Question

A coil of inductance $8.4mH$ and resistance $6\Omega$ is connected to a $12V$ battery. The current in the coil is $1.0A$ at the time, approximately

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

Answer 1

The correct option is D $1ms$

In the given growth circuit as,

$i=\frac{V}{R}(1-e^{-\frac{Rt}{2}})$

Here, $V=12v$

$R=6\Omega$ and $L=8.4mH$

$\Rightarrow i=2(1-e^{\frac{-{10}^{3}t}{1.4}})$

For $i=1A$,

$1=2(1-e^{\frac{-{10}^{3}t}{1.4}})$

$1/2=1-e^{\frac{{10}^{3}t}{1.4}}$

$\Rightarrow e^{\frac{-{10}^{3}t}{1.4}}=\frac{1}{2}\to t=\frac{1.4\left(\ln 2\right)}{{10}^3}s$

$\Rightarrow t=\left(1.4\right)\left(0.69\right)ms=1ms$

option $-D$ is correct.