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## Homework Statement

The current in a series RLC circuit leads the generator voltage by

*φ*= 30°. The circuit, containing an inductor

*L*= 400 mH and a resistor

*R*= 50 Ω, is driven by a generator operating at

*ω*= 100 rad/s with a maximum emf of 10 V. The capacitance is unknown.

The first question regarding this prompt is to find the capacitance, which is 145e-6F.

This is the question I am stumped on:

In terms of the maximum energy

*UC,max*stored in the capacitor and the angle

*φ*by which the current leads the generator voltage, the energy

*UC*stored in the capacitor when the time is

*t*=

*π*/2

*ω*is:

The correct answer is

*UC*=

*UC,max*sin^2

*φ*

## Homework Equations

## The Attempt at a Solution

I've drawn my phasor diagrams, but I don't understand the correct answer. Is the voltage across the capacitor the component of the voltage across the generator pointing in the direction of X_c, the capacitor's impedance? If so, I get how a sin^2(phi) term would be used, because that would be the V^2 part of U = 1/2*cV^2, but I don't see how that would give me UC,max *sin^2(phi).

I will appreciate any help!