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

• A
  At $t = \frac{\tau}{2}$,$q = CV(1 - e^{-0.5})$
• B
  Work done by the battery is half of the energy dissipated in the resistor
• C
  At $t = \tau$,$q = \frac{CV}{2}$
• D
  At $t = 2\tau$,$q = CV(1 - e^{-2})$