Maximum Current in LC Circuit: Solving for the Peak Amplitude

[ttiger2k7]

[SOLVED] Finding current in LC circuit

Homework Statement

A $18.0 \mu {\rm F}$ capacitor is placed across a $22.5 {\rm V}$ battery for a few seconds and is then connected across a $12.0 \rm mH$ inductor that has no appreciable resistance.

After connecting the capacitor and inductor together, find the maximum current in the circuit.

Homework Equations

$$i=-\omega*Q*sin(\omega*t+\varphi)$$

The Attempt at a Solution

This sounds like a pretty simple question and I think I'm complicating it too much. Does this have anything to do with finding the angular frequency. I know current is maximum when capacitor potential and induced emf is zero. But I don't know what the relationship using an equation. Do I have to derive one? I can't seem to find one.

 

[gneill]

The trick here is to realize that during the oscillations that ensue when the charged capacitor is connected to the inductor, at certain instants of time the voltage on the capacitor will cross through zero volts. That leaves zero energy stored in the capacitor at those instants. So where did the energy go? It all ended up stored in the inductor's magnetic field thanks to the current flowing through it.

Equating the maximal stored energies:

$½~C V_{max}^2 = ½~L I_{max}^2$

$I_{max} = V_{max} \sqrt{C/L}$

$I_{max} = 871~mA$