How Is Energy Stored in a Resonant LRC Circuit?

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The discussion focuses on expressing the energy stored in a capacitor within a resonant LRC circuit using the variables L, R, and V. The initial equation for energy, E = 1/2 CV^2, is modified by substituting the capacitance C with 1/(Lw^2). The user encounters difficulties while manipulating the equation, particularly with the term involving 4pi^2. Ultimately, the user resolves the issue independently, indicating a successful understanding of the problem. The conversation highlights the process of deriving energy storage equations in resonant circuits.
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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?
 
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