Question

An inductor coil stores $32\text{J}$ of magnetic field energy and dissipates energy as heat at the rate of $320\text{W}$ when a current of $4\text{A}$ is passed through it. Find the time constant of the circuit when this coil is joined across an ideal battery.

• A. $0.02\text{s}$
• B. $0.2\text{s}$
• C. $2\text{s}$
• D. $0.002\text{s}$

Answer 1

The correct option is B $0.2\text{s}$

The magnetic energy stored in an inductor is,

$U=\frac{1}{2}L{i}^2$

$32=\frac{1}{2}\times L\times (4{)}^2\Rightarrow L=4\text{H}$

The power dissipated as heat is given by,

$P=i^{2}R$

$320=(4{)}^2\times R\Rightarrow R=20\Omega$

The time constant of the circuit will be,

$\tau =\frac{L}{R}=\frac{4}{20}=0.2\text{s}$

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

Why this question ? This question is an example of how different concepts can be combined.