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 below : If a student plots graphs of the square of maximum charge (Q2Max) 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? (plots are schematic and not drawn to scale) :

Engineering

Physics

L C Oscillation and LCR Damped Oscillation

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 below :

If a student plots graphs of the square of maximum charge (Q²_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? (plots are schematic and not drawn to scale) :

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$Q = Q_{0} e^{- \frac{Rt}{2 L}}$

$Q^{2} = {Q_{0}}^{2} e^{- \frac{Rt}{L}}$