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NTA Abhyas JEE Main2020PhysicsAlternating CurrentPractice

The figure below shows a battery of emf ε connected to an inductor L and a resistance R in series. If the switch is closed at t = 0 , then the total charge that flows from the battery in one time constant of the circuit is

Options

  1. Aε L R 2 1 - 1 e
  2. Bε L 2 e R 2
  3. Cε L 4 e R 2
  4. Dε L e R 2

Correct answer

D. ε L e R 2

Step-by-step solution

q = ∫ 0 τ ε R ( 1 - e - t / τ ) d t q = ε R t - e - t / τ - 1 τ 0 τ = ε R τ + τ e - 1 - τ q = ε R × 1 e × L R = ε L R 2 e

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