Question

20Ω 30 Ω j20Ω Fig. 1.7 In the circuit of Fig. 1.8, find the RMS phasor voltage V so that the 60 Ω resistor absorbs an average power of 240 W. Hence, determine the complex power delivered to each component, the complex power and the power factor delivered by voltage source. Fig. 1.8 2) P1.8

Answer 1

Given I^2 R = 240 watts I^2 = 240/60 I = 2A I^2 X = 2^2 times 20 = 80 VARS complex power of (60 + j20) = (240 + j80)VA S = v^2/Z V^2 = SZ V^2 = (240 + j80)(60 + j20) V = root 16000 angle 36.86 = 126.4 angle 36.96/2 V = 126.4 angle 180.43 degree I_2 = V/30 - j10 = 126.4 angle 18.43/30 - j10 I_2 = 2.528 angle 71.56 degree I = I_1 + I_2 = 4 angle 18.43 degree + 2.528 angle 71.56^angle I = 5.875 angle 38.56 V_S = 20I + V = 20(5.875 angle 38.50) + 126.4 angle 18.43 degree = 117.5 angle 38.56 + 126.4 angle 18.43 V_rms = 240.15 angle 28.1239 \r\n power factor = cos (38.56 - 28.1239) = 0.9834 1.7 j^th: - (j6 + 8) Vertical-bar Vertical-bar 5 = (j6 + 8)5/13 + j6 = j30 + 40/13 + j6 = RTh = 3.492 angle 12.09 VTh VTh = (2 times 8 - j4/(- j4