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JEE Advanced 2006
Exam
JEE Advanced
Year
2006
Subject
Physics
Chapter
Alternating Current

JEE Advanced 2006 · Physics · Alternating Current

Paragraph: The capacitor of capacitance C can be charged (with the...

Paragraph: The capacitor of capacitance CC can be charged (with the help of a resistance RR ) by a voltage source VV, by closing switch S1S_1 while keeping switch S2S_2 open. The capacitor can be connected in series with an inductor LL by closing switch S2S_2 and opening S1S_1.Paragraph: The capacitor of capacitance C can be charged (with the help of a resistance R ) by a voltage source V , by
Question: Initially, the capacitor was uncharged. Now, switch S1S_1 is closed and S2S_2 is kept open. If time constant of this circuit is τ\tau, then

Options

  1. Aafter time interval τ\tau, charge on the capacitor is CV/2C V / 2
  2. Bafter time interval 2τ2 \tau, charge on the capacitor is C V /\left(1-e^{-2}\right)
  3. Cthe work done by the voltage source will be half on the heat dissipated when the capacitor is fully charged
  4. Dafter time interval 2τ2 \tau, charge on the capacitor is C V\left(1-e^{-1}\right)

Correct answer

B. after time interval 2τ2 \tau, charge on the capacitor is C V /\left(1-e^{-2}\right)

Step-by-step solution

Charge on capacitor at time tt is q=q0(1−e−t/τ)q=q_0\left(1-e^{-t / \tau}\right) Here, q0=CV and t=2τ∴q=CV(1−e−2τ/τ)=CV(1−e−2)\begin{array}{ll}\text{ Here, } & q_0=C V \text{ and } t=2 \tau \\ \therefore & q=C V\left(1-e^{-2 \tau / \tau}\right)=C V\left(1-e^{-2}\right)\end{array}$$
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