Chapter 2 Fundamentals 2.1 (a) ????̅ 1 = 9∠30° = 9[???????????? 30° + ???? ???????????? 30°] = 7.8 + ????4.5 (b) ????̄ 2 = 4 + ????5 = √16 + 25 ∠????????????−1 5 4 = 6.40∠128.66° = 6.40???? ????128.66° (c) ????̅ 3 = (7.8 + ????4.5) + (−4 + ????5) = (11.8 + ????9.5) = 15.15∠38.8° (d) ????4 ̅̅̅ = (9∠30°)(6.4∠51.34°) = 57.6∠81.34° = 8.673 + ????56.9 (e) ????5 ̅̅̅ = 9∠30° 6.4∠−52.34° = 1.41∠81.34° = 1.41???? ????81.34° 2.2 (a) ????̄ = 500∠ − 30° = 433.01 − ????250 (b) ????(????) = 4????????????(???????? + 15°) = 4????????????(???????? + 15° − 90°) = 4co s(???????? − 75°) ????̅= 4 √2 ∠ − 75° = 2.83∠ − 75° = 0.73 − ????2.73 (c) ????̄ = (5/√2)∠ − 15° + 4∠ − 60° = (3.42 − ????0.92) + (2 − ????3.46) = 5.42 − ????4.38 = 6.964∠ − 38.94° 2.3 ????̅ 2 = 13 √2 ∠(−(125 × 10−6 )(2????60)) kV = 9.19∠ − 2.7° kV 2.4 (a) ( ) ( ) ( ) 1 2 1 2 6 6 90 10 0 10 7.5 90 A 8 6 6 8 10 0 7.3 90 10 7.5 12.5 36.87 A 6 12.5 36.87 6 90 75 53.13 V