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 = 2kW at P_f = 0.8 lagging Z_B: P = 3kW at P_f = 0.6 leading Z_C: P = 1.5 kW and Q = 500Var Find the power factor at terminal \"ab\". Assume omega = 6000Rad/s,V_m = 10 V, theta_omega = 15degree, I_m = 15 A, and theta_t = 50degree.

Solution

for ZA LOAD ACTIVE POWER =2KW pf 0.8

ZA LOAD RACTIV POWER =2Tan(pi) pi=inverse cos(pf) pi=36.86

2*0.75=1.5kvr

for ZB LOAD ACTIVE POWER =3KW pf 0.6 LADING

ZB LOAD RACTIV POWER =3*Tan(pi) pi=inverse cos(pf) pi=53.13

3*1.33=4 KVAR

for ZC LOAD ACTIVE POWER =1.5KW

ZA LOAD RACTIV POWER =0.5 KVAR

TOTAL ACTIV POWER =2+3+1.5=6.5

TOTAL REACTIVE POWER 1.5-4+0.5=-2

tan(pi)=(active/reactive)=(6.5/-2)

pi(-72.89)

cos(pi)=0.29 leading