In an LCR circuit as shown below both switches are open initially.

Question:

In an $L C R$ circuit as shown below both switches are open initially. Now switch $S_{1}$ is closed, $S_{2}$ kept open, ( $\mathrm{q}$ is charge on the capacitor and $\tau=\mathrm{RC}$ is Capacitive time constant). Which of the following statement is correct?

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

  2. At $\mathrm{t}=\tau, \mathrm{q}=\mathrm{CV} / 2$

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

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

Correct Option: , 3

Solution:

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