# LC/Resonant circuit - the maximum capacitor energy

## Homework Statement

The effective voltage in an LC circuit is 200V while the capacitance of the capacitor in the circuit is 20pF. What is the maximum capacitor energy?

## Homework Equations

We = CU^2/2

Uefective = U / sqrt(2)

## The Attempt at a Solution

Well it seems a fairly simple problem. It solves by just calculating the energy by putting the given information in the energy equation above, and the answer is supposed to be 4*10^-7 J.
However, this is not the way I solved it. As it states in the problem, the effective voltage of the system is supposed to be 200V, as there is AC going through it. So shouldnt we calculate the peak voltage first, which is 200*sqrt(2) and use it to calculate the maximum energy of the capacitor, which would be when the capacitor is fully charged and there is no current goingh through the system? By doing this we get the answer to be 8*10^-7 J.

So where does my logic fail?

Thanks in advance,
fawk3s

## Answers and Replies

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gneill
Mentor
I suspect that the author of the problem made a poor choice in using the word "effective" here, and didn't realize that it could be taken to have the connotation of RMS value.

English is not my native language, but Im pretty certain he intended to use these words, as in the effective value of the AC voltage. Now does my logic fail somewhere or did the author make a mistake (which is highly unlikely)?
Because by my logic, the maximum voltage on the charged capacitor (when there is currently no current in the system) should be equal to the peak voltage of the AC voltage, not the effective value of the AC voltage.

Thanks in advance,
fawk3s

gneill
Mentor
The energy stored in a capacitor is

$$\xi = \frac{1}{2} C\; V^2$$

Where V is the voltage on the capacitor (Joules/Coulomb). There's no quibbling about that. Since there's no concept of "effective energy", the answer should use the actual instantaneous voltage on the capacitor to calculate the stored energy.

So either the author's choice of word was poor, or his answer is wrong. Your choice!

Edit: Maybe I spoke to soon. After thinking about it, it might not be unreasonable to speak of the RMS energy handled by the capacitor in some context. But still, this would not be the maximum capacitor energy.

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