In an LCR circuit as shown below both switches are open initially. Now switch `S_(1)` is closed and `S_(2)` 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 disslpaled 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

`q=CV(1-e^(t//tau))` at `t=2tau`
`q=CV(1-e^(-2))`