# Homework Help: Total power factor, 1 motor, three phase, two loads

1. Sep 8, 2011

### SPYazdani

1. The problem statement, all variables and given/known data
A balanced three phase Y-connected source has a line voltage of 208V and feeds two balanced Y-connected loads. The per-phase impedances of the two loads are 20+j70 and 50+j30 ohms respectively. Calculate the power supplied to each load by the source. What is the power factor of each load? What is the overall power factor.

2. Relevant equations

$P=VI cos \theta$

$V=IZ$

3. The attempt at a solution

$P_{1}=VI cos \theta = E_{AN1}I_{AN1}cos\theta=208\angle 0 \times 3.56\angle-30.96\times cos 30.96 = 635 W$

$PF=cos30.96 = 0.86$

Similarly for $P_{2}=VI cos \theta = E_{AN2}I_{AN2}cos\theta=208\angle 0\times 2.86\angle-74.05\times cos 74.05 = 163.47 W$

$PF=cos74.05 = 0.27$

I don't know where to go from here to get the total power factor. The solution provided by the tutor is 0.64. I've tried averaging the two power factors, but that didn't work, I tried subtracting them from one another, but that didn't work either.

How do I get the total power factor?