An LCR circuit is equivalent to a damped osci | vedclass

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(A) In an $LCR$ circuit, the charge on the capacitor at any time $t$ is given by $Q(t) = Q_0 e^{-Rt/2L} \cos(\omega' t + \phi)$.The maximum charge on

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(A) In an $LCR$ circuit, the charge on the capacitor at any time $t$ is given by $Q(t) = Q_0 e^{-Rt/2L} \cos(\omega' t + \phi)$.The maximum charge on the capacitor at any cycle is given by $Q_{max}(t) = Q_0 e^{-Rt/2L}$.Squaring both sides, we get $Q^2_{max}(t) = Q^2_0 e^{-Rt/L}$.This equation represents an exponential decay of the square of the maximum charge with time.The rate of decay depends on the factor $R/L$. Since $L_1 > L_2$, the decay constant $R/L_1$ is smaller than $R/L_2$.Therefore, the charge in the circuit with $L_2$ decays faster than the circuit with $L_1$.Thus, the graph for $L_1$ will show a slower decay compared to the graph for $L_2$.

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