Power dissipated in circuit when voltage/current out of phase

[Revvi]

Homework Statement

In a different RLC circuit the generator provides a voltage V(t) = 120 sin(2π60t) so that the current in the circuit is I(t) = 5 sin(2π60t +Φ). The phase angle Φ is 25° (0.436 radians). What is the maximum power dissipated in this circuit?

Homework Equations

P = IV (both rms)

The Attempt at a Solution

I simply took the max voltage and current (120 and 5) and plugged them into the rms & power equations. From that, I got the answer to be 600 watts. However, I know that the answer is going to be decreased by some factor because of the phase angle difference. Should end up being 543.8 watts but I don't know how to get to that answer.

 

[GRB 080319B]

Since the question is asking for the maximum power dissipated, you don't want to use rms values. This circuit is AC because the voltage and current are sine functions of time. Power in AC is $$P = V_{max}I_{max}cos$$$$\theta$$, where $$cos$$$$\theta$$ is the power factor. The power factor tells you how much real power the circuit can dissipate, since only part of the voltage V is in the direction of I ($$V_{max}cos$$$$\theta$$). In DC, V and I are always synchronized, so the phase angle between them is $$\theta$$ = 0 and the power factor is $$cos(0) = 1$$.