j 10 \u03a9 14142 \u03a9 45 I ab I bc I ca 220 V 14142 V Z \u03c6 \u03c6 \u03a9 1556 A 17 a I ab 16 kV

J 10 ω 14142 ω 45 i ab i bc i ca 220 v 14142 v z φ

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j 10 Ω = 14.142 Ω∠ 45 ° I ab = I bc = I ca = 220 V 14.142 V = Z φ φ Ω = 15.56 A 17. a. I ab = 16 kV 0 16 kV 0 = = 300 + 1000 1044.03 73.30 ab ab j ∠ ° ∠ ° Ω Ω Ω ∠ ° V Z I ab = 15.33 A ∠− 73.30 ° I bc = 16 kV 120 = 1044.03 73.30 bc bc ∠ − ° Ω ∠ ° V Z = 15.33 A ∠− 193.30 ° I ca = 16 kV 120 = 1044.03 73.30 ca ca ° Ω ∠ ° V Z = 15.33 A 46.7 ° b. I Aa I ab + I ca = 0 I Aa = I ab I ca = 15.33 A ∠− 73.30 ° 15.33 A 46.7 ° = (4.41 A j 14.68 A) (10.51 A + j 11.16 A) = 4.41 A 10.51 A j (14.68 A + 11.16 A) = 6.11 A j 25.84 A = 26.55 A ∠− 103.30 ° I Bb + I ab = I bc I Bb = I bc I ab = 15.33 A ∠− 193.30 ° 15.33 A ∠− 73.30 ° = 26.55 A 136.70 ° I Cc + I bc = I ca I Cc = I ca I bc = 15.33 A 46.7 ° 15.33 A ∠− 193.30 ° = 26.55 A 16.70 ° c. E AB = I Aa (10 Ω + j 20 Ω ) + V ab I Bb (22.361 Ω 63.43 ° ) = (26.55 A ∠− 103.30 ° )(22.361 Ω 63.43 ° ) + 16 kV 0 ° (26.55 A 136.70 ° )(22.361 Ω 63.43 ° ) = (455.65 V j 380.58 V) + 16,000 V ( 557.42 V j 204.32 V) = 17.01 kV j 176.26 V = 17.01 kV ∠− 0.59 ° E BC = I Bb (22.361 Ω 63.43 ° ) + V bc I Cc (22.361 Ω 63.53 ° ) = (26.55 A 136.70 ° )(22.361 Ω 63.53 ° ) + 16 kV ∠− 120 ° (26.55 A 16.70 ° )(22.361 Ω 63.53 ° ) = 17.01 kV ∠− 120.59 ° E CA = I Cc (22.361 Ω 63.43 ° ) + V ca I Aa (22.361 Ω 63.43 ° ) = 17.01 kV 119.41 °
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CHAPTER 23 323 18. a. E φ = E L = 208 V b. V φ = 208 V 1.732 3 L E = = 120.1 V c. I φ = 120.1V 30 V = Z φ φ Ω = 4.00 A d. I L = I φ 4 A 19. a. E φ = E L = 208 V b. V φ = E L 3 = 120.09 V c. I φ = 120.09 V 16.971 V = Z φ φ Ω = 7.08 A d. I L = I φ = 7.08 A 20. a, b. The same as problem 18. c. φ Z = 15 Ω 0 ° || 20 Ω ∠− 90 ° = 12 Ω ∠− 36.87 ° I φ = 120.1V 12 V = Z φ φ Ω 10 A d. I L = I φ 10 A 21. V an = V bn = V cn = 120 V 120 V = 1.732 3 = 69.28 V I an = I bn = I cn = 69.28 V 24 Ω = 2.89 A I Aa = I Bb = I Cc = 2.89 A 22. V an = V bn = V cn = 120 V 3 = 69.28 V φ Z = 10 Ω + j 20 Ω = 22.36 Ω∠ 63.43 ° I an = I bn = I cn = 69.28 V = 22.36 φ φ Ω V Z = 3.10 A I Aa = I Bb = I Cc = I φ = 3.10 A 23. V an = V bn = V cn = 69.28 V φ Z = 20 Ω 0 ° || 15 Ω ∠− 90 ° = 12 Ω ∠− 53.13 ° I an = I bn = I cn = 69.28 V 12 Ω = 5.77 A I Aa = I Bb = I Cc = 5.77 A 24. a. E φ = E L = 440 V b. V φ = E L = E φ = 440 V c. I φ = 440 V 220 V = Z φ φ Ω = 2 A d. I L = 3 I φ = (1.732)(2 A) = 3.46 A
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324 CHAPTER 23 25. a. E φ = E L = 440 V b. V φ = E L = 440 V c. φ Z = 12 Ω j 9 Ω = 15 Ω ∠− 36.87 ° I φ = 440 V 15 V = Z φ φ Ω = 29.33 A d. I L = 3 I φ = (1.732)(29.33 A) = 50.8 A 26. a, b. The same as problem 24. c. φ Z = 22 Ω 0 ° || 22 Ω 90 ° = 15.56 Ω 45 ° I φ = 440 V 15.56 V = Z φ φ Ω = 28.28 A d. I L = 3 I φ = (1.732)(28.28 A) = 48.98 A 27. a. θ 2 = 120 ° , θ 3 = +120 ° b. V ab = 100 V 0 ° , V bc = 100 V ∠− 120 ° , V ca = 100 V 120 ° c. d. I ab = 100 V 0 = 20 0 ab ab ∠ ° Ω ∠ ° V Z = 5 A 0 ° I bc = 100 V 120 = 20 0 bc bc ∠ − ° Ω ∠ ° V Z = 5 A ∠− 120 ° I ca = 100 V 120 = 20 0 ca ca ° Ω ∠ ° V Z = 5 A 120 ° e. I Aa = I Bb = I Cc = 3 (5 A) = 8.66 A 28. a. θ 2 = 120 ° , θ 3 = +120 ° b. V ab = 100 V 0 ° , V bc = 100 V ∠− 120 ° , V ca = 100 V 120 ° c. d. φ Z = 12 Ω + j 16 Ω = 20 Ω 53.13 ° I ab = 100 V 0 = 20 53.13 ab ab ∠ ° Ω ∠ ° V Z = 5 A ∠− 53.13 ° I bc = 100 V 120 = 20 53.13 bc bc ∠ − ° Ω ∠ ° V Z = 5 A ∠− 173.13 °
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CHAPTER 23 325 I ca = 100 V 120 = 20 53.13 ca ca ° Ω ∠ ° V Z = 5 A 66.87 ° e. I Aa = I Bb = I Cc = 3 I φ = (1.732)(5 A) = 8.66 A 29. a. θ 2 = 120 ° , θ 3 = 120 ° b. V ab = 100 V 0 ° , V bc = 100 V ∠− 120 ° , V ca = 100 V 120 ° c. d. φ Z = 20 Ω 0 ° || 20 Ω ∠− 90 ° = 14.14 Ω ∠− 45 ° I ab = 100 V 0 14.14 45 ∠ ° Ω ∠ − ° = 7.07 A 45 ° I bc = 100 V 120 14.14 45 ∠ − ° Ω ∠ − ° = 7.07 A ∠− 75 ° I ca = 100 V 120 14.14 45 ° Ω ∠ − ° = 7.07 A 165 ° e. I Aa = I Bb = I Cc = ( ) 3 (7.07 A) = 12.25 A 30. P T = 2 3 I R φ φ = 3(6 A) 2 12 Ω = 1296 W Q T = 2 3 I X φ φ = 3(6 A) 2 16 Ω =
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