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IIT JEE Advanced 2006 Paper 1

Paragraph Type
This section contains 4 paragraphs. Based on each paragraph, there are 3 questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Paragraph for Questions 21–23:
The capacitor of capacitance C can be charged (with the help of a resistance R) by a voltage source V, by closing switch S1 while keeping switch S2 open. The capacitor can be connected in series with an inductor L by closing switch S2 and opening S1.

Question : 21

Total: 120

Initially, the capacitor was uncharged. Now, switch S1 is closed and S2 is kept open. If time constant of this circuit is τ, then

after time interval τ, charge on the capacitor is CV/2.
after time interval 2τ, charge on the capacitor is CV(1 − e−2).
the work done by the voltage source will be half of the heat dissipated when the capacitor is fully charged.
after time interval 2τ, charge on the capacitor is CV(1 − e−1).

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