Max Power Dissipated in RLC circuit

[pynergee]

Homework Statement

For this sample exam, we are given an RLC circuit, with an alternative emf of 1 V, connected all in series with a 500 ohm resistor, a .4 mH inductor, and two capacitors in parallel of 50 pF each.
It asks for the "maximum power dissipated by the resistance" and at what frequencies w would the max power be half as large.

Homework Equations

I am not sure if the question is asking for the power dissipated by resistor, or the entire circuit.
If it were just the resistor, Pmax = (Ipeak)squared * R
But if it were the entire circuit, Pmax = (Irms)(Vrms)cos(phi)
where, (Irms) = (Vpeak/Z)/Sqrt(2) and (Vrms) = (Vpeak)/Sqrt(2) and cos(phi) = (R/Z) I believe.
The frequency = 1/Sqrt(LC)

The Attempt at a Solution

I know how to find the Pmax, but I just need to know for that, if it is the resistor or the entire circuit its asking for.
However for the frequency, I am somewhat stuck.
Would I try to use the derivation of <P> = <[(Ipeak)sin(wt-phi)][(Vpeak)sin(wt)]?

Please help, thank you.

 

[marcusl]

Don't get hung too up on cosinusoids, but look at the impedance of your resonant circuit. What is it exactly on resonance? This will answer the first question. It should show you the way to the second question, too. As a practical matter, the quality factor or Q of the resonator is related to the frequencies you'll find for part two.