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?
  • AAt $t=\frac{\tau}{2}$,$q=C V$ $(1-e^{-1})$
  • B
    Work done by the battery is half of the energy dissipated in the resistor
  • CAt $t=$$\;\tau $ ,$q= $ $\frac{{{\rm{CV}}}}{2}$
  • DAt $t= $${2 \tau }$ ,$q=CV$ $(1-e^{-2})$
JEE MAIN 2013, Medium
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