Answer to Question #199876 in Electrical Engineering for A jaif

Question

For the circuit shown in Fig.6, Impedance A receives 2kW at 0.8 power factor impedance receives 3kVA at 0.4 power factorleading, while impedance C is inductive and consumes 1kW and receives 500VAR. (i) Find the power factor of the entire system, (ii) Find the current I, if VVs=120/_45`v..

Answer 1

$S_A=2000+j \frac{2000}{0.8}*0.6=2000+j1500$

$S_B=3000*0.4-j3000*0.9165=12002749$

$S_C=1000+j500$

$S=S_A+S_B+S_C=4200-j749$

a) $pf=\frac{4200}{\sqrt{4200^2+749}}=0.9845$ leading

b) $S=V_{rms}I_{rms}^* \implies I_{rms}^*=\frac{4200-j749}{120\angle{45^0}}=35.55 \angle -55.11^0 A$