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# A coil of inductance $84\;mH$ and resistance $8 \Omega$ is connected to $12 V$ battery. The current in the coil is 1 A at approximately

$(a)\;5\;ms \\ (b)\;1\;ms \\(c)\;500\;ms \\(d)\;10\;ms$

Time constant
$T= \large\frac{L}{R}$
$\quad= \large\frac{8.4}{6 \Omega}$$mH \quad= 1.4 \;mH Current in the circuit at time t is I= \large\frac{V}{R}$$(1-e^{-t/T})$
$1A= \bigg( \large\frac{12 V}{6 \Omega}\bigg)$$(1-e^{-t/1.4})$
$e^{-t/1.4}=1-\large\frac{1}{2}$
$\qquad=\large\frac{1}{2}$
$-t/1.4=ln \bigg(\large\frac{1}{2}\bigg)$
$\qquad=-0.693$
$t= 1.4 \times 0.693$
$\qquad= 0.97\;ms$
$\qquad=1\;ms$
Hence b option is correct.