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JEE Main 2021 (18 Mar, Shift 2) · Combination of Inductors, LR & LC Circuits

Combination of Inductors, LR & LC Circuits question from JEE Main 2021 (18 Mar, Shift 2)

Q26JEE Main 2021 · 18 MAR · SHIFT 2Medium

Combination of Inductors, LR & LC Circuits

The time taken for the magnetic energy to reach 25% of its maximum value, when a solenoid of resistance R, inductance L is connected to a battery, is:

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Answer: (c)

  1. U=12LI2∝I2U = \frac{1}{2}LI^2 \propto I^2, so U=0.25 UmaxU = 0.25\,U_{max} when I=0.5 I0I = 0.5\,I_0.
  2. 1−e−Rt/L=12⇒e−Rt/L=121 - e^{-Rt/L} = \frac{1}{2} \Rightarrow e^{-Rt/L} = \frac{1}{2}
  3. t=LRln⁡2t = \frac{L}{R}\ln 2
  4. So the answer is (c).
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