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 Capacitance time constant). Which of the following statement is correct ?

Question

Work done by the battery is half of the energy dissipated in the resistor

$t = \,\tau ,\,q = CV/2$

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

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

Solution

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