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## Homework Statement

I am given a RLC circuit in series with a fully charged C. There is no applied voltage at this part of the problem.

Using kirchhoff I arrive at a second order diff.eq which leads me to the (correct) solution for the charge in the capacitor: q(t) = Q0exp(-t/T)cos(wt + Ø)

Now I am to derive an expression for the current in the circuit.

I am also given I(0) = 0, and q(0) = 1. T and W are known. The problem here is finding I(t) for the circuit, I have no clue what to do with the phase angle Ø.

## Homework Equations

Unknowns are Q0 and Ø

## The Attempt at a Solution

I know that since all elements are in series the current is equal everywhere, and that I(t) = dq/dt.

I know that if the circuit is driven the current/voltage is out of phase over the RLC. But this is not driven, what happens to the phase? If someone could clarify the physics of the phase in a driven and undriven RLC I would greatly appreciate it.

I can make the math work but the expression for I(t) is looking very with a cos(wt + atan(ugly expression)).