In an LCR circuit as shown below both switches are open initially. Now switch $S_1$ is closed, $S_2$ kept open. (q is charge on the capacitor and $\tau = RC$ is capacitive time constant). Which of the following statement is correct? <br>

Question

( A ) At $t = 2 \tau, q = CV (1-e^{-2})$
( B ) At $t = {\tau}, q = CV/2$
( C ) At $t = \frac{\tau}{2}, q = CV (1-e^{-1})$
( D ) Work done by the battery is half of the energy dissipated in the resistor.