Question

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

• A. $5\text{s}$
• B. $2\text{ms}$
• C. $10\text{s}$
• D. $1\text{ms}$

Answer 1

The correct option is D $1\text{ms}$

Given,

$L=8.4\text{mH};R=6\Omega E=12\text{V};I=1\text{A}$


$I=I_0(1-e^{-\frac{t}{\tau }})$

$\because I_0=\frac{E}{R}=\frac{12}{6}=2\text{A}$

$\Rightarrow 1=2(1-e^{-6t/8.4\times {10}^{-3}})$

$\Rightarrow e^{-6t/8.4\times {10}^{-3}}=\frac{1}{2}$

$\Rightarrow \frac{6t}{8.4\times {10}^{-3}}=\ln 2$

$\Rightarrow t=1.4\times 0.693$

$\Rightarrow t=0.97\text{ms}\approx 1\text{ms}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.