Question

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?

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

Answer 1

Answer: (B)

At $t=2\tau ,q=CV(1-e^{-2})$

$C$harge on the capacitor at any time ` $t$' is

$q=CV(1-e^{-t/\tau })$

at $t=2\tau$

$q=CV(1-e^{-2})$