For the circuit of Fig P970 with ZA ZB and ZC loads specifie

For the circuit of Fig. P9.70 with Z_A, Z_B and Z_C loads specified as follows Z_A: P = 2 kW at P f = 0.8 Z_B: P = 3kW at Pf = 0.6 Z_C: P = 1.5 kW at Q = 500 Var Find the power factor at terminal \"ab\". Assume omega = 6000 Rad/s, V_m = 10 V, Theta_v = 15 degree, l_m = 15 A & theta_i = 50 degree.

Solution

ZA P=2KW ACTIVE POWER =2KW

REACTIVE POWER=P*TAN(CIS INVERSE(pf))=1.5 KVAR

ZB P=3KW ACTIVE POWER =3KW

REACTIVE POWER=P*TAN(CIS INVERSE(pf))=4 KVAR

ZC P=1.5KW ACTIVE POWER =1.5KW

REACTIVE POWER=0.5KVAR

TOTAL ACTIVE POWER=6.5 KW

TOTAL REACTIVE POWER=6

PI=TAN INVERS(QT/PT)

TAN INVERS(6/6.5)=42.7

COS(pI)=0.73 LAG IS POWER FACTOR