Question
A coil of inductance $$8.4\,mH$$ and resistance $$6\,\Omega $$ is connected to a $$12\,V$$ battery. The current in the coil is $$1.0\,A$$ at approximately the time
A.
$$500\,s$$
B.
$$25\,s$$
C.
$$35\,ms$$
D.
$$1\,ms$$
Answer :
$$1\,ms$$
Solution :
$$\eqalign{
& {\text{Using}}\,\,I = {I_0}\left( {1 - {e^{\frac{{ - t}}{\tau }}}} \right) \cr
& {\text{But}}\,\,{I_0} = \frac{V}{R}\,\,{\text{and}}\,\,\tau = \frac{L}{R} \cr
& \therefore I = \frac{V}{R}\left( {1 - {e^{\frac{{ - Rt}}{L}}}} \right) \cr
& = \frac{{12}}{6}\left[ {1 - {e^{\frac{{ - 6t}}{{8.4 \times {{10}^{ - 3}}}}}}} \right] \cr
& = 1\,\,\left( {{\text{given}}} \right) \cr
& \therefore t = 0.97 \times {10^{ - 3}}\,s \cr
& \approx 1\,ms \cr} $$