Calculating Power Factor in and RLC Circuit

AI Thread Summary
To calculate the power factor in an RLC circuit with a resistance of 105 ohms, inductance of 85.0 mH, and capacitance of 13.2 μF connected to a 125-HZ AC generator, the impedance (z) can be determined using the formula z=sqrt[R^2+(X_L-X_C)^2]. The phase angle (ϕ) is found using tan ϕ = (X_L - X_C)/R, and the power factor is given by cos ϕ. The voltage of the generator is necessary to calculate current, but the power factor can still be derived from the phase angle. Clarification on the equations used for power factor calculation is provided, confirming that it is indeed cos ϕ.
rott3np3anut
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Homework Statement


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?

Homework 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.

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

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