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In an LCR circuit as shown below both switches are open initially. Now switch \( S_{1} \) is closed, \( S_{2} \) 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 \( t=\tau, q=C V / 2 \)
(B) At \( t=2 \tau, q=C V\left(1-e^{-2}\right) \)
\( -\left(\right. \) C) At \( t=\frac{\tau}{2}, q=C V\left(1-e^{-1}\right) \)
-(D) Work done by the battery is half of the energy dissipated in the resistor
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