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

Solution

ZA P =2KW

PF =0.8 LAG

Q=P*TAN(COS INVRSE(0.8))

1.5 KVAr

ZB P =3KW

PF =0.6 LEAD

Q=P*TAN(COS INVRSE(0.6))

-4KVAr

ZC P =1.5KW

Q=0.5 KVAr

QTOTAL=0.5-4+1.5=-2KVAr

PTOTOAL=2+3+1.5=6.5KW

PI=INVERSE TAN(QT/PT)

PI=-17.10

PF=COS(PI)=0.955 LAED