Electromagnetic Induction and Alternating Current 4 Question 9

9. In a $L-C-R$ circuit as shown below, both switches are open initially. Now, switch $S _1$ and $S _2$, are closed. ( $q$ is charge on the capacitor and $\tau=R C$ is capacitance time constant). Which of the following statement is correct?

(2013 Main)

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

(b) At $t=\tau q=C V / 2$

(c) At $t=2 \tau q=C V\left(1-e^{-2}\right)$

(d) At $t=\tau / 2, q=C V\left(1-e^{-1}\right)$

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Answer:

Correct Answer: 9. (c)

Solution:

  1. For charging of capacitor $q=C V\left(1-e^{t / \tau}\right)$

At $t=2 \tau$

$$ q=C V\left(1-e^{-2}\right) $$



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