Chapter 2
Fundamentals
2.1 (a) ????Ì…
1 = 9∠30° = 9[???????????? 30° + ???? ???????????? 30°] = 7.8 + ????4.5
(b) ????Ì„
2 = 4 + ????5 = √16 + 25 ∠????????????−1
5
4
= 6.40∠128.66° = 6.40????
????128.66°
(c) ????Ì…
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
Ì…Ì…Ì… =
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°)
????Ì…=
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 ????Ì…
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