Electro Magnetic Induction And Alternating Currents Question 602

Question: An inductance L and a resistance R are first connected to a battery. After some time the battery is disconnected but L and R remain connected in a closed circuit. Then the current reduces to 37% of its initial value in [MP PMT 1994]

Options:

A) RL sec

B) $ \frac{R}{L}sec $

C) $ \frac{L}{R}sec $

D) $ \frac{1}{LR}sec $

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Answer:

Correct Answer: C

Solution:

When battery disconnected current through the circuit start decreasing exponentially according to $ i=i_{0}{{e}^{-Rt/L}} $

Þ $ 0.37i_{0}=i_{0}{{e}^{-Rt/L}} $

Þ $ 0.37=\frac{1}{e}={{e}^{-Rt/L}} $

Þ $ t=\frac{L}{R} $



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