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JEE Main20208 Jan 2020Evening ShiftPhysicsAlternating CurrentActual

As shown in the figure, a battery of emf ∈ is connected to an inductor L and resistance R in series. The switch is closed at t = 0 . The total charge that flows from the battery, between t = 0 and t = t c ( t c is the time constant of the circuit) is:

Options

  1. A∈ L e R 2
  2. B∈ L R 2 1 - 1 e
  3. C∈ L R 2
  4. D∈ R e L 2

Correct answer

A. ∈ L e R 2

Step-by-step solution

q = ∫ 0 T c i d t = ∈ R t - e - t T c - 1 T c 0 T c = ∈ R T c + T c e - 1 - T c = ∈ R × 1 e × L R q = ∈ L R 2 e

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