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 ?

Question

$\begin {array} {1 1} (A)\;At \: t=\tau, \: q=\large\frac{CV}{2} \\ (B)\;At \: t=2\tau, \: q=CV(1-e^{-2}) \\ (C)\;At \: t=\large\frac{\tau}{2},\normalsize \: q=CV(1-e^{-1}) \\ (D)\;Work\: done \: by\: the \: battery \: is \: half\: of \: the \: energy\: dissipated \: in \: the \: resistor \end {array}$