# Calculating Power Factor in and RLC Circuit

1. Jun 4, 2012

### rott3np3anut

1. The problem statement, all variables and given/known data
An RLC circuit has a resistance of 105 ohms, an inductance of 85.0 mH, and a capacitance of 13.2 μF. What is the power factor for this circuit when it is connected to a 125-HZ ac generator?

2. Relevant equations
Well I'm not completely sure which equations to use, so here's some I know:
z=sqrt[R^2+(X_L-X_C)^2]
where X_L and X_C are inductance and capacitance. R is resistance, z is impedanc

tan ϕ = (X_L-X_C)/R

p=1/2 VI cosϕ
My book gives me a different equation for power factor, so I don't know if I copied to notes wrong or if it's the same but written differently.

3. The attempt at a solution
Well I know enough to find ϕ. I then found z and was going to use that to find I, but that was when I realized the problem didn't give me the voltage of the generator. So I'm not sure how to solve for the current and the voltage without having one of them. Is there a different equation I should use for power factor? Please help!

Last edited: Jun 4, 2012
2. Jun 4, 2012

### Sleepy_time

Hi rott3np3anut. The Power factor for an AC circuit is just $cos\phi$. Also $tan\phi=\frac{X_L+X_C}{R}$.