Question

An inductor coil carries a steady state current of $2.0\text{A}$ when connected across an ideal battery of emf $4.0\text{V}$. If its inductance is $1.0\text{H}.$ Find the time constant of the circuit.

• A. $1\text{s}$
• B. $\frac{1}{2}\text{s}$
• C. $\frac{3}{2}\text{s}$
• D. $2\text{s}$

Answer 1

The correct option is B $\frac{1}{2}\text{s}$

Given, $i_0=2\text{A};E=4\text{V};L=1\text{H}$

We know that the steady state current is,

$i_0=\frac{E}{R}$

$\Rightarrow R=\frac{E}{i_0}=\frac{4}{2}=2\Omega$

$\therefore$ Time constant of the given circuit is,

$\tau =\frac{L}{R}=\frac{1}{2}\text{s}$

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