$(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.

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