In an LCR circuit as shown below both switches are open initially. Now switch `S_(1)` kept open. (q is charge on the capacitor and `tau = RC` is Capacitive time constant). Which of the following statement is correct?

Options

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

Answer

C

Explanation

Charge on the capacitor at any time t is given by `q = CV(1 - e^(t/tau))` at `t = 2tau, q = CV(1 - e^(-2))`