Introductory Circuit Analysis
|
|
- Χαρικλώ Δελή
- 7 χρόνια πριν
- Προβολές:
Transcript
1 Instructor s Resource Manual to accompany Introductory Circuit Analysis Eleventh Edition Robert L. Boylestad Upper Saddle River, New Jersey Columbus, Ohio
2 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 CHAPTER 5 34 TEST ITEM FILE 353 iii
3 Chapter.. 3. d 0,000 ft mi 60 s 60 min 4. υ t 0 s 5,80 ft min h mph 5. h 4 min h 60 min d 3mi υ t.067 h 9.05 mph 6. a. 95 mi 5,80 ft h min ft/s h mi 60 min 60 s b. d 60 ft t υ ft/s 0.43 s c. d 60 ft 60 s 60min mi υ 40.9 mph t s min h 5,80 ft MKS, CGS, C ( F 3) (68 3) (36) SI: K C ft - lb 000 J ft-lbs J 3 ft in..54 cm. 0.5 yd yd ft in cm 3. a. 0 4 b. 0 6 c. 0 3 d. 0 3 e. 0 0 f a b c d e f. 0 0 Chapter
4 5. a b c d a. (0 )(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 ) a. ( )(3 0 4 ) b. (. 0 3 )( 0 3 ) c. (8 0 6 )( ) d. ( )(4 0 3 )(7 0 8 ) a. 0 / b. 0 / c. 0 4 / d. 0 7 / e / f. 00 /0 0 / a. ( 0 3 )/(8 0 5 ) b. (4 0 3 )/( ) 4/ c. ( 0 5 )/(5 0 5 ) / d. ( )/(4 0 6 ) a. (0 ) b. (0 4 ) / c. (0 4 ) d. (0 7 ) a. (4 0 ) b. (6 0 3 ) c. (4 0 3 )(6 0 ) (4 0 3 )( ) d. (( 0 3 )( )( )) 3 ( ) 3 (4.8) 3 (0 3 ) a. ( 0 3 ) b. c. d. 4 (0 )(0 ) 0 / (0 ) (0 ) (0 )(0 ) (0 )(0 ) 0 7 / Chapter
5 e. ( 0 4 ) 3 (0 )/0 6 (0 )(0 )/ / [(0 )(0 )] f [(0 ) ][ 0 ] (0 )(0 ) a. (3 0 ) (0 ) (9 0 4 )(0 )/(3 0 4 ) (9 0 6 )/(3 0 4 ) b. 4 8 (4 0 ) (0) c. 4 8 (6 0 ) ( 0 ) d. ( / 3 5 ) e. 3 (4 0 ) (3 0 ) (6 0 )(3 0 ) f. (6 0 6 ) / (0 5 ) 5 ( 0 ) (4 0 3 )(0 5 )( 0 ) g / (3 0 ).60 0 ( 0 )(8 0 ) 5 (7 0 ) 9 4 / (7 0 )(.56 0 )(6 0 ) (69. 0 )(4 0 ) a b c Chapter 3
6 d a s s 50 ms b s 0 3 s ms 3 3 c s s 40 μs d s s μs 6 3 e m m m 4000 mm increase by 3 f m 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 μs μs 0 6 s d. mm 0.6 m mm 60 mm 0 3 m 4 Chapter
7 e ns s 0 9 s. 0 ns 0 ns f min h day s 60 s 60 min 4 h 4.90 days 6 0 F pf 7. a. 0. μf μf 0 F pf 0 5 pf b cm m m cm 8 cm m km c. 60 cm 00 cm 000 m km 60 min 60 s ms d. 3. h ms h min 0 3 s 3 0 m μ m e mm 6 mm 0 m μm 6 μm f. 60 cm m m 00 cm 00 cm m m 8. a. 00 in in..54 m in. m b. 4 ft ft in.. m 4.45 N c. 6 lb lb 6.7 N d N lb dynes 5 0 dynes 4.45 N 0.3 lb in. ft e. 50,000 cm.54 cm in ft 580 ft in. m f mi 3. m mi ft in. Chapter 5
8 yd ft, 580 ft 760 yds 3 ft in. m 580 ft m,.6 km ft in. m in. ft mi 60 s 60 min ,79,458 s m in. 580 ft min h 670,65,88. mph mph 3 ft mi yds yd 5,80 ft 60 mi h min h 60 min 60 s mi mi/s 3. d mi t υ mi/s 3.40 s 30 mi 580 ft in. m h min h mi ft in. 60 min 60 s 3.4 m/s 50 yd 60 min 3 ft mi mi/h min h yd 5,80 ft d 3000 mi day t 760 h days υ.705 mi/h 4 h 000 m in. ft mi km km m in. 580 ft mi d 6.4 mi υ, t min 6.5 min υ mi 6.5 min 6.4 mi 3 ft in yds yd ft 3600 in 3600 quarters 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
9 cm 60 min 60 s m h 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 min min/mile mile 0.8 miles 0.8 miles 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 Btu J b. 3 gallon m 4 ounces 8 ounces 64.7 gallons m 3 c. 86,400 s.4 days. 0 5 s day d. m gallons 8 pints 3.38 pints 3 m gallon 4. 6(4 + 8) (0 + 3)/ (8 + ) MODE DEGREES: cos MODE DEGREES: tan (3/4) Chapter 7
10 47. ( 400/(6 0) ) Chapter
11 Chapter. QQ. a. F ( 9 0 )(C)( C) k 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 N r (0 m) 9 r3 0 m d. Exponentially, r m 0 while F 8 0 N 9 F N a. r mi: 580 ft in. m mi m mi ft in. kqq (9 0 )(8 0 C)(40 0 C) F r ( m) μn b. r 0 ft: in. m 0 ft ft in m F kq Q r 0.3 N (3.05 m) 9.30 in. m c..59 mm in. 3 3 kqq F r (.59 0 m) kn 3 N 4. kqq kqq (9 0 )( F r 4 r F ) 0 mm Chapter 9
12 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 ) ( Q ) Q 9 Q 0 μc 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 C electrons 3.5 C electrons Q 3.5 C I 0.9 A t s 7. Q It (4 ma)(90 s) 360 mc electrons 360 mc electrons C 0 Chapter
13 8. I Q t 86 C (.)(60 s).94 A > A (yes) C electrons.346 mc electrons Q.346 mc I.43 ma t 60 ms 0. a. Q It ( ma)(0.0 μs) 0 C electrons C C electron $ million b. Q It (00 μa)(.5 ns) C electrons $ C C electron (a) > (b) 0.94 million. Q It ( 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 C 4 Q 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
14 60 min 60 s Ah(for h): W Q I t ( )(40 A)( h) J h min 60 min 60 s 60 Ah(for h): W ( )(60 A)( h) 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( h) 60 s 60 min 40 Ah and I 400 A h min h 60 Ah It I [ 60 s] I( h) 60 s 60 min 60 Ah and I 3600 A 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 s 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 )( C).5 J Chapter
15 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 mils. a. A CM (30 mils) 900 CM b in. 6 mils, A CM (6 mils) 56 CM c. " 8 0.5" 5 mils, A CM (5 mils) CM in. 000 mils d. cm.54 cm in mils, A CM (393.7 mils) CM in. 000 mils e. 0.0 ft ft in. 40 mils, A CM (40 mils) CM in. f m m in mils, A CM (65.4 mils) 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
16 d. d 65 CM 5 mils 0.05 in. e. d 6.5 CM.5 mils in. f. d 00 CM 0 mils 0.0 in 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 a. A ρ CM R.5 Ω (50 ft) ( 9.9) 9.8 Ω 6 CM b. d A 544 CM 3.3 mils in. CM 7. " 3 R 0.035" 3.5 mils, A CM (3.5 mils) CM l ρ l R RA ρ (. Ω)( CM) 3.58 ft 600 l 8. a. A CM ρ (0.37)(300 ) CM A 3.3 Ω d CM mils 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 nickel 4 Chapter 3
17 . a. 3" 3000 mils, /" 0.5 in. 500 mils Area (3 0 3 mils)(5 0 mils) sq. mils / π CM sq mils CM sq mil l (0.37)(4 ) R ρ.7 μω 5 A CM l (7)(4 ) b. R ρ μω 5 A 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, 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, CM) 4. a..60 Ω #: 450 ft 000 ft.55 Ω #4: 450 ft 000 ft Ω.36 Ω b. Resistance: #4:#.36 Ω:0.567 Ω : c. Area: #4:# CM:834.0 CM : Chapter 3 5
18 0.68 Ω 5. a. #8: R 800 ft 000 ft.3 Ω Ω #8: R 800 ft.49 Ω 000 ft b. #8:#8.49 Ω:.3 Ω 0.7: 0: c. #8:# 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 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 in..54 cm in. 0. cm π d (3.4)(0. cm) A cm RA ( Ω)(0.035 cm ) l 6 ρ ,603 cm 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) μω 6 Chapter 3
19 c. increases d. decreases 6 ρ ρ R s 00 d d 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 cm 4 4 in..54 cm l 000 ft ft in. 30,480 cm RA ( m Ω)(5.067 cm ) ρ Ω-cm l 30,480 cm c. k 7 ρ.66 0 Ω-cm ρ CM- Ω / ft Ω R Ω R R (0.0 Ω)(336) 36, R (34.5)( Ω ) Ω.57 Ω C ( F 3) (3 3) 0 (3 F) C (70 3). (70 F) Ω R ( 34.5)(4 Ω ) R 3.67 Ω 55.6 Chapter 3 7
20 Ω R R ( 94.5)(0.76 Ω ) 0.56 Ω ( 30) Ω R R (43)(40 m Ω ) 3 46 mω 8. a. 68 F 0 C, 3 F 0 C R R (34.5)( m Ω ) mω F 00 C m Ω R R (334.5)( m Ω ) mω b. ΔR.63 m Ω mω 0.63 mω Δ T 00 C 0 C 80 C 7.88 μω/ C or Ω/0 C 9. a t, Ω. Ω t 7.85 C t b. Ω 0.Ω, t 0.65 C 30. a. K C C C Ω R R c. F.35 (0 Ω) Ω C + 3 ( 73.5 ) b. K C C C Ω R 34.5 ( 0)0 Ω R 0 Ω 54.5 Recall: 34.5 Inferred absolute zero R 0 Ω 8 Chapter 3
21 3. a. α 0 T i + 0 C b. R R 0 [ + α 0 (t 0 C)] Ω 0.8 Ω[ (t 0 )] t t t t C 3. R R 0 [ + α 0 (t 0 C)] 0.4 Ω[ (6 0)] 0.4 Ω[ 0.057] 0.39 Ω 33. Table: 000 of # copper wire C C 9 5 (F 3) 9 5 (5 3) 46. C R R 0 [ + α 0 (t 0 C)].588 Ω[ (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 Ω Ω #: Area 659 CM.54 cm d 659 CM 80.8 mils in. in. πd π (0.05 cm) A cm 4 4 MA I [0.033 cm ] 33 ka >> 0 A cm 0.05 cm a. times larger b. 4 times larger 4. 0 kω 3.5 kω 6.5 kω Chapter 3 9
22 kω and 8.75 kω 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 Ω± 0% 8 Ω Ω no overlap, continuance 5 Ω± 0% Ω 8 Ω 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 Ω 60 Ω 0.6 kω b Ω 33 kω c. Q Ω 390 Ω d. C 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/ Ω G R 69.7 ms.588 Ω or G A CM (Table 3.) ρ l (0.37)(000 ) ms (Cu) b. G c. G CM (7)(000 ) CM (74)(000 ) 384. ms (Al) 88.4 ms (Fe) 0 Chapter 3
23 5. A A 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 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 Ω cm ΔT 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 ma, ma, 5 ma, 5 b. Δ total 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
24 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) m 6. I 6 R 5 k Ω 4.3 ma 7. R 0 I. A 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) 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) J 4. IR (.4 μa)(3.3 MΩ) Chapter 4
25 6. b. (0.3 ma)(500 h) 65 mah 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) 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 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
26 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 ) P EI (9 )(45 ma) 405 mw P 00 W 34. P I, I A 0 R I A 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 W 0.3 ma 3 b. Ah rating (0.3 ma)(500 h) 66.5 mah P R 00 W kω 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
27 39. 4 weeks h 3 [5 months] 60 h week month (30 W)(60 h) kwh kwh kwh Pt (000)(kWh) (000)( kwh) t 8 h 000 P 500 W (4 W)(3 h) 4. kwh kwh 000 (7 0 3 kwh)(9 /kwh) a. kwh Pt (000)(kWh) (000)(00 kwh) P 0 kw 000 P 0 h b. I 3 P 0 0 W 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 #kwh $ Pt (kwh)(000) (.)(000) kwh t h 000 P.50 t (kwh)(000) (.)(000).3 h P 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) kwh Chapter 4 5
28 45. a. P EI (9 )(0.455 A) 4. W b. R E 9 I A 9.78 Ω c. W Pt (4. W)(,600 s) 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 W W 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 Wh +400 Wh Wh 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 Wh Wh + 05 Wh + 35 Wh.63 kwh 000 (.63 kwh)(9 /kwh) η P o P i 746 W (0.5 hp) hp % 00% 00% 94.43% 395 W η Po P, P P i o i P i P i EI, I (.8 hp)(746 W/hp) η W W E A 5. η Po 746 W % 00% 00% P (4 A)(0 ) % i 6 Chapter 4
29 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) W 55. P i b. P i EI W (0 )I W I W 5.07 A 0 c. P o ( hp)(746 W/hp) P i η W P i EI 3.43 W (0 )I 3.43 W I 3.43 W A I P o η P i E (5 hp)(746 W/hp) 0.9, W A, W 56. η T η η η η η T η η (0.87)(0.75) % 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 η η % 0.9 Chapter 4 7
30 60. a. η T η η η 3 (0.98)(0.87)(0.) % 6. η T b. η T η η η 3 (0.98)(0.87)(0.90) % 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
31 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 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 kω 7.7 kω b. R T kω + kω + 3 kω kω 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 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 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) a. the most: R 3, the least: R b. R 3, R T. kω 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
32 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) 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 c. R 3 kω I 3 ma d.. kω 6.6, 3 kω 9, 3.3 kω 9.9. a. I E R T kω 8.8 ma, E (36 ) 8 b. R T kω +.4 kω kω 9 kω E.5 I.5 ma,.5 ma(.4 kω kω) 0 9 kω R T c. R T 0 kω + kω + 33 kω + 0 MΩ MΩ E 00 I 9.94 μa MΩ R T (9.935 μa)(0 MΩ) 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 W W.4 W R R R3 d. P T EI s (0 )(0 ma).4 W 30 Chapter 5
33 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 mw 3 3 P R I R (50 ma) 47 Ω.94 W P R I R (50 ma) 3 Ω mw 4 c. P T P + P + P + P.38 W mw +.94 W 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 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
34 5. a. R T NR 8 8 Ω 5 Ω 8 E 0 I 0.53 A R T 5 Ω b. P I R A 8 Ω W 8 5 c. IR A Ω 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 I 4 I I 4 I I ( 4) ± ( 4) () 4()(4) 4 ± A P 4 W ( A) R, R 4 Ω 6 Ω 4 7. a. ab b. ab c. ab a. E T , I 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
35 0. a b c a b. +E E 8 4. a b a , , 8 b , , , 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 ) kω Chapter 5 33
36 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 a. 6 Ω 4 Ω 0, Ω 0, Ω (6 Ω)(0 ) Ω (4 Ω)(0 ) Ω E b , , 3 70 c. 000 Ω(000 ), 0 00 Ω Ω 00 Ω 000 Ω(000 ), 0 00 Ω Ω 00 Ω E d , , kω kω kω( ) kω 4 4, 4 kω 3 kω 3 kω( ) kω 6 I ma kω E Chapter 5
37 9. a. 4 R(0 ), R.6 kω kω + 6 kω (6 Ω+ R)40 b Ω+ 6 Ω+ R 300 Ω Ω + 00R 840 Ω + 40 R 40R 00R 840 Ω Ω 40R 60 Ω R 60 Ω.5 Ω a. 4 0 Ω(4 ) 0 Ω 0 Ω 0 Ω 8 b. 3 E c. 4 8 (8 )(0 Ω) R3 70 Ω 0 Ω R 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 R R R + R R + 7, R 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 ) a. R 3 4 R 4(3 R ) R E 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 kω Chapter 5 35
38 MΩ b. R T 6.4 MΩ, R 400 kω, R. MΩ, R MΩ 0 μa 6 I 0 ma 0 3 R 400 kω and I 0 μa R 400 Ω 03 also 35. a. a b 8 ab a b 4 ( 8 ) b. a b +4 ab a b c. a b +6 ab a b a. I(CW) 6 Ω+ 3 Ω 54 9 Ω 6 A IR (6 A)(3 Ω) b. I(CW) 0 Ω+ 0 Ω+ 30 Ω Ω A IR ( A)(0 Ω) 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) b. I ma. k Ω+ 3.3 k Ω 5.5 k Ω a I(. kω) + 0 (5.455 ma)(. kω) I(. kω) (5.455 ma)(. kω) I 3 ma (CCW) k Ω+ 3 k Ω+ 4 kω 9 kω kω 6, 3kΩ 9, 4kΩ a. a 0, b , c d, e 0 b. ab 6, dc 47, cb 9 c. ac 5, db Chapter 5
39 39. R I R Ω 8 Ω A, R I R 3 R Ω I A A Ω, A A 40. R R 36 R.5 kω I 6 ma R 3 0 R3 R kω I 6 ma R 4 0 R4 0 R 4.5 kω I 6 ma R E R R 3 R R 3 R kω I 6 ma 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 , c d 0 b. ab kω 4, cb 4kΩ 8 cd 6kΩ c. ad a d ca c a , I.5 A 4Ω 4Ω 4 Ω Chapter 5 37
40 , , ( ma)(3 kω + kω) ( ma)(4 kω) , 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 int 4 R int I A Ω b. R NL FL FL 00% % 7.4% 45. a. L 3.3 Ω( ) 3.3 Ω Ω.8 b. R NL FL FL 00% %.5% c. I s I L 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 kω 0.5 kω.7 ma c. not for most applications. 38 Chapter 5
41 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 kω kω 3 kω Ω S c. R T d. R T R T e. R T f. R T 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 MΩ 3 S S Ω 5 Ω Ω S + 0 S S S S S S S S 4. a. R T kω. kω 0.3 kω Ω S S S S Chapter 6 39
42 b. R T kω +. k Ω S. kω Ω kω 0 S S 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 Ω S S. kω R. kω R Ω R Ω R 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 kω 3. kω 6. a.. kω b. about kω c. R T kω kω 0 kω. MΩ S S S kω S d. (. kω)( kω) 0 kω,. MΩ: R T. kω + kω.38 kω e. R T reduced. 6 6 S 40 Chapter 6
43 7. a. R T ( Ω)(8 Ω) Ω + 8 Ω.6 Ω b. Ω c. Ω d. R T S S S 0.85 S 4 Ω Ω 0 Ω.8 Ω R R R R T 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 S S 0. S R S R 0. S S S R 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
44 . a. R T + + Ω 9 Ω 3 36 Ω. Ω S b. R R R 8 3 E 8 c. I s R. Ω 8.5 A T R S + 0.S 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 A 8.5 A (checks). a. R T S S kω. kω 6.8 kω Ω S b. R R R 4 3 E 4 c. I s R 5.9 ma T Ω 4 R R 4 IR.4 ma, I R 0 ma, R 0 kω R. kω R R 4 3 IR 3.53 ma 3 R3 6.8 kω d. I T 5.9 ma.4 ma + 0 ma ma 5.93 ma (checks) 3. a. R T kω b. R T kω kω. kω 56 kω S S S S.003 kω, very close 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 ma, I 3 R 0.79 ma 4 R. kω R 56 kω 3 4 S 4 Chapter 6
45 4. e. I s E R T ma.003 kω I s ma 4.4 ma + ma ma ma 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 kω E 8 I s R 9.6 ma kω T R T 0 kω kω kω RI T s (0.909 k Ω)(9.6 ma) 8.77 ma I R + 0 kω kω+ 0 kω T 0.8 ma 8. a. I b. 4 c. I s 4 0 kω kω 4 kω 4 ma + 4 ma + 4 kω.4 ma + 4 ma + ma 8.4 ma Chapter 6 43
46 9. a. R T S S kω 33 kω 8. kω Ω 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 Ω 5.3 ma P s E s I s (00 )(5.3 ma).5 W d. P s.5 W 0 W 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 ma.8 kω.8 kω Ω 5 Ω A d. (0 ) P R.8 kω 8 W e. P s 8(8 W) 64 W f. none, I s drops by ma + + Ω 0 Ω 5 0 Ω.86 Ω 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 S S S 44 Chapter 6
47 . 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 A 00 W P 3 00 W 0 I 3, I A 0 W P 4 0 W 0 I 4, I A b. I s 5 A A +.67 A 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 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 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 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 ma, I.5 ma I 3 ma I 3 + ma, I 3 ma I 4 5 ma b. I 3.5 μa 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
48 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
49 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 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 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 S kω. kω 0. kω Ω 6 6,88 0 S RT Ω I x I, I (8 ma).30 ma Rx. kω Ω I (8 ma).39 ma. kω Ω I 3 (8 ma) 4.3 ma 0. kω I 4 8 ma S S Chapter 6 47
50 c. R T 50 0 S Ω 8 Ω Ω.8 Ω 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 S S 3. a. I 0 9 (0 A) 9 A b. I /I 0 Ω/ Ω 0, I 9 A I 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, μa e. very little effect, /00,000 f. R T Ω 0 Ω kω 00 kω 3 6 S + 0. S + 0 S 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 Ω (0 A) 9. ma excellent (9 ma) kω i. I Ω (0 A) 9 μa excellent (90 μa) 00 kω 48 Chapter 6
51 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 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 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
52 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 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 a. I 0 4 Ω 5 A, I 0 A b. 0, 0 c. I s I 5 A kω(0 ) 4. a kω kω b. R T MΩ kω.956 kω.956 kω(0 ) 6.47 (very close to ideal).956 kω kω c. R m 0 [0,000 Ω/] 400 kω R T 400 kω kω kω kω(0 ) 6.3 (still very close to ideal) kω kω d: a. 00 kω(0 ) 00 kω + 00 kω 3.33 b. R T 00 kω MΩ kω (96.49 kω)(0 ) 3.5 (very close to ideal) kω + 00 kω 50 Chapter 6
53 c. R m 400 kω R T 400 kω 00 kω kω ( kω)(0 ).43 (a.84 drop from R int MΩ level) 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) supply connected in reverse so that I 3. ma kω + 4 kω 5 kω and ab (3. ma)( kω) obtained Chapter 6 5
54 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 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 A c. I 5 A d. I R ( A)(6 Ω) 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 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
55 6. a. R T. kω 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 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 Ω 8 Ω)(4 A) (4 Ω 8 Ω ) + (6 Ω+ Ω) (.67)(4 A) A.67 Ω + 8 Ω Chapter 7 53
56 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) I 0 5 Ω 4 A R T 6 Ω 5 Ω Ω 7 I Ω 0.7 A 0. a, b. I 4 4 Ω 6 A, I Ω 0.8 A I 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 I R + R 0 Ω+ 0 Ω 0 Ω A I 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) 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) Ω+ 3 Ω (3 Ω+ 3 Ω) 3 Ω+ 3 Ω 6 Ω 3 Ω+ Ω 4 A 54 Chapter 7
57 R4( I) 3 Ω(4 A) b. CDR: I R4 + R + R3 R5 3 Ω+ 3 Ω+ 6 Ω 6 Ω A A I I 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 μa 0 kω 0 kω c. B BE + E.7 C CC I C R C 8 ( ma)(. kω) d. CE C E BC B C a. 70 k Ω(6 ) I G 0 G 70 k Ω+ 000 kω G GS S 0 S G GS.9 (.75 ) 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) d. DD I D R D DG G 0 DG DD I D R D G 6 (.43 ma)(.5 kω) Chapter 7 55
58 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 Ω Ω R T 30 Ω Ω 74. Ω b. a 4.94 Ω(3 ) 4.94 Ω+ 40 Ω.89 c. 3 a d. a.89 e. I 600Ω ma 600 Ω I 0Ω ma 0 Ω I + I 600Ω I 0Ω I I 00Ω I 600Ω 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 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
59 I 3 I I 5 A 3 A 3 A Ω A RI I 6 R7 + R6 3 Ω+ 6 Ω. A I 8 0 A b. 4 I 3 (R 4 R 5 ) A 3 (3 Ω) Ω 8 Ω 4 Ω 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 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
60 0. a. KL: ab 0 ab 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": Ω 0 8Ω 38 I 8Ω 38 8 Ω 4.75 A 8 8 I 3Ω 3 Ω+ 6 Ω 9 Ω A KCL: I A + A 6.75 A b. (I 3Ω )(6 Ω) + 0 ( A)(6 Ω) 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 R3 KL: 0 I + I 3 R R 3 and 0.R R 3 3.R 3 96 Ω R 3 96 Ω 30 Ω Chapter 7
61 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) A (0 Ω) A (0 Ω) E E 8.33 R T 8.33 Ω I A kω 6 kω kω 3.6 kω 3.6 k Ω(45 ) 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
62 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 ma Ω( I) Ω(36.66 ma) c. I 3 Ω+ 6.56Ω Ω Ω I 8 Ω(84.5 ma) 8.78 ma Ω+ 7 Ω 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 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 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 A d. I 0 A 6 A 60 Chapter 7
63 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 R 0.5 kω IR 3 ma 3 ma R 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 R IR 40 ma 40 ma 0.5 kω R 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 R 5 I 40 ma 40 ma 0.6 kω R5 Chapter 7 6
64 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, kω R 55 Ω R kω R 745 Ω 80 Ω(40 ) 3. a. ab 3 00 Ω bc b. 80 Ω kω Ω 0 Ω 0 kω 9.96 Ω Ω(40 ) ab Ω Ω 3.5 bc Chapter 7
65 c. P (3.5 ) (8.49 ) + 80 Ω 0 Ω.4 W 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) 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 ) : R s 4.9 kω ma : R s 49.9 kω ma : R s kω ma MΩ (0.5 )(Ω/) Ω/ I CS /(Ω/) 0.05 μa a. R s E zero adjust 3 R m kω k 8 kω I 00 μa Ω m Chapter 7 63
66 b. xi m R unk E R series E xi m + R m + zero adjust + R unk zero adjust Rseries + R m kω x00 μa x x 3 4, R unk 0 kω; x, R unk 30 kω; x 4, R unk 90 kω 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
67 Chapter 8. a. I I 3 0 ma b. I R (0 ma)( kω) 0 c. R T kω +. kω kω 3.76 kω s IR T (0 ma)(3.76 kω) a. Rs ( I) 0 kω(4 A) I 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) R IR (6 A)(3 Ω) 8 E + R s 0, s E + R 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 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 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
68 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) ( )/(0 Ω Ω + 39 Ω) Ω c. ab I R 3 ( ma)(39 Ω) 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) 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 Ω.07 A ma 4. a. I E R. k Ω 5.45 ma, R p. kω 66 CHAPTER 8
69 b. I T 8 ma ma 3 ma 0.45 ma R 6.8 kω. kω.66 kω I T R (0.45 ma)(.66 kω) 7.35 c d. I R. k Ω.43 ma 5. a. 4 4I 8I I 8I 3 0 I + I I 3 I A, I A, I3 A IR I A, IR I A, IR I 3 3 A b I 3 4I 0 I 3.06 A 3I 3 I 0 I 0.9 A I + I I 3 I 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 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 kω I kω I + 8. kω I I + I 3 I I.03 ma, I.3 ma, I ma I R I.03 ma I I ma I R R I I.3 ma R 3 4 I R ma CHAPTER 8 67
70 7. (I): 5 I 3I I I 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 I 4I 6I I 4 8I I I 3 + I 4 I.7 A ab + I 4 Ω 6 (.7 A)4 Ω 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 I 3 R 4 I 5 (R 4 + R 5 ) E 3I + I I 9I 3 + 5I I 3 8I 5 6 d. I 3 I R ma 3 68 CHAPTER 8
71 9. a. 0 I B (70 kω) 0.7 I E (0.5 kω) 0 I E (0.5 kω) 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) E I E R E (4.48 ma)(50 Ω).8 C 0 I C (. kω) 0 (4.4 ma)(. kω) c. β I C /I B 4.4 ma/63.0 μa 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 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 ) 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
72 (II): I (. kω) 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 ) (I I ) + 6 5I 0 0 I.87 A, I 8.55 A ab + 0 I 5 0 (8.55 A)(5) (II): Source conversion: E 9, R 3 Ω 9 3I 4I + 6 6(I I 3 ) 0 6(I 3 I ) 8I I.7 A, I A ab + 3. (a): 0 I (I I ) 0 (I I ) I 4 5(I I 3 ) 0 5(I 3 I ) I I I I + 0I 5I I + 8I 6 I 3 I R 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) I 4 6 (.7 A)(4 Ω) CHAPTER 8
73 b. Network redrawn: 6I 4(I I ) 0 4(I I ) 5I (I I 3 ) (I 3 I ) 3I 3 0 I I 5Ω.95 A a (I 3 )(3 Ω) (.4 ma)(3 Ω) (I): I (. kω + 9. kω) 9. kω I 8 I (9. kω kω kω) 9. kω I 6.8 kω I 3 8 I 3 (6.8 kω kω) I 6.8 kω 3 I. ma, I 0.48 ma, I 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 ) 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 ) kω I 4. kω(i 4 I ) kω(i 4 I 3 ) 0 I 0.03 ma, I 0.88 ma, I ma, I ma b. Network redrawn: I 6 4I + 4I 0 4I + 4I I + I I 3 + I + 6 8I 3 0 I 3.8 A, I 4.0 A, I A CHAPTER 8 7
74 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 I 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
75 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 ) I (. kω 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 (3 + 5)I 3I 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. ( )I 6I (6 + 8)I 3 6I 4 CHAPTER 8 73
76 b. I.7 A, I A c. I R I.7 A, I R 3 I 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 ( ) I 5I 3 0 I 3 (5 + 3) 5I 6 I I ma (exact match with problem 8) R 3 3. From Sol. 4(b) I (6 + 4) 4I I ( ) 4I I I 3 ( + 3) I 6 I 5Ω I.95 A I 3.4 A, a (I 3 )(3 Ω) (.4 A)(3 Ω) (I): (. kω + 9. kω)i 9. kωi 8 (9. kω kω kω)i 9. kω I 6.8 kωi 3 8 (6.8 kω kω)i kωi 3 I. ma, I 0.48 ma, I 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 kω +. kω) 4.7 kω I. kω I 4 6 I (.7 kω + 8. kω 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 ma, I 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 A 74 CHAPTER 8
77 35. a Symmetry is present b Symmetry is present 36. (I): , R R 4 R R3 (II): , R R R R 4 R CHAPTER 8 75
78 37. (I): a ma. k 9. k 7.5 k Ω Ω Ω 7.5 kω 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 , R R R R R (II): a b. 8.88, 9.83, c. R , R R , R 5 + R R ( + ) ( ) R R R R R CHAPTER 8
79 38. (I): ,.45, 3.4 (II): Source conversion: I 4 A, R 4 Ω ,.9, (I) , 0.6, CHAPTER 8 77
80 (II) ,, a. ΣI i ΣI o Node : A + 6Ω 0Ω Supernode, 3 : Ω 4 Ω Ω Independent source: 3 4 or 3 4 eq. unknowns: + 6Ω 0Ω A Ω 4 Ω Ω , CHAPTER 8
81 b. Supernode: eq. unk. ΣI i ΣI o 3 A + 4 A 3 A Ω 40 Ω 4 A + 0 Ω 40 Ω 6 4. a , 9.39 Symmetry present , 6.4 b. Symmetry present Subt. 6 + (6 + ) 4 A + 0 Ω 40 Ω and CHAPTER 8 79
82 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 ) Note the solution to problem 36(II). b..56, 4.03 c. R.56, R R (+) ( ) 6.59 R R (I): a. Source conversion: I 5 A, R 3 Ω b. 7.4,.45, 3.4 c. R R R.45, R (+) ( ) R (.45 ) 3.86 R (.45 ) 9.69 R CHAPTER 8
83 (II): a. Source conversion: I 4 A, R 4 Ω b. 6.64,.9, c. R R 6.64, R R 3.9, R 5 (+) ( ) R 4 + (+) ( ) ( 6.64 ) R 6 (+) ( ) ( 6.64 ) a. Note the solution to problem 39(I). 5.3, 0.6, A 5.3 b. Note the solution to problem 39(II). 6.9,, 3.3 (+) ( ) (+) ( ) A 3 9.7, 5A a. I ( ) 5I 0I 3 6 I ( ) 5I 5I 3 0 I 3 ( ) 0I 5I 0 I 0.39 A, I 0.8 A, I A b. I 5 I I 3 40 ma (direction of I ) c, d. no CHAPTER 8 8
84 46. Source conversion: I A, R 6 Ω m, no R a. I ( kω + 33 kω 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 kω) 36 kω I 3.3 kω I 0 I 0.97 ma, I I ma b. I 5 I I ma 0.36 ma 0 c, d. yes 48. Source conversion: I A, R kω k 33 k 56 k Ω Ω Ω 56 kω 33 kω k 36 k 5.6 k Ω Ω Ω 56 kω 36 kω k 3.3 k 36 k Ω Ω Ω 33 kω 36 kω I 0 A, yes R Source conversion: I 9 ma, R kω ma k 00 k 00 k Ω Ω Ω 00 kω 00 kω ma 00 k 00 k k Ω Ω Ω 00 kω kω ma 00 k 00 k k Ω Ω Ω 00 kω kω 8 CHAPTER 8
85 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 ma Source conversion: I 0 / kω 0 ma, R kω ma k k k Ω Ω Ω kω kω k k k Ω Ω Ω kω kω k k k Ω Ω Ω kω kω 6.67 E IR s 0 I( kω) I k Ω 3.33 ma b. Source conversion: E 0, R 0 Ω ( )I 0I 0I 3 0 ( )I 0I 0I 3 0 ( )I 3 0I 0I 0 I I A I s.70 R 0 Ω.7A s I.7 A R R s s CHAPTER 8 83
Answers to practice exercises
Answers to practice exercises Chapter Exercise (Page 5). 9 kg 2. 479 mm. 66 4. 565 5. 225 6. 26 7. 07,70 8. 4 9. 487 0. 70872. $5, Exercise 2 (Page 6). (a) 468 (b) 868 2. (a) 827 (b) 458. (a) 86 kg (b)
Διαβάστε περισσότεραMetal Oxide Leaded Film Resistor
SURFACE TEMP. RISE ( ) Power Ratio(%) MOF0623, 0932, 1145, 1550, 1765, 2485 MOF Series Features -Excellent Long-Time stability -High surge / overload capability -Wide resistance range : 0.1Ω~10MΩ -Controlled
Διαβάστε περισσότεραMetal Oxide Leaded Film Resistor
Features -Excellent Long-Time stability -High surge / overload capability -Wide resistance range : 0.1Ω~22MΩ -Controlled temperature coefficient -Resistance standard tolerance: ±5% (consult factory for
Διαβάστε περισσότεραCapacitors - Capacitance, Charge and Potential Difference
Capacitors - Capacitance, Charge and Potential Difference Capacitors store electric charge. This ability to store electric charge is known as capacitance. A simple capacitor consists of 2 parallel metal
Διαβάστε περισσότεραPotential Dividers. 46 minutes. 46 marks. Page 1 of 11
Potential Dividers 46 minutes 46 marks Page 1 of 11 Q1. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf of 30 V. The pd across the lamp is 6.0 V and
Διαβάστε περισσότεραExercises in Electromagnetic Field
DR. GYURCSEK ISTVÁN Exercises in Electromagnetic Field Sources and additional materials (recommended) Gyurcsek I. Elmer Gy.: Theories in Electric Circuits, Globe Edit 206, ISBN:97833307343 Simonyi K.:
Διαβάστε περισσότεραMetal Film Leaded Precision Resistor
Power ratio(%) MFR Series Features Excellent overall stability Very tight tolerance down to ±0.05% Extremely low TCR down to ±5 PPM/ C High power rating up to 3 Watts Excellent ohmic contact Applications
Διαβάστε περισσότεραMicroelectronic Circuit Design Third Edition - Part I Solutions to Exercises
Microelectronic Circuit Design Third Edition - Part I Solutions to Exercises Page 11 CHAPTER 1 V LSB 5.1V 10 bits 5.1V 104bits 5.00 mv V 5.1V MSB.560V 1100010001 9 + 8 + 4 + 0 785 10 V O 786 5.00mV or
Διαβάστε περισσότεραCarbon Film Leaded Resistor
Features -The most economic industrial investment -Standard tolerance: +/-5% (available +/-2%) -Excellent long term stability -Termination: Standard solder-plated copper lead Applications -Telecommunication
Διαβάστε περισσότεραthe total number of electrons passing through the lamp.
1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy
Διαβάστε περισσότεραMetal Film Leaded Precision Resistor
Features Excellent overall stability Very tight tolerance down to ±0.05% Extremely low TCR down to ±5 PPM/ C High power rating up to 3 Watts Excellent ohmic contact Construction Applications Telecommunication
Διαβάστε περισσότερα[1] P Q. Fig. 3.1
1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One
Διαβάστε περισσότεραMetal Film Flame-Proof Resistors
Features -Low Noise -Low TCR from ±15~100PPM/ -High Precision from ±0.1%~1% -Complete Flameproof Construction UL-1412. -Coating meets UL94V-0 Applications -Telecommunication -Medical Equipment -Consumer
Διαβάστε περισσότερα( )( ) ( ) ( )( ) ( )( ) β = Chapter 5 Exercise Problems EX α So 49 β 199 EX EX EX5.4 EX5.5. (a)
hapter 5 xercise Problems X5. α β α 0.980 For α 0.980, β 49 0.980 0.995 For α 0.995, β 99 0.995 So 49 β 99 X5. O 00 O or n 3 O 40.5 β 0 X5.3 6.5 μ A 00 β ( 0)( 6.5 μa) 8 ma 5 ( 8)( 4 ) or.88 P on + 0.0065
Διαβάστε περισσότεραCHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS
CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =
Διαβάστε περισσότεραPhys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)
Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts
Διαβάστε περισσότεραIXBH42N170 IXBT42N170
High Voltage, High Gain BIMOSFET TM Monolithic Bipolar MOS Transistor IXBH42N17 IXBT42N17 S 9 = 1 = 42A (sat) 2.8V Symbol Test Conditions Maximum Ratings TO-247 (IXBH) S = 25 C to 15 C 17 V V CGR = 25
Διαβάστε περισσότερα➆t r r 3 r st 40 Ω r t st 20 V t s. 3 t st U = U = U t s s t I = I + I
tr 3 P s tr r t t 0,5A s r t r r t s r r r r t st 220 V 3r 3 t r 3r r t r r t r r s e = I t = 0,5A 86400 s e = 43200As t r r r A = U e A = 220V 43200 As A = 9504000J r 1 kwh = 3,6MJ s 3,6MJ t 3r A = (9504000
Διαβάστε περισσότεραMetal thin film chip resistor networks
Metal thin film chip resistor networks AEC-Q200 Compliant Features Relative resistance and relative TCR definable among multiple resistors within package. Relative resistance : ±%, relative TCR: ±1ppm/
Διαβάστε περισσότεραEE101: Resonance in RLC circuits
EE11: Resonance in RLC circuits M. B. Patil mbatil@ee.iitb.ac.in www.ee.iitb.ac.in/~sequel Deartment of Electrical Engineering Indian Institute of Technology Bombay I V R V L V C I = I m = R + jωl + 1/jωC
Διαβάστε περισσότεραHOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:
HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying
Διαβάστε περισσότεραMatrices and Determinants
Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z
Διαβάστε περισσότεραCurrent Sensing Chip Resistor SMDL Series Size: 0201/0402/0603/0805/1206/1010/2010/2512/1225/3720/7520. official distributor of
Product: Current Sensing Chip Resistor SMDL Series Size: 0201/0402/0603/0805/1206/1010/2010/2512/1225/3720/7520 official distributor of Current Sensing Chip Resistor (SMDL Series) 1. Features -3 Watts
Διαβάστε περισσότεραHomework 3 Solutions
Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For
Διαβάστε περισσότεραData sheet Thick Film Chip Resistor 5% - RS Series 0201/0402/0603/0805/1206
Data sheet Thick Film Chip Resistor 5% - RS Series 0201/0402/0603/0805/1206 Scope -This specification applies to all sizes of rectangular-type fixed chip resistors with Ruthenium-base as material. Features
Διαβάστε περισσότεραk A = [k, k]( )[a 1, a 2 ] = [ka 1,ka 2 ] 4For the division of two intervals of confidence in R +
Chapter 3. Fuzzy Arithmetic 3- Fuzzy arithmetic: ~Addition(+) and subtraction (-): Let A = [a and B = [b, b in R If x [a and y [b, b than x+y [a +b +b Symbolically,we write A(+)B = [a (+)[b, b = [a +b
Διαβάστε περισσότεραSMD - Resistors. TThin Film Precision Chip Resistor - SMDT Series. Product : Size: 0201/0402/0603/0805/1206/1210/2010/2512. official distributor of
Product : TThin Film Precision Chip Resistor - SMDT Series Size: 0201/0402/0603/0805/1206/1210/2010/2512 official distributor of 1. Features -Advanced thin film technology -Very tight tolerance down to
Διαβάστε περισσότεραAluminum Electrolytic Capacitors (Large Can Type)
Aluminum Electrolytic Capacitors (Large Can Type) Snap-In, 85 C TS-U ECE-S (U) Series: TS-U Features General purpose Wide CV value range (33 ~ 47,000 µf/16 4V) Various case sizes Top vent construction
Διαβάστε περισσότεραCSR series. Thick Film Chip Resistor Current Sensing Type FEATURE PART NUMBERING SYSTEM ELECTRICAL CHARACTERISTICS
FEATURE Operating Temperature: -55 ~ +155 C 3 Watts power rating in 1 Watt size, 1225 package High purity alumina substrate for high power dissipation Long side terminations with higher power rating PART
Διαβάστε περισσότεραΚεφάλαιο 3 Ο Νόμος του Ohm
Κεφάλαιο 3 Ο Νόμος του Ohm 1 3 Ο Νόμος του Ohm (Ohm s Law) ΠΕΡΙΕΧΟΜΕΝΑ ΚΕΦΑΛΑΙΟΥ Ο Νόμος του Ohm Εφαρμογή του Νόμου του Ohm Ενέργεια και Ισχύς Ισχύς σε ένα Ηλεκτρικό Κύκλωμα Οι Ονομαστικές Τιμές Ισχύος
Διαβάστε περισσότεραSurface Mount Multilayer Chip Capacitors for Commodity Solutions
Surface Mount Multilayer Chip Capacitors for Commodity Solutions Below tables are test procedures and requirements unless specified in detail datasheet. 1) Visual and mechanical 2) Capacitance 3) Q/DF
Διαβάστε περισσότεραMAX-QUALITY ELECTRIC CO; LTD Thin Film Precision Chip Resistors. Data Sheet
Data Sheet Customer: Product: Size: Current Sensing Chip Resistor CS Series 0201/0402/0603/0805/1206/1010/2010/2512 1225/3720/7520 Issued Date: Edition : 12-Nov-10 REV.C5 Current Sensing Chip Resistor
Διαβάστε περισσότερα1000 VDC 1250 VDC 125 VAC 250 VAC J K 125 VAC, 250 VAC
Metallized Polyester Film Capacitor Type: ECQE(F) Non-inductive construction using metallized Polyester film with flame retardant epoxy resin coating Features Self-healing property Excellent electrical
Διαβάστε περισσότεραMicroelectronic Circuit Design Fourth Edition - Part II Solutions to Exercises
Page 9 Microelectronic Circuit Design Fourth Edition - Part II olutions to Exercises CHAPTER 6 NM 0.8V 0.4V 0.4 V NM H 3.6V.0V.6 V Page 94 V 0% V + 0. ΔV [ ].4 V [ ].4 V.6V + 0. 0.6 (.6) 0.6V 0.9 0.6 (.6)
Διαβάστε περισσότεραMetal Oxide Varistors (MOV) Data Sheet
Φ SERIES Metal Oxide Varistors (MOV) Data Sheet Features Wide operating voltage (V ma ) range from 8V to 0V Fast responding to transient over-voltage Large absorbing transient energy capability Low clamping
Διαβάστε περισσότεραSecond Order RLC Filters
ECEN 60 Circuits/Electronics Spring 007-0-07 P. Mathys Second Order RLC Filters RLC Lowpass Filter A passive RLC lowpass filter (LPF) circuit is shown in the following schematic. R L C v O (t) Using phasor
Διαβάστε περισσότεραSmaller. 6.3 to 100 After 1 minute's application of rated voltage at 20 C, leakage current is. not more than 0.03CV or 4 (µa), whichever is greater.
Low Impedance, For Switching Power Supplies Low impedance and high reliability withstanding 5000 hours load life at +05 C (3000 / 2000 hours for smaller case sizes as specified below). Capacitance ranges
Διαβάστε περισσότεραLR Series Metal Alloy Low-Resistance Resistor
LR Series Metal Alloy LowResistance Resistor This specification is applicable to lead free, halogen free of RoHS directive for metal alloy lowresistance resistor. The product is for general purpose. The
Διαβάστε περισσότεραUDZ Swirl diffuser. Product facts. Quick-selection. Swirl diffuser UDZ. Product code example:
UDZ Swirl diffuser Swirl diffuser UDZ, which is intended for installation in a ventilation duct, can be used in premises with a large volume, for example factory premises, storage areas, superstores, halls,
Διαβάστε περισσότεραLR Series Metal Alloy Low-Resistance Resistor
Tel : 881745 Fax : 881749 LR Series Metal Alloy LowResistance Resistor This specification is applicable to lead free, halogen free of RoHS directive for metal alloy lowresistance resistor. The product
Διαβάστε περισσότερα4. Construction. 5. Dimensions Unit mm
1. Scope This specification applies to all sizes of rectangular-type fixed chip resistors with Ni/Cr as material. 2. Features Tolerance from 0.01%1% Thin film & Ni/Cr Resistor TCR from 5ppm 50ppm for thin
Διαβάστε περισσότεραGenX3 TM 300V IGBT IXGA42N30C3 IXGH42N30C3 IXGP42N30C3 V CES = 300V I C110. = 42A V CE(sat) 1.85V t fi typ. = 65ns
GenX3 TM V IGBT High Speed PT IGBTs for -1kHz switching IXGA42NC3 IXGH42NC3 IXGP42NC3 V CES = V 1 = 42A V CE(sat) 5V t fi typ = 65ns TO-263 (IXGA) Symbol Test Conditions Maximum Ratings V CES = 25 C to
Διαβάστε περισσότεραis like multiplying by the conversion factor of. Dividing by 2π gives you the
Chapter Graphs of Trigonometric Functions Answer Ke. Radian Measure Answers. π. π. π. π. 7π. π 7. 70 8. 9. 0 0. 0. 00. 80. Multipling b π π is like multipling b the conversion factor of. Dividing b 0 gives
Διαβάστε περισσότεραAluminum Electrolytic Capacitors
Aluminum Electrolytic Capacitors Snap-In, Mini., 105 C, High Ripple APS TS-NH ECE-S (G) Series: TS-NH Features Long life: 105 C 2,000 hours; high ripple current handling ability Wide CV value range (47
Διαβάστε περισσότερα± 20% ± 5% ± 10% RENCO ELECTRONICS, INC.
RL15 RL16, RL17, RL18 MINIINDUCTORS CONFORMALLY COATED MARKING The nominal inductance is marked by a color code as listed in the table below. Color Black Brown Red Orange Yellow Green Blue Purple Grey
Διαβάστε περισσότεραElectronic Devices and Circuit Theory
nstructor s Resource Manual to accompany Electronic Devices and Circuit Theory Tenth Edition Robert L. Boylestad Louis Nashelsky Upper Saddle River, New Jersey Columbus, Ohio Copyright 009 by Pearson Education,
Διαβάστε περισσότεραCSK series. Current Sensing Chip Resistor. Features. Applications. Construction FAITHFUL LINK
CSK series Current Sensing Chip Resistor Features» 3 Watts power rating in 1 Watt size, 1225 Package» Low TCR of ±100 PPM/ C» Resistance values from 1m to 1 ohm» High purity alumina substrate for high
Διαβάστε περισσότεραHomework 8 Model Solution Section
MATH 004 Homework Solution Homework 8 Model Solution Section 14.5 14.6. 14.5. Use the Chain Rule to find dz where z cosx + 4y), x 5t 4, y 1 t. dz dx + dy y sinx + 4y)0t + 4) sinx + 4y) 1t ) 0t + 4t ) sinx
Διαβάστε περισσότεραAnti-Corrosive Thin Film Precision Chip Resistor-SMDR Series. official distributor of
Product : Anti-Corrosive Thin Film Precision Chip Resistor-SMDR Series Size : 0402/0603/0805/1206/2010/2512 official distributor of Anti-Corrosive Thin Film Precision Chip Resistor (SMDR Series) 1. Features
Διαβάστε περισσότεραMICROMASTER Vector MIDIMASTER Vector
s MICROMASTER Vector MIDIMASTER Vector... 2 1.... 4 2. -MICROMASTER VECTOR... 5 3. -MIDIMASTER VECTOR... 16 4.... 24 5.... 28 6.... 32 7.... 54 8.... 56 9.... 61 Siemens plc 1998 G85139-H1751-U553B 1.
Διαβάστε περισσότεραΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007
Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο
Διαβάστε περισσότεραRight Rear Door. Let's now finish the door hinge saga with the right rear door
Right Rear Door Let's now finish the door hinge saga with the right rear door You may have been already guessed my steps, so there is not much to describe in detail. Old upper one file:///c /Documents
Διαβάστε περισσότεραST5224: Advanced Statistical Theory II
ST5224: Advanced Statistical Theory II 2014/2015: Semester II Tutorial 7 1. Let X be a sample from a population P and consider testing hypotheses H 0 : P = P 0 versus H 1 : P = P 1, where P j is a known
Διαβάστε περισσότεραΑπόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ.
Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο The time integral of a force is referred to as impulse, is determined by and is obtained from: Newton s 2 nd Law of motion states that the action
Διαβάστε περισσότεραThin Film Precision Chip Resistor-AR Series
hin Film Precision Chip Resistor-AR Series Construction L D1 3 4 5 6 D2 9 8 7 1 2 1 Alumina Substrate 4 Edge Electrode (NiCr) 7 Resistor Layer (NiCr) 2 Bottom Electrode (Ag) 5 Barrier Layer (Ni) 8 Overcoat
Διαβάστε περισσότεραDigital motor protection relays
Digital motor protection relays Specification DMP -S & DMP -Sa DMP -T & DMP -Ta Model No. DMP06-S/Sa DMP60-S/Sa DMP06-T/Ta DMP60-T/Ta Wiring Screw type Tunnel type Panel mount Unit or Extension Note1)
Διαβάστε περισσότεραSurface Mount Aluminum Electrolytic Capacitors
FEATURES CYLINDRICAL V-CHIP CONSTRUCTION LOW COST, GENERAL PURPOSE, 2000 HOURS AT 85 O C NEW EXPANDED CV RANGE (up to 6800µF) ANTI-SOLVENT (2 MINUTES) DESIGNED FOR AUTOMATIC MOUNTING AND REFLOW SOLDERING
Διαβάστε περισσότεραType 947D Polypropylene, High Energy Density, DC Link Capacitors
Type 947D series uses the most advanced metallized film technology for long life and high reliability in DC Link applications. This series combines high capacitance and very high ripple current capability
Διαβάστε περισσότεραSCOPE OF ACCREDITATION TO ISO 17025:2005
SCOPE OF ACCREDITATION TO ISO 17025:2005 TFF CORPORATION TEKTRONIX COMPANY 1-14-1 Midorigaoka, Naka-gun, Ninomiya-machi, Kanagawa Pref. 259-0132 JAPAN Hideki Yuyama Phone: 81 463 70 5634 CALIBRATION Valid
Διαβάστε περισσότεραSMD Wire Wound Ferrite Chip Inductors - LS Series. LS Series. Product Identification. Shape and Dimensions / Recommended Pattern LS0402/0603/0805/1008
SMD Wire Wound Ferrite Chip Inductors - LS Series LS Series LS Series is the newest in open type ferrite wire wound chip inductors. The wire wound ferrite construction supports higher SRF, lower DCR and
Διαβάστε περισσότεραANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =?
Teko Classes IITJEE/AIEEE Maths by SUHAAG SIR, Bhopal, Ph (0755) 3 00 000 www.tekoclasses.com ANSWERSHEET (TOPIC DIFFERENTIAL CALCULUS) COLLECTION # Question Type A.Single Correct Type Q. (A) Sol least
Διαβάστε περισσότερα3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β
3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle
Διαβάστε περισσότεραLR(-A) Series Metal Alloy Low-Resistance Resistor
LR(A) Series Metal Alloy LowResistance Resistor This specification is applicable to lead free, halogen free of RoHS directive for metal alloy lowresistance resistor. The product is for general purpose.
Διαβάστε περισσότεραThin Film Precision Chip Resistor (AR Series)
Construction D1 L (AR Series) Features -Advanced thin film technology -Very tight tolerance down to ±0.01% -Extremely low TCR down to ±5PPM/C -Wide resistance range 1ohm ~ 3Mega ohm -Miniature size 0201
Διαβάστε περισσότεραSMD AVR AVR-M AVRL. Variable resistor. 2 Zener diode (1/10) RoHS / / j9c11_avr.fm. RoHS EU Directive 2002/95/EC PBB PBDE
(1/1) SMD RoHS AVR AVR-M AVRL Variable resistor 2Zener diode Current(A) Positive direction 1 1 1 2 1 3 1 4 1 5 Zener diode /Vz:6.8V Chip varistor /V1mA:12V 2 Zener Diodes A capacitance content 18 14 1
Διαβάστε περισσότεραDerivation of Optical-Bloch Equations
Appendix C Derivation of Optical-Bloch Equations In this appendix the optical-bloch equations that give the populations and coherences for an idealized three-level Λ system, Fig. 3. on page 47, will be
Διαβάστε περισσότεραNTC Thermistor:SCK Series
Features. RoHS compliant 2. Body size Ф5mm~ Ф 30mm 3. Radial lead resin coated 4. High power rating 5. Wide resistance range 6. Cost effective 7. Operating temperature range: Φ5mm:-40~+50 Φ8~Φmm:-40~+70
Διαβάστε περισσότεραTerminal Contact UL Insulation Designation (provided with) style form system approval Flux tight
eatures A miniature PCB Power Relay. form A contact configuration with quick terminal type. 5KV dielectric strength, K surge voltage between coils to contact. Ideal for high rating Home Appliances of heating
Διαβάστε περισσότεραJesse Maassen and Mark Lundstrom Purdue University November 25, 2013
Notes on Average Scattering imes and Hall Factors Jesse Maassen and Mar Lundstrom Purdue University November 5, 13 I. Introduction 1 II. Solution of the BE 1 III. Exercises: Woring out average scattering
Διαβάστε περισσότεραEE512: Error Control Coding
EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3
Διαβάστε περισσότεραAnti-Corrosive Thin Film Precision Chip Resistor (PR Series)
(PR Series) Features -Long term life stability and demonstrated the Anti Corrosion claims -Special passivated NiCr film for Anti-Acid and Anti-Damp -Tight tolerance down to ±0.1% -Extremely low TCR down
Διαβάστε περισσότερα( )( ) ( )( ) 2. Chapter 3 Exercise Solutions EX3.1. Transistor biased in the saturation region
Chapter 3 Exercise Solutios EX3. TN, 3, S 4.5 S 4.5 > S ( sat TN 3 Trasistor biased i the saturatio regio TN 0.8 3 0. / K K K ma (a, S 4.5 Saturatio regio: 0. 0. ma (b 3, S Nosaturatio regio: ( 0. ( 3
Διαβάστε περισσότεραNo Item Code Description Series Reference (1) Meritek Series CRA Thick Film Chip Resistor AEC-Q200 Qualified Type
Qualified FEATURE Excellent Mechanical Strength and Electrical Stability Ideal for Pick and Place Machinery Stable High Frequency Characteristics Miniature, High Board Density Equivalent Specification
Διαβάστε περισσότεραNo item Digit Description Series Reference (1) Meritek Series SI Signal Inductor LI: Leaded Inductor PI: Power Inductor
PART NUMBERING SYSTEM SI F 0805 K 780 F (1) (2) (3) (4) (5) (6) No item Digit Description Series Reference (1) Meritek Series SI Signal Inductor LI: Leaded Inductor PI: Power Inductor (2) Type F Ferrite
Διαβάστε περισσότεραRC series Thick Film Chip Resistor
RC series Thick Film Chip Resistor Features» Small size and light weight» Compatible with wave and reflow soldering» Suitable for lead free soldering» RoHS compliant & Halogen Free Applications Configuration»
Διαβάστε περισσότεραDESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0.
DESIGN OF MACHINERY SOLUTION MANUAL -7-1! PROBLEM -7 Statement: Design a double-dwell cam to move a follower from to 25 6, dwell for 12, fall 25 and dwell for the remader The total cycle must take 4 sec
Διαβάστε περισσότεραApplications. 100GΩ or 1000MΩ μf whichever is less. Rated Voltage Rated Voltage Rated Voltage
Features Rated Voltage: 100 VAC, 4000VDC Chip Size:,,,,, 2220, 2225 Electrical Dielectric Code EIA IEC COG 1BCG Applications Modems LAN / WAN Interface Industrial Controls Power Supply Back-Lighting Inverter
Διαβάστε περισσότεραwave energy Superposition of linear plane progressive waves Marine Hydrodynamics Lecture Oblique Plane Waves:
3.0 Marine Hydrodynamics, Fall 004 Lecture 0 Copyriht c 004 MIT - Department of Ocean Enineerin, All rihts reserved. 3.0 - Marine Hydrodynamics Lecture 0 Free-surface waves: wave enery linear superposition,
Διαβάστε περισσότεραStrain gauge and rosettes
Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified
Διαβάστε περισσότεραTrimmable Thick Film Chip Resistor
rimmable hick ilm Chip Resistor R Series rimmable hick ilm Chip Resistor Scope -his specification applies to all sizes of rectangular-type fixed chip resistors with Ruthenium-base as material. eatures
Διαβάστε περισσότερα65W PWM Output LED Driver. IDLV-65 series. File Name:IDLV-65-SPEC
~ A File Name:IDLV65SPEC 07050 SPECIFICATION MODEL OUTPUT OTHERS NOTE DC VOLTAGE RATED CURRENT RATED POWER DIMMING RANGE VOLTAGE TOLERANCE PWM FREQUENCY (Typ.) SETUP TIME Note. AUXILIARY DC OUTPUT Note.
Διαβάστε περισσότερα= 0.927rad, t = 1.16ms
P 9. [a] ω = 2πf = 800rad/s, f = ω 2π = 27.32Hz [b] T = /f = 7.85ms [c] I m = 25mA [d] i(0) = 25cos(36.87 ) = 00mA [e] φ = 36.87 ; φ = 36.87 (2π) = 0.6435 rad 360 [f] i = 0 when 800t + 36.87 = 90. Now
Διαβάστε περισσότεραSection 8.3 Trigonometric Equations
99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.
Διαβάστε περισσότεραInverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- -----------------
Inverse trigonometric functions & General Solution of Trigonometric Equations. 1. Sin ( ) = a) b) c) d) Ans b. Solution : Method 1. Ans a: 17 > 1 a) is rejected. w.k.t Sin ( sin ) = d is rejected. If sin
Διαβάστε περισσότερα2. THEORY OF EQUATIONS. PREVIOUS EAMCET Bits.
EAMCET-. THEORY OF EQUATIONS PREVIOUS EAMCET Bits. Each of the roots of the equation x 6x + 6x 5= are increased by k so that the new transformed equation does not contain term. Then k =... - 4. - Sol.
Διαβάστε περισσότεραUnshielded Power Inductor / PI Series
.Features: 1. Excellent solderability and high heat resistance. 2. Excellent terminal strength construction. 3. Packed in embossed carrier tape and can be used by automatic mounting machine..applications:
Διαβάστε περισσότεραFirst Sensor Quad APD Data Sheet Part Description QA TO Order #
Responsivity (/W) First Sensor Quad PD Data Sheet Features Description pplication Pulsed 16 nm laser detection RoHS 211/65/EU Light source positioning Laser alignment ø mm total active area Segmented in
Διαβάστε περισσότεραChapter 7 Transformations of Stress and Strain
Chapter 7 Transformations of Stress and Strain INTRODUCTION Transformation of Plane Stress Mohr s Circle for Plane Stress Application of Mohr s Circle to 3D Analsis 90 60 60 0 0 50 90 Introduction 7-1
Διαβάστε περισσότεραRECIPROCATING COMPRESSOR CALCULATION SHEET
Gas properties, flowrate and conditions 1 Gas name Air RECIPRCATING CMPRESSR CALCULATIN SHEET WITH INTERCLER ( Sheet : 1. f 4.) Item or symbol Quantity Unit Item or symbol Quantity Unit 2 Suction pressure,
Διαβάστε περισσότεραTHICK FILM LEAD FREE CHIP RESISTORS
Features Suitable for lead free soldering. Compatible with flow and reflow soldering Applications Consumer Electronics Automotive industry Computer Measurement instrument Electronic watch and camera Configuration
Διαβάστε περισσότεραSection 7.6 Double and Half Angle Formulas
09 Section 7. Double and Half Angle Fmulas To derive the double-angles fmulas, we will use the sum of two angles fmulas that we developed in the last section. We will let α θ and β θ: cos(θ) cos(θ + θ)
Διαβάστε περισσότεραCurrent Sensing Chip Resistor
Features -3 atts power rating in 1 att size, 1225 package -Low CR of ±100 PPM/ C -Resistance values from 1m to 1 ohm -High purity alumina substrate for high power dissipation -Long side terminations with
Διαβάστε περισσότεραMECHANICAL PROPERTIES OF MATERIALS
MECHANICAL PROPERTIES OF MATERIALS! Simple Tension Test! The Stress-Strain Diagram! Stress-Strain Behavior of Ductile and Brittle Materials! Hooke s Law! Strain Energy! Poisson s Ratio! The Shear Stress-Strain
Διαβάστε περισσότεραMINIATURE ALUMINUM ELECTROLYTIC CAPACITORS. Characteristics. Leakage Current(MAX) I=Leakage Current(µA) C=Nominal Capacitance(µF) V=Rated Voltage(V)
SERIES 5 C Long Life. Low impedance. (Rated Voltage 6.3~V.DC) FEATURES Load Life : 5 C 4~hours. Low impedance at khz with selected materials. SPECIFICATIONS Items Operating Temperature Range Rated Voltage
Διαβάστε περισσότεραIXBK64N250 IXBX64N250
High Voltage, High Gain BiMOSFET TM Monolithic Bipolar MOS Transistor IXBK64N25 IXBX64N25 V CES = 25V 11 = 64A V CE(sat) 3.V TO-264 (IXBK) Symbol Test Conditions Maximum Ratings V CES = 25 C to 15 C 25
Διαβάστε περισσότεραAPPLICATIONS TECHNOLOGY. Leaded Discs N.03 N.06 N.09
NC Disc hermistors ND 03/06/09 NE 03/06/09 NV 06/09 APPLICAIONS ND or NE: Commerical, Industrial and Automotive Applications AEC-Q200 Qualified NV: Professional Applicationsl Alarm and temperature measurement
Διαβάστε περισσότεραSuitable for DC-DC Converters, Voltage Regulators, Decoupling Applications for Computer Motherboards, etc. Performance Characteristics
+105 C, Higher Ripple, Lower than ULG Features Higher Ripple, Lower than ULG Wide Temperature Range RoHS Compliant Applications Suitable for DC-DC Converters, Voltage Regulators, Decoupling Applications
Διαβάστε περισσότεραAreas and Lengths in Polar Coordinates
Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the
Διαβάστε περισσότεραThick Film Chip Resistors
FEATURES STANDARD SIZING 0402 (1/16W), 0603 (1/10W), 0805 (1/8W), 1206 (1/4W), 2010 (1/2W) AND 2512 (1W) HIGH VOLTAGE (100VDC ~ 3,000VDC) HIGH RESISTANCE VALUES (UP TO 100MW) THICK FILM ON ALUMINA SUSTRATE,
Διαβάστε περισσότεραRating to Unit ma ma mw W C C. Unit Forward voltage Zener voltage. Condition
MA MA Series Silicon planer e For stabilization of power supply ø.56. Unit : mm Features Color indication of VZ rank classification High reliability because of combination of a planer chip and glass seal
Διαβάστε περισσότερα