Question #199876

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..

Expert's answer

"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"

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