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A coil having inductance L and resistance R is connected to a battery of emf ε at t = 0 . If t 1 and t 2 are the time for 90 % and 99 % completion of the current growth in the circuit, then t 1 t 2 will be-

Correct answer

0.5

Step-by-step solution

I = I 0 1 - e - t τ 9 1 0 I 0 = I 0 1 - e - t 1 τ ⇒    e - t 1 τ = 1 1 0 ⇒    e t 1 τ = 1 0 ⇒    t 1 = τ ln 1 0 and 9 9 1 0 0 I 0 = I 0 1 - e - t 2 τ ⇒    e - t 2 τ = 1 1 0 0 ⇒    t 2 = τ ln 1 0 0 = 2 τ ln 1 0 ⇒    t 1 t 2 = 0 . 5

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