How Is Energy Stored in a Resonant LRC Circuit?

[jesuslovesu]

Homework Statement

Express the energy stored on a capacitor in terms of L, R, V in a standard LRC circuit. The circuit is at resonance.

Homework Equations

E = 1/2 CV^2

The Attempt at a Solution

Well I start with substituting C with something else.
1) C = 1/(Lw^2)
So E = 1/2 V^2/(Lw^2)

2) That's where I begin to have problems. I've then tried w = 2pi*f and f = R/L

Therefore E = V^2 * L /(2R^2 * 4pi^2). Unfortunately, I'm close to the answer but the 4pi^2 term is where my problem lies. Anyone know where I went wrong?

 

[jesuslovesu]

Cancel that, I figured it out