In an LCR circuit as shown below both switches are open initially. Now switch S 1 is closed, S 2 kept open.…

In an $\text{LCR}$ circuit as shown below both switches are open initially. Now switch ${\text{S}}_1$ is closed, ${\text{S}}_2$ kept open. ($\text{q}$ is charge on the capacitor and $\tau =\text{RC}$ is capacitive time constant). Which of the following statement is correct?

1. At $\text{t}=2\tau \text{, q}=\text{CV }\left(1-{\text{e}}^{-2}\right)$
2. At $\text{t}=\frac{\tau }{2}\text{, q}=\text{CV }\left(1-{\text{e}}^{-1}\right)$
3. Work done by the battery is half of the energy dissipated in the resistor
4. $\text{At t}=\tau \text{, q}=\text{CV}/2$

Solution

Asked in: JEE Main 2013 (07 Apr)

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