Maximum Energy Stored in a Capacitor in an AC circuit

[TMO]

Homework Statement

A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as ε = Va - Vb = m*sin(ωt), where m = 24.0 V and ω = 187.0 radians/second. At this frequency,the circuit is in resonance with the maximum value of the current I = 0.5 A. The capacitance C = 130.0μF. L = 0.2199751 H.

Homework Equations

Energy capacity of a capacitor = ½CV²
Energy capacity of an inductor = ½LV²

The Attempt at a Solution

I tried to calculate the energy in terms of plugging in the peak voltage into the energy equation. However, this doesn't yield the correct answer. So I tried combining the energy capacity of both the conductor an the inductor, but this didn't work either. I'm not sure where to proceed.

 

[gneill]

"as shown" doesn't help much without a picture...

And how are we to interpret Va and Vb?

 

[TMO]

My apologies. The picture referenced is here:

https://www.smartphysics.com/Content/Media/Images/EM/20/h20_AC1.png

 

[gneill]

Okay, so it's a series circuit in resonance. What do you you know about the current in a series circuit? And, since you're given the frequency of operation, what can you say about the impedances of L and C? (or reactances, if you haven't covered impedances yet).

 

[TMO]

Because the circuit is in resonance, I = ε_max/R*sin(ωt). The impedance is only equal to the resistance.

 

[gneill]

Because the circuit is in resonance, I = ε_max/R*sin(ωt). The impedance is only equal to the resistance.

Right. Note that you are given the value of I_max. If you then have the individual impedances of the components you can determine the potentials across them. What's the impedance of the capacitor? What's the impedance of the inductor?

 

[TMO]

I see the solution. V_c = IX_c. Thanks.