Question

An inductor coil stores $64\text{J}$ of magnetic field energy and dissipates energy at the rate of $640\text{W}$ when a current of $8\text{A}$ is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit, in seconds.

• A. $0.8$
• B. $0.4$
• C. $0.80$
• D. $0.2$

Answer 1

The correct option is D $0.2$

The energy stored in an inductor is, $U=\frac{1}{2}L{I}_0^2$
$64=\frac{1}{2}\times L\times (8{)}^2$
$\therefore L=2\text{H}$

Power utilized in an $R-L$ circuit, in steady state, is,
$P=I_0^{2}R$
$\Rightarrow 640=(8{)}^2\times R$
$\therefore R=10\Omega$

The time constant of an $R-L$ circuit is,
$\tau =\frac{L}{R}=\frac{2}{10}=2\text{sec}$

Hence, $\left(A\right)$ is the correct answer.