LC circuit with 2 capacitors, one charged, one uncharged

Question

I have started to learn about LC circuits, in particular in the case where the initial conditions are where the capacitor has previously been charged.

I am struggling to understand what would happen in a case where there is two capacitors and an inductor all connected in parallel, where one of the capacitors has been previously charged, and the other capacitor is uncharged. The capacitors are of equal capacitance.

I have read that you just treat the capacitors as an equivalent capacitor in parallel (2C capacitance) for determining the frequency of the circuit. But what about at the initial conditions? If just one is charged then Q=CV. But in parallel, then Q=2CV, which adds extra charge to the system.

Can anybody explain this to me or provide a link to a solution?

Answer 1

In real caps ESR loses Pd*T= \$ V^2/ESR~*~ESR(C1+C2)\$ energy on connection but if Voltage drops to 1/2 or less the total Q is not 2Q since if C1=C2 then ideally V final =1/2Vi