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

$\begin{array}{1 1} (1)\;\text{Work done by the battery is half of the energy dissipated in the resistor} \\ (2)\;At \;t=\tau,q= CV/2 \\ (3)\;At \;t=2 \tau,q= CV(1-e^2) \\ (4)\;At \;t=\large\frac{\tau}{2} ,q= CV (1-e^{-1})\end {array}$