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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 42

  • question_answer
    In an LCR circuit as shown below both switches \[{{S}_{1}}\] and \[{{S}_{2}}\]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 statements is correct?

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

    B) At \[t=\tau ,\,\,q=-CV/2\]

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

    D) At \[t=\frac{\tau }{2},\,q=CV\,(1-{{e}^{-1}})\]

    Correct Answer: C

    Solution :

    Charge on the capacitor at any time t is given by \[q=CV(1-{{e}^{t/\tau }})\] at \[t=2\tau \] \[q=CV(1-{{e}^{-2}})\]


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