# 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 (L 1>L2) of L then which of the following represents this graph correctly ? (plots are schematic and not drawn to scale) Option 1) Option 2) Option 3) Option 4)

As we learnt in

LR Circuit Voltage -

$V_{R}= IR$

$V_{L}= {I}X_{L}$

- wherein

damping constant for a simple pendulum is inversely proportional to m.

Here damping constant is inversely proportional to L.

$q = q_{o} . e ^{-\gamma t}$

$\therefore \gamma_{1} < \gamma_{2}$

$\therefore$ second case will have higher rate of decay & the graph will follow the exponential equation.

Option 1)

This option is correct.

Option 2)

This option is incorrect.

Option 3)

This option is incorrect.

Option 4)

This option is incorrect.

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