R-L-C oscillations, not L-C oscillations.

Electricity and Magnetism Level 5

Consider a circuit that consists of an ideal inductor of inductance \(L\), an ideal capacitor of capacitance \(C\) and a linear resistor of resistance \(R\).

Let the capacitor be given a initial charge of \({q}_{0}\) and the circuit is left undisturbed to oscillate.

Find the ratio of the energy stored in the inductor due to the magnetic field to the energy stored in the capacitor due to the electric field at the instant when the current in the circuit is maximum.

Let that ratio be of the form of \(\dfrac {\psi{L}^{\alpha}} {{C}^{\beta} {R}^{\gamma}}\)

Find \(\psi+ \alpha +\beta+\gamma\).


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