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-

Question

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-,

MARKS App · Accepted Answer

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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