4 4 Ω I A A 4 8 8 Ω, A A 40. R 48 36 R 36 R.5 kω I 6 ma R 3 0 R3 R 3 0.75 kω I 6 ma R 4 0 R4 0 R 4.5 kω I 6 ma R E R R 3 R4 00 36 0 3 R 3 R kω I 6 ma 44 0 4 4. I ma (CW) k Ω+ 4 k Ω+ 6 k Ω k Ω k Ω IR ( ma)( kω) 4 4k Ω IR ( ma)(4 kω) 8 Ω IR ( ma)(6 kω) 6k a. a 44, b 44 4 40, c 44 4 8 3 d 0 b. ab kω 4, cb 4kΩ 8 cd 6kΩ c. ad a d 44 0 4 ca c a 3 44 4. 0 0 4 + 0, 4 +0 7 4 0 0 3 +6 30 8 67 0 56 6 4 3 6 I.5 A 4Ω 4Ω 4 Ω Chapter 5 37

43. 0 0, 03 0 3 0, ( ma)(3 kω + kω) ( ma)(4 kω) 8 3 3 8 0 8, 0-8, ΣI i ΣI o I i ma + 5 ma + 0 ma 7 ma 44. a. L I L R L ( A)(8 Ω) 56 int 60 56 4 int 4 R int I A Ω b. R NL FL FL 00% 60 56 56 00% 7.4% 45. a. L 3.3 Ω( ) 3.3 Ω + 0.05 Ω.8 b. R NL FL FL 00%.8.8 00%.5% c. I s I L.8 3.3 Ω 3.58 A P s EI s ( )(3.58 A) 4.96 W P int I R int (3.58 A) 0.05 Ω 0.64 W 46. a. I E R T kω + 8 kω 0 kω. ma b. I E R T 0 kω + 0.5 kω 0.5 kω.7 ma c. not for most applications. 38 Chapter 5

Chapter 6. a. R and R 3 b. E and R 3 c. E and R d. R, R 3 and R 4 e. E, R, R, R 3, and R 4 f. E, R, R, and R 3 g. R and R 3. a. R 3 and R 4, R 5 and R 6 b. E and R 3. a. R T (9. Ω)(8 Ω) 9. Ω + 8 Ω 6.04 Ω b. R T + + 0 kω kω 3 kω 545.55 Ω 3.833 0 S c. R T d. R T R T e. R T f. R T 00 90.09 Ω + + Ω kω 8 kω 6 kω 3 (6 kω)(6 MΩ) 6 kω + 6 MΩ 0 kω 5.99 kω Ω 5.5 Ω, R T 4 (5.5 Ω)(5 Ω) R T.6 Ω 5.5 Ω + 5 Ω + + Ω kω 00.00 0 MΩ 3 S S + 0.5 0 3 3 3 0 0 0 Ω 5 Ω 000 0 0.99 Ω S + 0 S + 0.333 0 S + 0. 0 S S. 0 3 3 3 3 S + 0 3 3 3 S + 0.00 0 S S 4. a. R T + + 0 kω. kω 0.3 kω 93.57 Ω 3 5.66 0 S S + 0.833 0 3 3 3 S + 3.333 0 S Chapter 6 39

b. R T kω +. k 3.88 0 3 + Ω S. kω + 304.4 Ω kω 0 S + 0.833 0 S + 0.455 0 3 3 3 3 S + 0 S 5. a. R T 3 Ω 6 Ω Ω ( Ω)( R) R T.6 Ω Ω + R b. R T 6 kω kω 3 ( k, R 8 Ω Ω)( R) R T.8 kω, kω + R R 8 kω c. (0 kω)( R) R T 0 kω, 0 kω + R R 0 kω d. R T 68.93 Ω 3 3 + + 833.33 0 S + + 454.55 0 S. kω R. kω R 8.3 0 3 + 68.93 Ω R 68.93 Ω R 3 8.3 0 3.3 kω R R e. R R R, R 3 R R RR 3 R R T.6 kω R + R R 3 R + 4 R 4(.6 kω) 6.4 kω R R 3 6.4 kω 3. kω 6. a.. kω b. about kω c. R T + + +. kω kω 0 kω. MΩ 6 6 833.333 0 S + 45.455 0 S + 4.545 0 S + 0.455 0.3 kω 6 883.788 0 S d. (. kω)( kω) 0 kω,. MΩ: R T. kω + kω.38 kω e. R T reduced. 6 6 S 40 Chapter 6

7. a. R T ( Ω)(8 Ω) Ω + 8 Ω.6 Ω b. Ω c. Ω d. R T + + 0.5 S + 0.50 S + 0.0 S 0.85 S 4 Ω Ω 0 Ω.8 Ω 8. + + R R R R T 3 + + 3. 0 R 5R R + + Ω R 5 R R R and R 3.(0 Ω) 64 Ω R 5R 5(64 Ω) 30 Ω R 3 64 Ω R 3 Ω 9. 4 Ω 4 Ω Ω + + RT R Ω 0 Ω 0. S R + 0.08333 S + 0.00833 S 0. S R + 0.0967 S R 0. S 0.0967 S 0.00833 S R 0.00833 S 0 Ω 0. a. (8 Ω)(4 Ω) R T 8 Ω + 4 Ω 6 Ω b. R R 36 c. E 36 I s R T 6 Ω 6 A R 36 I R 8 Ω 4.5 A R 36 I R 4 Ω.5 A d. I s I + I 6 A 4.5 A +.5 A 6 A (checks) Chapter 6 4

. a. R T + + Ω 9 Ω 3 36 Ω. Ω 3 47 0 S b. R R R 8 3 E 8 c. I s R. Ω 8.5 A T R 0.333 S + 0.S + 0.08 S R 8 I R 3 Ω 6 A, 8 I R 9 Ω A, 8 3 I3 R3 36 Ω 0.5 A d. I s 8.5 A 6 A + A + 0.5 A 8.5 A (checks). a. R T + + 00 0 S + 833.333 0 S + 47.059 0 0 kω. kω 6.8 kω 95.93 Ω 3.080 0 S b. R R R 4 3 E 4 c. I s R 5.9 ma T 95.93 Ω 4 R R 4 IR.4 ma, I R 0 ma, R 0 kω R. kω R 6 6 6 R 4 3 IR 3.53 ma 3 R3 6.8 kω d. I T 5.9 ma.4 ma + 0 ma + 3.53 ma 5.93 ma (checks) 3. a. R T kω b. R T + + + 0 kω kω. kω 56 kω 6 6 6 6 00 0 S + 45.46 0 S + 833.333 0 S + 7.86 0 S.003 kω, very close 6 996.65 0 S c. I 3 the most, I 4 the least d. R 44 R 44 IR 4.4 ma, I R ma R 0 kω R kω R 44 3 R4 44 I R 36.67 ma, I 3 R 0.79 ma 4 R. kω R 56 kω 3 4 S 4 Chapter 6

4. e. I s E R T 44 43.87 ma.003 kω I s 43.87 ma 4.4 ma + ma + 36.67 ma + 0.79 ma 43.86 ma (checks) f. always greater 5. R T 3 Ω 6 Ω Ω, R T R T R 3 Ω Ω Ω I s I E R T Ω A E I R 4 A R 3 Ω I I I R A 4 A 8 A E (0 Ω)(0.8 A) 6. I 3 9 A 0 Ω + 4 Ω E R I3R3 (9 A)(4 Ω) 36 3 I.3 A 0.8 A.5 A R R I R R 36.5 A 4 Ω 7. a. R T 0 Ω 5 Ω 4 Ω E 30 I s R 4 Ω 7.5 A T CDR: I 5 Ω I s (7.5 A) 5 Ω+ 0 Ω 5.5 A b. 0 kω 0 kω 5 kω R T kω 5 kω 0.833 kω E 8 I s R 9.6 ma 0.833 kω T R T 0 kω kω 0.909 kω RI T s (0.909 k Ω)(9.6 ma) 8.77 ma I R + 0 kω 0.909 kω+ 0 kω 0.909 T 0.8 ma 8. a. I b. 4 c. I s 4 0 kω 4 8 6 4 kω 4 kω 4 ma + 4 ma + 4 kω.4 ma + 4 ma + ma 8.4 ma Chapter 6 43

9. a. R T 6 + + 000 0 S + 30.303 0 S +.95 0 kω 33 kω 8. kω 867.86 Ω 3.5 0 S R 00 R 00 IR 00 ma, I R 3.03 ma R kω R 33 kω b. R 00 3 IR. ma 3 R 8. kω P P P R 3 I (00 )(00 ma) 0 W R R R R I (00 )(3.03 ma) 0.30 W R R I (00 )(. ma). W 3 R3 R3 6 6 c. E 00 I s R T 867.86 Ω 5.3 ma P s E s I s (00 )(5.3 ma).5 W d. P s.5 W 0 W + 0.30 W +. W.5 W (checks) e. R the smallest parallel resistor 0. a. I bulb b. R T c. I s. R T R N E R T E R bulb 0 66.667 ma.8 kω.8 kω 8 0 5 Ω 5 Ω 0.533 A d. (0 ) P R.8 kω 8 W e. P s 8(8 W) 64 W f. none, I s drops by 66.667 ma + + Ω 0 Ω 5 0 Ω.86 Ω 3 350 0 S E 60 I s R.86 Ω 0.98 A T 00 0 P E I s (60 )(0.98 A).6 kw S + 00 0 3 3 3 S + 50 0 S S 44 Chapter 6

. a. 600 W P 0(60 W) 600 W E I 0 I, I 0 5 A 400 W P 400 W 0 I, I 0 3.33 A 00 W P 3 00 W 0 I 3, I 3 0.67 A 0 W P 4 0 W 0 I 4, I 4 0 0.9 A b. I s 5 A + 3.33 A +.67 A + 0.9 A 0.9 A (no) c. E 0 R T 0.99 Ω Is 0.9 A d. P s E I s (0 )(0.9 A).3 kw P s.3 kw 600 W + 400 W + 00 W + 0 W.3 kw (the same) 3. a. 8 Ω Ω 4.8 Ω, 4.8 Ω 4 Ω.8 Ω I 4 + 8.8 Ω 4.67 A (4 + 8 ) b. P 4 56 W R 4 Ω c. I I 4.67 A 4. I.6 ma 8.5 ma 4. ma I 8.5 ma 4 ma 4.5 ma 5. a. 9 A + A + I A, I A A A I + A A + 3 A, I 4 A A 3 A b. 6 A A + I, I 6 A A 4 A 4 A + 5 A I, I 9 A 9 A I 3 + 3 A, I 3 9 A 3 A 6 A 3 A + 0 A I 4, I 4 3 A 6. a. I + 5 ma 8 ma, I 3 ma 5 ma I + 3.5 ma, I.5 ma I 3 ma I 3 + ma, I 3 ma I 4 5 ma b. I 3.5 μa + 0.5 μa.0 μa 6 μa I + I 3 I + μa, I 4 μa I +.5 μa I 4, I 4 4 μa +.5 μa 5.5 μa I 6 μa Chapter 6 45

7. I R 5 ma ma 3 ma E R (3 ma)(4 kω) R R I (9 ma 5 ma) 4 ma R 3 I R T R R3 R3 E I T ma 9 ma 6 kω.33 kω 3 kω 8. a. R E I 0 A 5 Ω I I I 3 A A A E 0 R 0 Ω I A b. E I R ( A)(6 Ω) E I.33 A 9 Ω R P W I 3 A E R 3 Ω I3 A I I + I + I 3 A +.33A + A 4.33 A 64 c. I 64 ma kω 64 I 3 6 ma 4 kω I s I + I + I 3 I I s I I 3 00 ma 64 ma 6 ma 0 ma E 64 R 3. kω I 0 ma I I + I 3 0 ma + 6 ma 36 ma 46 Chapter 6

d. P PR (30 W)(30 Ω ) R E 30 E 30 I A 30 Ω R 30 Because R 3 R, I 3 I, and I s I + I + I 3 I + I A A + I I ( A) 0.5 A I 3 0.5 A E 30 R R 3 60 Ω I 0.5 A 4 Ω 9. I I I A Ω 3 4 Ω I 3 I I A Ω P R I R (0.5 A) 60 Ω 5 W 4 Ω I 4 I I 0.6 A 40 Ω 0 I T I + I + I 3 + I 4 6 A + A + A + 0.6 A 0.6 A 8 kω(0 ma) 30. a. I 6 ma kω + 8 kω I 0 ma 6 ma 4 ma b. R T + + 454.55 0 S + 833.33 0. kω. kω 0. kω 59.03 Ω 6 6,88 0 S RT 59.03 Ω I x I, I (8 ma).30 ma Rx. kω 59.03 Ω I (8 ma).39 ma. kω 59.03 Ω I 3 (8 ma) 4.3 ma 0. kω I 4 8 ma 6 6 6 S + 5000 0 S Chapter 6 47

c. R T 50 0 S + 5 0 + + 4 Ω 8 Ω Ω.8 Ω 3 458.333 0 RT I x I, I.8 Ω (6 A) 3.7 A Rx 4 Ω I.8 Ω (6 A).64 A 8 Ω I 3.8 Ω (6 A).09 A Ω I 4 6 A 0 Ω(9 A) d. I I 6 A 0 Ω + 0 Ω I 3 9 A I 9 A 6 A 3 A I 4 9 A 3 3 3 S + 83.333 0 S 3. a. I 0 9 (0 A) 9 A b. I /I 0 Ω/ Ω 0, I 9 A I 0 0 0.9 A c. I /I 3 kω/ Ω 000, I 3 I /000 9 A/000 9 ma d. I /I 4 00 kω/ Ω 00,000, I 4 I /00,000 9 A/00,000 90 μa e. very little effect, /00,000 f. R T + + + Ω 0 Ω kω 00 kω 3 6 S + 0. S + 0 S + 0 0 S.0 S 0.9 Ω RT I x I, I 0.9 Ω (0 A) 9. A excellent (9 A) R Ω x g. I 0.9 Ω (0 A) 0.9 A excellent (0.9 A) 0 Ω h. I 3 0.9 Ω (0 A) 9. ma excellent (9 ma) kω i. I 4 0.9 Ω (0 A) 9 μa excellent (90 μa) 00 kω 48 Chapter 6

Ω I 3. a. CDR: I 6Ω A Ω + 6 Ω A(8 Ω) I 4 A I Ω I I A 3 A b. I 3 I 7 μa By inspection: I μa I I ( μa) 7 μa 4 μa 3 μa R ( μa)(9 Ω) 8 μ R 8 μ R 6 Ω I 3 μa R 33. a. R 3( kω) 6 kω 6 k Ω(3 ma) b. I 4 ma 6 kω+ kω I 4 ma I 8 ma 3 3 34. 84 ma I + I + I 3 I + I + I I + I + (I ) 84 ma I + I + 4I 7I 84 ma and I ma 7 I I ( ma) 4 ma I 3 I (4 ma) 48 ma R 4 R kω I ma R R I R 3 R 3 I 3 4 kω 4 ma 4 0.5 kω 48 ma 35. a. P L L I L 7 W I L 7 W I L 6 A I 6 A I I L 3 A b. P source EI ( )(3 A) 36 W c. P s + P s 36 W + 36 W 7 W (the same) d. I drain 6 A (twice as much) Chapter 6 49

36. R T 8 Ω 56 Ω 7 Ω E I I 3.7 A R T 7 Ω I I (.7 A) 0.86 A 6 37. I 8 Ω 8 Ω I R 5 A + 3 A 8 A, R A, I 5 A A 3 A I R R 6 8 A Ω 38. a. E I s R T 0. k 0 k.88 ma Ω+ Ω 0. kω L I s R L (.9 ma)(0 kω).90 b. I s 0 ma 00 Ω c. L E 39. a. 4.7 k Ω(9 ) 4.3 L 4.7 kω+. kω 6.9 b. L E 9 c. L E 9 6.3 40. a. I 0 4 Ω 5 A, I 0 A b. 0, 0 c. I s I 5 A kω(0 ) 4. a. 6.48 kω + 4.7 kω b. R T MΩ kω.956 kω.956 kω(0 ) 6.47 (very close to ideal).956 kω + 4.7 kω c. R m 0 [0,000 Ω/] 400 kω R T 400 kω kω 0.853 kω 0.853 kω(0 ) 6.3 (still very close to ideal) 0.853 kω + 4.7 kω d: a. 00 kω(0 ) 00 kω + 00 kω 3.33 b. R T 00 kω MΩ 96.49 kω (96.49 kω)(0 ) 3.5 (very close to ideal) 96.49 kω + 00 kω 50 Chapter 6

c. R m 400 kω R T 400 kω 00 kω 33.333 kω (33.333 kω)(0 ).43 (a.84 drop from R int MΩ level) 33.333 kω + 00 kω e. DMM level of MΩ not a problem for most situations OM level of 400 kω can be a problem for some situations. 4. a. ab 0 MΩ(0 ) b. ab 8.33 MΩ + MΩ c. R m 00 [0,000 Ω/] 4 MΩ 4 MΩ(0 ) ab 6.0 (significant drop from ideal) 4 MΩ + MΩ R m 0 [0,000 Ω/] 400 kω 400 kω(0 ) ab 5.7 (significant error) 400 kω + MΩ 43. not operating properly, 6 kω not connected at both ends 6 R T.7 kω 3.5 ma R T 3 kω 4 kω.7 kω 44. ab E + I 4 kω R 4 kω 4 8 I 4 kω.6 ma kω + 4 kω 5 kω ab 4 + (.6 ma)(4 kω) 4 + 6.4 0.4 4 supply connected in reverse so that + 4 6 I 3. ma kω + 4 kω 5 kω and ab (3. ma)( kω) 3. 8.8 obtained Chapter 6 5

Chapter 7. a. E and R in series; R, R 3 and R 4 in parallel b. E and R in series; R, R 3 and R 4 in parallel c. R and R in series; E, R 3 and R 4 in parallel d. E and R in series, R 4 and R 5 in series; R and R 3 in parallel e. E and R in series, R and R 3 in parallel f. E, R and R 4 in parallel; R 6 and R 7 in series; R and R 5 in parallel. a. R T 4 Ω + 0 Ω + 4 Ω 8 Ω b. 0 Ω R T 0 Ω + 0 Ω + 5 Ω 5 Ω c. R T 4 Ω (4 Ω + 4 Ω) + 0 Ω 4 Ω 8 Ω + 0 Ω.67 Ω + 0 Ω.67 Ω d. R T 0 Ω 3. a. yes b. I I s I 0 A 4 A 6 A c. yes d. 3 E 4 8 6 e. R T 4 Ω Ω.33 Ω, R T 4 Ω 6 Ω.4 Ω R T R T + RT.33 Ω +.4 Ω 3.73 Ω f. R T RT R T + R T 0 Ω + 0 Ω 0 Ω E 0 I s R T 0 Ω A g. P s EI s P absorbed (0 )( A) 0 W 4. a. Ω 6 Ω R T R 3 R 4 6 Ω, R T R R T 3 Ω R T R + R T 4 Ω + 3 Ω 7 Ω b. E 4 A I s A, I I s A 7 Ω R T A I 3 0.5 A c. I 5 A d. I R ( A)(6 Ω) 6 4 6 5. a. R T R R 0 Ω 5 Ω 6 Ω R T R T (R 3 + R 4 ) 6 Ω (0 Ω + Ω) 6 Ω Ω 4 Ω b. I s E R T 36 4 Ω E 9 A, I R T 36 36 Ω + Ω Ω 36 6 Ω E I 3 A R 3 + R 4 0 c. 4 I 4 R 4 I R 4 (3 A)( Ω) 6 6 A 5 Chapter 7

6. a. R T. kω + 6.8 kω 8 kω, R T kω R T kω 8 kω.6 kω R T R T +.4 kω.6 kω +.4 kω 4 kω R T kω R T kω 4 kω 0.8 kω b. E 48 I s R T 0.8 kω 60 ma c. RT E (.6 kω)(48 ) R +.4 k Ω.6 kω +.4 kω 9. T 7. a. R T (R R R 3 ) (R 6 + R 4 R 5 ) ( kω kω 3 kω) (0.4 kω + 9 kω 6 kω) (6 kω 3 kω) (0.4 kω + 3.6 kω) kω 4 kω.75 kω E 8 I s 6 ma, I R T.75 kω R R R R 3 kω R R 6 + R 4 R 5 4 kω R ( I Ω I 6 s ) k (6 ma) ma R + R kω + 4kΩ b. E 8 R R 4 R 5 6 kω 9 kω 3.6 kω 5 I 6 R ( ma)(3.6 kω) 7. R (8 ) 3 c. P 6.33 mw R 3 kω 3 E R 8.33 ma kω 8. a. R R 4 R 5 (R 7 + R 8 ) 4 Ω 8 Ω (6 Ω + Ω) 4 Ω 8 Ω 8 Ω 4 Ω 4 Ω Ω R (R 3 + R ) (R 6 + R 9 ) (8 Ω + Ω) (6 Ω + 4 Ω) 0 Ω 0 Ω 5 Ω R T R (R + R ) 0 Ω (5 Ω + 5 Ω) 0 Ω 0 Ω 5 Ω E 80 I 5 Ω 6 A R T b. 6 A I I R 8 A 8 A I 3 I 9 4 A ( R4 R5)( I3) c. I 8 ( R R ) + ( R + R ) 4 5 7 8 (4 Ω 8 Ω)(4 A) (4 Ω 8 Ω ) + (6 Ω+ Ω) (.67)(4 A) A.67 Ω + 8 Ω Chapter 7 53

d. I 8 R 8 x + I 9 R 9 0 x I 9 R 9 I 8 R 8 (4 A)(4 Ω) ( A)( Ω) 6 4 9. I 0 5 Ω 4 A R T 6 Ω 5 Ω 9.756 Ω 7 I 9.756 Ω 0.7 A 0. a, b. I 4 4 Ω 6 A, I 3 8 0 Ω 0.8 A I 4 + 8 3 Ω Ω 6 A I I + I 6 A + 6 A A. a. R R 4 + R 5 4 Ω + 6 Ω 0 Ω R R R 0 Ω 0 Ω 0 Ω R R + R 0 Ω + 0 Ω 0 Ω R T R 3 R 5 Ω 0 Ω 4 Ω E 0 I s RT 4 Ω 5 A 0 0 0 I R + R 0 Ω+ 0 Ω 0 Ω A I 3 0 5 Ω 4 A I I 4 (since R R ) A 0.5 A b. a I 3 R 3 I 4 R 5 (4 A)(5 Ω) (0.5 A)(6 Ω) 0 3 7 I bc R (0.5 A)(0 Ω) 0. a. E 0 I R + R4 ( R + R3 R 5) 3 Ω+ 3 Ω (3 Ω+ 6 Ω 6 Ω) 0 0 0 3 Ω+ 3 Ω (3 Ω+ 3 Ω) 3 Ω+ 3 Ω 6 Ω 3 Ω+ Ω 4 A 54 Chapter 7

R4( I) 3 Ω(4 A) b. CDR: I R4 + R + R3 R5 3 Ω+ 3 Ω+ 6 Ω 6 Ω A 6 + 3.33 A I I 3 0.67 A c. I 4 I I 4 A.33 A.67 A a I 4 R 4 (.67 A)(3 Ω) 8 b I 3 R 3 (0.67 A)(6 Ω) 4 3. a. E I E R E kω I C I E ma R ( ) 8 (0.7 + ) B CC BE + E b. I B RB RB 0 k Ω 8.7 5.3 4 μa 0 kω 0 kω c. B BE + E.7 C CC I C R C 8 ( ma)(. kω) 8 4.4 3.6 d. CE C E 3.6.6 BC B C.7 3.6 0.9 4. a. 70 k Ω(6 ) I G 0 G 70 k Ω+ 000 kω G GS S 0 S G GS.9 (.75 ) 3.65 6 b. I I 7.05 μa 70 k Ω+ 000 kω S 3.65 I D I S.43 ma R.5 kω S c. DS DD I D R D I S R S DD I D (R D + R S ) since I D I S 6 (.43 ma)(4 kω) 6 9.7 6.8 d. DD I D R D DG G 0 DG DD I D R D G 6 (.43 ma)(.5 kω).9 6 6.08.9 8.0 Chapter 7 55

5. a. Network redrawn: 00 Ω + 0 Ω 30 Ω 400 Ω 600 Ω 40 Ω 400 Ω 0 Ω 4.94 Ω 40 Ω + 4.94 Ω 38.94 Ω R T 30 Ω 38.94 Ω 74. Ω b. a 4.94 Ω(3 ) 4.94 Ω+ 40 Ω.89 c. 3 a 3.89 0. d. a.89 e. I 600Ω 0. 33.5 ma 600 Ω I 0Ω.89 54.05 ma 0 Ω I + I 600Ω I 0Ω I I 00Ω I 600Ω 54.05 ma 33.5 ma 0.53 ma E 6. a. I R + R 9 7 Ω+ 8 Ω 0.6 A 3 b. E + E 0 E + E 9 + 9 8 7. a. R 8 "shorted out" R R 3 + R 4 R 5 + R 6 R 7 0 Ω + 6 Ω 6 Ω + 6 Ω 3 Ω 0 Ω + 3 Ω + Ω 5 Ω R T R + R R 0 Ω + 30 Ω 5 Ω 0 Ω + 0 Ω 0 Ω E 00 I RT 0 Ω 5 A R ( I) (5 Ω)(5 A) I R + R 5 Ω+ 30 Ω.67 A 56 Chapter 7

I 3 I I 5 A 3 A 3 A 3 0 3 Ω A RI 7 3 3 I 6 R7 + R6 3 Ω+ 6 Ω. A I 8 0 A b. 4 I 3 (R 4 R 5 ) 8 0 0 A 3 (3 Ω) 0 8. 8 Ω 8 Ω 4 Ω 30 30 I 4 Ω+ 6 Ω 0 Ω 3 A I(8 Ω 8 Ω) (3 A)(4 Ω) 9. a. All resistors in parallel (between terminals a & b) R T 6 Ω 6 Ω 8 Ω 4 Ω 3 Ω 8 Ω 8 Ω 4 Ω 3 Ω 4 Ω 4 Ω 3 Ω Ω 3 Ω.88 Ω b. All in parallel. Therefore, 4 E 3 c. I 3 3 /R 3 3 /4 Ω 8 A d. I s I + I + I 3 + I 4 + I 5 3 3 3 3 3 + + + + 6 Ω 8 Ω 4 Ω 3 Ω 6 Ω A + 4 A + 8 A + A + A 7 A E 3 R T.88 Ω as above I 7 A s Chapter 7 57

0. a. KL: +6 0 + ab 0 ab +0 6 4 b. I 5Ω 0 5 Ω 4 A ab 4 I Ω Ω Ω 7 A I 3Ω 6 3 Ω A I + I 3Ω I Ω and I I Ω I 3Ω 7 A A 5 A I I + I 5Ω 5 A + 4 A 9 A. a. Applying Kirchoff's voltage law in the CCW direction in the upper "window": +8 + 0 8Ω 0 8Ω 38 I 8Ω 38 8 Ω 4.75 A 8 8 I 3Ω 3 Ω+ 6 Ω 9 Ω A KCL: I 8 4.75 A + A 6.75 A b. (I 3Ω )(6 Ω) + 0 ( A)(6 Ω) + 0 + 0 3 IR 3 3 R3 R3. I R I 3 R 3 and I (since the voltage across parallel elements is the same) R 0 0 R 3 I I + I 3 + 0 R3 KL: 0 I + I 3 R 3 + 0 + R 3 and 0.R 3 + 4 + R 3 3.R 3 96 Ω R 3 96 Ω 30 Ω 3. 58 Chapter 7

3. Assuming I s A, the current I s will divide as determined by the load appearing in each branch. Since balanced I s will split equally between all three branches. 0 A (0 Ω) 3 3 0 A (0 Ω) 6 6 0 3 A (0 Ω) 3 3 0 0 0 E + + 3 + + 8.33 3 6 3 E 8.33 R T 8.33 Ω I A 4. 36 kω 6 kω kω 3.6 kω 3.6 k Ω(45 ) 6.88 7. Therefore, not operating properly! 3.6 k Ω+ 6 k Ω 6 kω resistor "open" R (45) 9 k Ω(45 ) R kω 36 kω 9 kω, R + 6 kω 9 kω+ 6 kω 7 5. a. R T R 5 (R 6 + R 7 ) 6 Ω 3 Ω Ω R T R 3 (R 4 + R T ) 4 Ω ( Ω + Ω) Ω R T R + R + R T 3 Ω + 5 Ω + Ω 0 Ω I 40 0 Ω 4 A b. I 4 I 7 4 Ω( I ) 4 Ω(4A) A 4Ω+ 4Ω 8 Ω 6 Ω( A) 7 A 8 A 6 Ω+ 3 Ω 9 Chapter 7 59

c. 3 I 3 R 3 (I I 4 )R 3 (4 A A)4 Ω 48 5 I 5 R 5 (I 4 I 7 )R 5 (4 A)6 Ω 4 7 I 7 R 7 (8 A) Ω 6 d. P I7R 7 (8 A) Ω 8 W P EI (40 )(4 A) 5760 W 6. a. R T R 4 (R 6 + R 7 + R 8 ) Ω 7 Ω.56 Ω R T R (R 3 + R 5 + R T ) Ω (4 Ω + Ω +.56 Ω).53 Ω R T R + R T 4 Ω +.53 Ω 5.53 Ω b. I /5.53 Ω 36.66 ma Ω( I) Ω(36.66 ma) c. I 3 Ω+ 6.56Ω Ω+ 6.56 Ω I 8 Ω(84.5 ma) 8.78 ma Ω+ 7 Ω 84.50 ma 7. The Ω resistors are in parallel. Network redrawn: R T Ω E 4 I s R Ω A T I s A I Ω A 4 Ω( I ) I Ω Ω A 4 Ω+ Ω 3 P 0Ω (I 0Ω ) 0 Ω A 0 Ω 3 4.44 W 8. a. R 0 + R R Ω + Ω Ω Ω R 4 (R 5 + R 6 ) 0 Ω 0 Ω 5 Ω R + R (R 3 + 5 Ω) 3 Ω + 6 Ω 6 Ω 6 Ω R T Ω 3 Ω 6 Ω Ω Ω Ω I / Ω A b. I /6 Ω A 6 Ω( A) I 3 6 Ω+ 6 Ω A I 4 A 0.5 A c. I 6 I 4 0.5 A d. I 0 A 6 A 60 Chapter 7

9. a. E (40 ma)(.6 kω) 64 b. c. 48 R L ma 4 kω 4 R L 3 8 ma 3 kω I R 7 ma 40 ma 3 ma I R 3 ma ma 0 ma I R 3 0 ma 8 ma ma R 64 48 6 R 0.5 kω IR 3 ma 3 ma R 48 4 4 R. kω IR 0 ma 0 ma R 4 3 R 3 kω I ma R3 30. I R 40 ma I R 40 ma 0 ma 30 ma I R 3 30 ma 0 ma 0 ma I R 5 40 ma I R 4 40 ma 4 ma 36 ma R 0 00 0 R IR 40 ma 40 ma 0.5 kω R 00 40 60 R IR 30 ma 30 ma kω R 40 3 R 3 IR 0 ma 3 4 kω R 36 4 R 4 IR 36 ma 4 kω R 60 36 4 5 R 5 I 40 ma 40 ma 0.6 kω R5 Chapter 7 6

3 3 4 4 P I R (40 ma) 0.5 kω 0.8 W ( watt resistor) P I R (30 ma) kω.8 W ( watt resistor) P 3 I R (0 ma) 4 kω 0.4 W (/ watt or watt resistor) P 4 I R (36 ma) kω.3 W ( watt resistor) P 5 I5R 5 (40 ma) 0.6 kω 0.96 W ( watt resistor) All power levels less than W. Four less than W. 3. a. yes, R L R max (potentiometer) b. DR: R( ) R( ) R 3 R + R k Ω R 3 ( k Ω ) 0.5 kω 50 Ω R kω 0.5 kω 0.75 kω 750 Ω c. R E L 3 9 R ( ) R 9 R + ( R R ) L (Chose R rather than R R since numerator of DR L equation "cleaner") 9R + 9(R R L ) R R 3( R RL ) eq. unk( RL 0 k Ω) R + R k Ω 3RRL 3 R 0 kω R R + RL R + 0 kω and R (R + 0 kω) 30 kω R R R + 0 kω R 30 kω R R + R kω: ( kω R )R + 0 kω ( kω R ) 30 kω R R + 39 kω R 0 kω 0 R 0.55 kω, 39.55 kω R 55 Ω R kω R 745 Ω 80 Ω(40 ) 3. a. ab 3 00 Ω bc 40 3 8 b. 80 Ω kω 74.07 Ω 0 Ω 0 kω 9.96 Ω 74.07 Ω(40 ) ab 74.07 Ω+ 9.96 Ω 3.5 bc 40 3.5 8.49 6 Chapter 7

c. P (3.5 ) (8.49 ) + 80 Ω 0 Ω.4 W + 3.604 W 6.0 W (3 ) (8 ) d. P +.8 W + 3. W 6 W 80 Ω 0 Ω The applied loads dissipate less than 0 mw of power. 33. a. I CS ma b. R shunt RmICS I I max CS (00 Ω)( ma) 0 A ma 0. 0 Ω 5 mω ( k Ω)(50 μa) 34. 5 ma: R shunt 5 ma 0.05 ma ( k Ω)(50 μ A) 50 ma: R shunt 50 ma 0.05 ma 00 ma: R shunt 0.5 Ω Ω Ω max S 5 (50 μa)( k Ω ) 35. a. R s 300 kω I 50 μa CS b. Ω/ /I CS /50 μa 0,000 5 ( ma)(00 Ω ) 36. 5 : R s 4.9 kω ma 50 0. 50 : R s 49.9 kω ma 500 0. 500 : R s 499.9 kω ma 37. 0 MΩ (0.5 )(Ω/) Ω/ 0 0 6 I CS /(Ω/) 0.05 μa 6 0 0 38. a. R s E zero adjust 3 R m kω k 8 kω I 00 μa Ω m Chapter 7 63

b. xi m R unk E R series E xi m + R m + zero adjust + R unk zero adjust Rseries + R m + 3 30 kω x00 μa 3 30 0 x 30 0 3 x 3 4, R unk 0 kω; x, R unk 30 kω; x 4, R unk 90 kω 39. 40. a. Carefully redrawing the network will reveal that all three resistors are in parallel R Ω and R T 4 Ω N 3 b. Again, all three resistors are in parallel and R T R 8 Ω 6 Ω N 3 64 Chapter 7

Chapter 8. a. I I 3 0 ma b. I R (0 ma)( kω) 0 c. R T kω +. kω + 0.56 kω 3.76 kω s IR T (0 ma)(3.76 kω) 37.6. a. Rs ( I) 0 kω(4 A) I 3.996 A, I I Rs + R + R 0 kω + 0 Ω b. I R (3.996 A)(6 Ω) 3.98 c. s I (R + R ) (3.996 A)(0 Ω) 39.96 3. R IR (6 A)(3 Ω) 8 E + R s 0, s E + R 0 + 8 8 4. a. s E 4 E 4 4 b. I 6 A R + R Ω + 3 Ω 4 Ω c. I + I s I, I s I I 6 A A 4 A 5. s IR T 0.6 A[6 Ω 4 Ω 4 Ω] 0.6 A[6 Ω Ω].4.4 I 0. A R 4 Ω 3 R3 s 6 Ω(.4 ).6 R + R 4 Ω 3 4 6. a. E 4 I R Ω A, E 4 4 Ω I R R + R3 6 Ω+ Ω 8 Ω 3 A KCL: I + I s I I R 0 I s I + I R I A + 3 A 4 A A b. s E 4 RE 3 Ω(4 ) 48 DR: 3 R + R 6 Ω+ Ω 8 Ω 6 3 7. a. I b. I E 8 R 6 Ω 3 A, R p R s 6 Ω s E 9 R. kω 4.09 ma, R p R s. kω s CHAPTER 8 65

8. a. E IR s (.5 A)(3 Ω) 4.5, R s 3 Ω b. E IR s (6 ma)(4.7 kω) 8., R s 4.7 kω 9. a. CDR: I L Rs ( I) 00 Ω( A) R + R 00 Ω+ Ω.76 A, I L I s L b. E s IR ( A)(00 Ω). k R s 00 Ω Es. k I R+R 00 Ω+ Ω.76 A s L 0. a. E IR ( A)(6.8 Ω) 3.6, R 6.8 Ω b. I (CW) ( + 3.6 )/(0 Ω + 6.8 Ω + 39 Ω) 5.6 55.8 Ω c. ab I R 3 (458.78 ma)(39 Ω) 7.89 +. a. I T 6.8 A. A 3.6 A A b. s I T R ( A)(4 Ω) 8. I T 7 A 3 A 4 A R ( I ) 6 (4 A) CDR: I T Ω R+ R 4 Ω+ 6 Ω.4 A I R (.4 A)(4 Ω) 9.6 3. a. Conversions: I E /R 9 /3 Ω 3 A, R 3 Ω I E /R 0 / Ω 0 A, R Ω b. I T 0 A 3A 7 A, R T 3 Ω 6 Ω Ω Ω Ω Ω Ω Ω Ω 0.9 Ω ab + ab I T R T (7 A)(0.9 Ω) 6.44 c. I 3 6.44 6 Ω.07 A 458.78 ma 4. a. I E R. k Ω 5.45 ma, R p. kω 66 CHAPTER 8

b. I T 8 ma + 5.45 ma 3 ma 0.45 ma R 6.8 kω. kω.66 kω I T R (0.45 ma)(.66 kω) 7.35 c. + 7.35 5.35 5.35 d. I R. k Ω.43 ma 5. a. 4 4I 8I 3 0 6 I 8I 3 0 I + I I 3 I A, I A, I3 A 7 7 7 5 4 IR I A, IR I A, IR I 3 3 A 7 7 7 b. 0 + 3I 3 4I 0 I 3.06 A 3I 3 I 0 I 0.9 A I + I I 3 I 3 3.5 A I I I 3.06 A, R I 3.5 A R 3 3 I I 0.9 A R 6. (I): 0 I 5.6 kω I 3. kω + 0 0 0 + I 3. kω + I 3.3 kω 30 0 I + I I 3 I I R.45 ma, I I R 8.5 ma, I 3 (II):. kω I + 9 8. kω I 3 0 0. kω I + 8. kω I 3 + 6 0 I + I 3 I I.03 ma, I.3 ma, I 3 0.8 ma I R I.03 ma I I 3 0.8 ma I R R I I.3 ma R 3 4 I R 3 9.96 ma CHAPTER 8 67

7. (I): 5 I 3I 3 + 60 0 60 + 3I 3 + 6 5I 0 0 I I + I 3 I 8.55 A ab + 0 I 5 Ω 0 (8.55 A)(5 Ω).75 (II): Source conversion: E IR (3 A)(3 Ω) 9, R 3 Ω 9 + 6 3I 4I 6I 4 0 + 6I 4 8I 3 4 0 I I 3 + I 4 I.7 A ab + I 4 Ω 6 (.7 A)4 Ω 6 0.9 8. I I 5 I R (CW), I I R 5 (CW) I R (down), I 3 I R 3 (right), I 4 I R 4 (down) a. E I R I R 0 I R I 3 R 3 I 4 R 4 0 I 4 R 4 I 5 R 5 E 0 I I + I 3 I 3 I 4 + I 5 b. E I (R + R ) I 3 R 0 I R I 3 (R 3 + R 4 ) + I 5 R 4 0 I 3 R 4 I 5 (R 4 + R 5 ) E 0 c. I (R + R ) + I 3 R + 0 E I (R ) I 3 (R 3 + R 4 ) + I 5 R 4 0 0 + I 3 R 4 I 5 (R 4 + R 5 ) E 3I + I 3 + 0 0 I 9I 3 + 5I 5 0 0 + 5I 3 8I 5 6 d. I 3 I R 63.69 ma 3 68 CHAPTER 8

9. a. 0 I B (70 kω) 0.7 I E (0.5 kω) 0 I E (0.5 kω) + 8 + I C (. kω) 0 0 I E I B + I C I B 63.0 μa, I C 4.4 ma, I E 4.48 ma b. B 0 I B (70 kω) 0 (63.0 μa)(70 kω) 0 7.0.98 E I E R E (4.48 ma)(50 Ω).8 C 0 I C (. kω) 0 (4.4 ma)(. kω) 0 9.7 0.8 c. β I C /I B 4.4 ma/63.0 μa 70.4 0. a. 4 4I 8(I I ) 0 8(I I ) I 6 0 I A, I 7 A I R I I R I I R 3 I I 5 A 7 7 5 A 7 A 7 5 A 7 4 A (dir. of I ) 7 b. 0 4I 3(I I ) 0 3(I I ) I 0 I 3.06 A, I 0.9 A I R I 3.06 A I R 3 I 0.9 A I R I I ( 3.06 A) (0.9 A) 3.5 A. (I): 0 I (5.6 kω). kω(i I ) + 0 0 0. kω(i I ) I 3.3 kω 30 0 I.45 ma, I 8.5 ma I I.45 ma, I I 8.5 ma R I R 3 I I 7.06 ma (direction of I ) R CHAPTER 8 69

(II): I (. kω) + 9 8. kω(i I ) 0 I (. kω) + 6 I (9. kω) 8. kω(i I ) 0 I.03 ma, I.3 ma I I.03 ma, I I I.3 ma R R3 R4 IR I I.03 ma.3 ma 0.80 ma (direction of I ). (I): 5 I 3(I I ) + 60 0 60 3(I I ) + 6 5I 0 0 I.87 A, I 8.55 A ab + 0 I 5 0 (8.55 A)(5) 0 4.75.75 (II): Source conversion: E 9, R 3 Ω 9 3I 4I + 6 6(I I 3 ) 0 6(I 3 I ) 8I 3 4 0 I.7 A, I 3 0.6 A ab + 3. (a): 0 I (I I ) 0 (I I ) I 4 5(I I 3 ) 0 5(I 3 I ) I 3 3 6 0 3I I + 0 0 I + 0I 5I 3 0 0 5I + 8I 6 I 3 I R 3 63.69 ma 4. a. I 4 5I + 6 (I I ) 0 (I I ) 6 3I 5 0I 0 I I 5Ω 7.6 ma a 4 (7.6 ma)(6 Ω) 4 0.433 4.43 I 4 6 (.7 A)(4 Ω) 6 5.08 6 0.9 70 CHAPTER 8

b. Network redrawn: 6I 4(I I ) 0 4(I I ) 5I (I I 3 ) + 6 0 6 (I 3 I ) 3I 3 0 I I 5Ω.95 A a (I 3 )(3 Ω) (.4 ma)(3 Ω) 7.6 5. (I): I (. kω + 9. kω) 9. kω I 8 I (9. kω + 7.5 kω + 6.8 kω) 9. kω I 6.8 kω I 3 8 I 3 (6.8 kω + 3.3 kω) I 6.8 kω 3 I. ma, I 0.48 ma, I 3 0.6 ma (II): 6 4I 3(I I ) 4(I I 3 ) 0 3(I I ) 0 I 5 4(I I 3 ) 0 6 4(I 3 I ) 4(I 3 I ) 7I 3 0 I 0.4 A, I 0.5 A, I 3.8 A 6. a. 6.8 kω I 4.7 kω(i I ) + 6. kω(i I 4 ) 0 6 4.7 kω(i I ).7 kω I 8. kω (I I 3 ) 0. kω I 3 kω(i 3 I 4 ) 8. kω(i 3 I ) 9 0 5. kω I 4. kω(i 4 I ) kω(i 4 I 3 ) 0 I 0.03 ma, I 0.88 ma, I 3 0.97 ma, I 4 0.64 ma b. Network redrawn: I 6 4I + 4I 0 4I + 4I I + I 3 6 0 I 3 + I + 6 8I 3 0 I 3.8 A, I 4.0 A, I 3 0.0 A CHAPTER 8 7

7. a. I 4 I 6Ω I 0Ω I 3 A (CW) I 4Ω 3 A (CCW) 4 6I 4I 0I + 0 and 6I + 4I 36 I I 6 A I I + 6 A 6[I + 6 A] + 4I 36 6I + 96 + 4I 36 0I 60 I 3 A I I + 6 A 3 A + 6 A 3 A b. 0 4I 6(I I ) 8(I 3 I ) I 3 0 0I 4I + 9I 3 0 I 3 I 3 A I 8 A 0I 4(8 A) + 9[I + 3 A] 0 9I 05 I 5.56 A I 3 I + 3 A 5.56 A + 3 A 8.56 A I 8 A I 0 I 4Ω 5.53 A (dir. of I ) I 6Ω I I.47 A (dir. of I ) I 8Ω I 3 I 0.53 A (dir. of I 3 ) I Ω 8.53 A (dir. of I 3 ) 7 CHAPTER 8

8. a. b. (4 + 8)I 8I 4 (8 + )I 8I 6 I A, I 7 5 A 7 (4 + 3)I 3I 0 (3 + )I 3I I 3.06 A, I 0.9 A 9. (I): a. I (5.6 kω +. kω). kω (I ) 0 + 0 I (. kω + 3.3 kω). kω (I ) 0 30 b. I.45 ma, I 8.5 ma c. I R I.45 ma, I R I 8.5 ma I R 3 I + I 8.5 ma +.44 ma 9.96 ma (direction of I ) (II): a. I (. kω + 8. kω) 8. kω I 9 I (8. kω +. kω + 9. kω) 8. kω I 6 b. I.03 ma, I.3 ma c. I R I.03 ma, IR I 3 R I 4.3 ma I I I.03 ma.3 ma 0.80 ma (direction of I ) R 30. (I): ( + 3)I 3I 5 + 60 (3 + 5)I 3I 60 + 6 0 b. I.87 A, I 8.55 A c. I R I.87 A, I R I 8.55 A I R 3 I I.87 A ( 8.55 A) 0.4 A (direction of I ) (II): a. (3 + 4 + 6)I 6I 3 9 + 6 (6 + 8)I 3 6I 4 CHAPTER 8 73

b. I.7 A, I 3 0.6 A c. I R I.7 A, I R 3 I 3 0.6 A I R 4 I I 3.7 A 0.6 A.0 A I R 3 A I 3 A.7 A.73 A 3. I ( + ) I 0 I ( + 4 + 5) I 5I 3 0 I 3 (5 + 3) 5I 6 I I 63.69 ma (exact match with problem 8) R 3 3. From Sol. 4(b) I (6 + 4) 4I I (4 + 5 + ) 4I I 3 + 6 I 3 ( + 3) I 6 I 5Ω I.95 A I 3.4 A, a (I 3 )(3 Ω) (.4 A)(3 Ω) 7.6 33. (I): (. kω + 9. kω)i 9. kωi 8 (9. kω + 7.5 kω + 6.8 kω)i 9. kω I 6.8 kωi 3 8 (6.8 kω + 3.3 kω)i 3 6.8 kωi 3 I. ma, I 0.48 ma, I 3 0.6 ma (II): (4 Ω + 4 Ω + 3 Ω)I 3 Ω I 4 Ω I 3 6 (4 Ω + 3 Ω + 0 Ω)I 3I 4 Ω I 3 5 (4 Ω + 4 Ω + 7 Ω)I 3 4I 4I 6 I 0.4 A, I 0.5 A, I 3.8 A 34. a. I (6.8 kω + 4.7 kω +. kω) 4.7 kω I. kω I 4 6 I (.7 kω + 8. kω + 4.7 kω) 4.7 kω I 8. kω I 3 6 I 3 (8. kω +. kω + kω) kω I 4 8. kω I 9 I 4 (. kω + kω +. kω). kω I kω I 3 5 I 0.03 ma, I 0.88 ma, I 3 0.97 ma, I 4 0.64 ma b. From Sol. 6(b): I ( + 4) 4I 6 I (4 + ) 4I I 3 6 I 3 ( + 8) I 6 I 3.8 A, I 4.0 A, I 3 0.0 A 74 CHAPTER 8

35. a. 8.08 + + 5 5 9.39 + 3 4 Symmetry is present b. 4.80 + 4 4 4 6.40 + + 4 0 5 4 Symmetry is present 36. (I): + + 5 3 3 6 4 4 + 3 4 8 4 4 4.86,.57 4.86 R R 4 R.57 + +.57 4.86 9.7 R3 (II): + + 6 5 3 3 + + + 7 3 4 8 3.56, 4.03.56 R R R 5 4.03 R 4 R 3 4.03 +.56 6.59 CHAPTER 8 75

37. (I): a. + +.98 ma. k 9. k 7.5 k Ω Ω Ω 7.5 kω + + 0.9 ma 7.5 k 6.8 k 3.3 k Ω Ω Ω 7.5 kω b..65, 0.95 c. (+) ( ) R 3.65, R 5 0.95, R 4 3.60 R R + 8.65 5.35 R R + 3 0.95.05 (II): a. + + 3 4 4 7 4 4 4 + + 3 4.5 4 3 0 + 4 3 3 + + 3 4 4 4 3 4 4 3 b. 8.88, 9.83, 3 3.0 c. R 6 8.88, R R 4 3 3.0, R 5 + R 6 + 3 4. R ( + ) ( ) 0.95 + R 3 0.84 R R R 3 - + 5 R3 5.7 76 CHAPTER 8

38. (I): + + 3 5 3 6 6 6 6 + + 3 3 6 4 5 6 5 3 + + 0 6 5 7 5 6 7.4,.45, 3.4 (II): Source conversion: I 4 A, R 4 Ω + + 3 9 0 0 0 0 + + 3 0 0 0 8 0 0 3 + + 4 0 0 4 0 0 6.64,.9, 3 0.66 39. (I) + 0 5 + + + + 3 0 9 7 + + 3 5 4 5.3, 0.6, 3 3.75 CHAPTER 8 77

(II) + 3 5 6 6 5 4 3 + 6 5 6 6.9,, 3.3 40. a. ΣI i ΣI o Node : A + 6Ω 0Ω Supernode, 3 : 3 0 + + 0 Ω 4 Ω Ω Independent source: 3 4 or 3 4 eq. unknowns: + 6Ω 0Ω A 4 + + 0 Ω 4 Ω Ω 0 0.67 0. +0. 0.433 0.08, 6.94 3 4 7.06 78 CHAPTER 8

b. Supernode: eq. unk. ΣI i ΣI o 3 A + 4 A 3 A + + 0 Ω 40 Ω 4 A + 0 Ω 40 Ω 6 4. a. + + 5 5 + 3 4 8.08, 9.39 Symmetry present + 4 4 4 + + 4 0 5 4 4.8, 6.4 b. Symmetry present Subt. 6 + (6 + ) 4 A + 0 Ω 40 Ω and 48 6 + 64 CHAPTER 8 79

4. (I): a. Note the solution to problem 36(I). b. 4.86,.57 c. (II): a. R 4.86, R 4 + R 3 R 3 R.57 R 3 + ( 4.86 ) (.57 ) + 9.7 Note the solution to problem 36(II). b..56, 4.03 c. R.56, R R 5 4.03 (+) ( ) 6.59 R R 3 4 43. (I): a. Source conversion: I 5 A, R 3 Ω + + 3 5 3 6 6 6 6 + + 3 3 6 4 5 6 5 3 + + 0 6 5 7 5 6 b. 7.4,.45, 3.4 c. R R 5 7.4 7.76 + R.45, R 3 3.4 (+) ( ) R 4 3.4 (.45 ) 3.86 R 5 7.4 (.45 ) 9.69 R 6 3 7.4.4 5.83 80 CHAPTER 8

(II): a. Source conversion: I 4 A, R 4 Ω + + 3 9 0 0 0 0 + + 3 0 0 0 8 0 0 3 + + 4 0 0 4 0 0 b. 6.64,.9, 3 0.66 c. R R 6.64, R R 3.9, R 5 (+) ( ) R 4 + (+) ( ) 6 0.66 5.34.9 ( 6.64 ) 7.93 3 0.66.9 9.37 R 6 (+) ( ) 3 0.66 ( 6.64 ) 7.30 44. a. Note the solution to problem 39(I). 5.3, 0.6, 3 3.75 5A 5.3 b. Note the solution to problem 39(II). 6.9,, 3.3 (+) ( ) (+) ( ) A 3 9.7, 5A 8.9 45. a. I (6 + 5 + 0) 5I 0I 3 6 I (5 + 5 + 5) 5I 5I 3 0 I 3 (5 + 0 + 0) 0I 5I 0 I 0.39 A, I 0.8 A, I 3 0.4 A b. I 5 I I 3 40 ma (direction of I ) c, d. no CHAPTER 8 8

46. Source conversion: I A, R 6 Ω + + 3 6 5 5 5 5 + + 3 0 5 5 0 5 5 + + 3 0 5 5 0 5 5 96.70 m, no R 5 47. a. I ( kω + 33 kω + 3.3 kω) 33 kω I 3.3 kω I 3 4 I (33 kω + 56 kω + 36 kω) 33 kω I 36 kω I 3 0 I 3 (3.3 kω + 36 kω + 5.6 kω) 36 kω I 3.3 kω I 0 I 0.97 ma, I I 3 0.36 ma b. I 5 I I 3 0.36 ma 0.36 ma 0 c, d. yes 48. Source conversion: I A, R kω + + 3 k 33 k 56 k Ω Ω Ω 56 kω 33 kω + + 3 0 56 k 36 k 5.6 k Ω Ω Ω 56 kω 36 kω + + 3 0 33 k 3.3 k 36 k Ω Ω Ω 33 kω 36 kω I 0 A, yes R 5 49. Source conversion: I 9 ma, R kω + + 3 4 ma k 00 k 00 k Ω Ω Ω 00 kω 00 kω + + 3 9 ma 00 k 00 k k Ω Ω Ω 00 kω kω 3 + + 9 ma 00 k 00 k k Ω Ω Ω 00 kω kω 8 CHAPTER 8

50. a. ( kω + kω + kω)i kω I kω I 3 0 ( kω + kω + kω)i kω I kω I 3 0 ( kω + kω + kω)i 3 kω I kω I 0 I I 0 3.33 ma Source conversion: I 0 / kω 0 ma, R kω + + 3 0 ma k k k Ω Ω Ω kω kω + + 3 k k k Ω Ω Ω kω kω 0 3 + + 0 k k k Ω Ω Ω kω kω 6.67 E IR s 0 I( kω) I 0 6.67 k Ω 3.33 ma b. Source conversion: E 0, R 0 Ω (0 + 0 + 0)I 0I 0I 3 0 (0 + 0 + 0)I 0I 0I 3 0 (0 + 0 + 0)I 3 0I 0I 0 I I 0 0.83 A 0 8.3.7 I s.70 R 0 Ω.7A s + + 3 0 0 0 0 0 + + 3 0 0 0 0 0 0 3 + + 0 0 0 0 0 0 I.7 A R R s s CHAPTER 8 83