Question

A coil of inductance $8.4mH$ and resistance $6\Omega$ is connected to $12V$ battery. The current in the coil is $1A$ at approximately the time

• A. $500s$
• B. $20s$
• C. $35ms$
• D. $1ms$

Answer 1

Answer: (D)

The current-time $(i-t)$ equation in $L-R$ circuit is givcn by (growth of current in $L-R$ circuit)
$i=i_0\left(1-e^{-t/{\tau }_L}\right)....(i)$
where,$i_0=\frac{V}{R}=\frac{12}{6}=2A$
and ${\tau }_L=\frac{L}{R}=\frac{8.4\times 10^{-3}}{6}$
$=1.4\times 10^{-3}s$
and $i=1A$ (given)
Putting the above values in Eq. (i), we get
$t=0.97\times 10^{-3}s$
$=1ms$