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JEE Main 2006 (AIEEE) · Combination of Inductors, LR & LC Circuits

Combination of Inductors, LR & LC Circuits question from JEE Main 2006 (AIEEE)

Q33JEE Main 2006 · AIEEEMedium

Combination of Inductors, LR & LC Circuits

An inductor (L=100 mH)(L = 100\text{ mH}), a resistor (R=100 Ω)(R = 100\,\Omega) and a battery (E=100 V)(E = 100\text{ V}) are initially connected in series as shown in the figure. After a long time the battery is disconnected after short circuiting the points AA and BB. The current in the circuit 1 ms1\text{ ms} after the short circuit is

Figure

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Answer: (a)

  1. Steady current before shorting: I0=E/R=100/100=1 AI_0 = E/R = 100/100 = 1\text{ A}.
  2. After shorting, the current decays: i=I0e−t/τi = I_0 e^{-t/\tau} with τ=L/R=0.1/100=1 ms\tau = L/R = 0.1/100 = 1\text{ ms}.
  3. At t=1 ms=τt = 1\text{ ms} = \tau: i=1⋅e−1=1/e Ai = 1 \cdot e^{-1} = 1/e\text{ A}
  4. So the answer is (a) 1/e A1/e\text{ A}.
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