A coil of inductance $8 .4 mH$ and resistance $6 Ω$ is connected to a 12V battery. The current in the coil is 1.0 A at time (approximately) _______

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1 ms

20 s

35 ms

500 s

answer is D.

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Detailed Solution

$i = i_{0} (1 - e^{- Rt / L})$

here $i_{0} = \frac{V}{R} = \frac{12}{6} = 2 A$

$\begin{array}{l} \Rightarrow 1 = 2 - 2 e^{\frac{- 6 t}{8 .4 \times 10^{- 3}}} \\ \Rightarrow 2^{- 1} = e^{\frac{- 6 t}{8 .4 \times 10^{- 3}}} \\ \Rightarrow \frac{0 .301 \times 2 .303 \times 8 .4 \times 10^{- 3}}{6} = t \\ t = 1 ms \end{array}$

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