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Question:

An LCR circuit is equivalent to a damped pendulum. In an LCR circuit, the capacitor is charged to Q0 and then connected to the L and R as shown above. If a student plots graphs of the square of maximum charge (Q^2_Max) on the capacitor with time (t) for two different values L1 and L2 (L1 > L2) of L, then which of the following represents this graph correctly?

Solution:

This is equivalent to a damped harmonic oscillator. Q = Q0e^(-Rt/2L) If L is more, Q falls slower.