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In an LCR circuit as shown below both switches are open initially. Now switch \( \mathrm{S}_{1} \) is closed, \( \mathrm{S}_{2} \) kept open. ( \( \mathrm{q} \) is charge on the capacitor and \( \tau=\mathrm{RC} \) is Capacitive time constant). Which of the following statement is correct?
(A) At \( \mathrm{t}=\tau, \mathrm{q}=\mathrm{CV} / 2 \)
(B) At \( \mathrm{t}=2 \tau, \mathrm{q}=\mathrm{CV}\left(1-\mathrm{e}^{-2}\right) \)
\( -(C) \) At \( \mathrm{t}=\frac{\tau}{2}, \mathrm{q}=\mathrm{CV}\left(1-\mathrm{e}^{-1}\right) \)
-(D) Work done by the battery is half of the energy dissipated in the resistor
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