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.
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)).