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

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

NTA AbhyasNTA Abhyas 2020

Solution:

We know that $U=\frac{1}{2}LI^{2}$
$\Rightarrow 32=\frac{1}{2}L\left(4\right)^{2}$
$\Rightarrow L=4 \, H$
And power $P=I^{2}R$
$\Rightarrow 320=\left(4\right)^{2}R$
$\Rightarrow R=20 \, \Omega $
We know that $\tau=\frac{L}{R}$
$\Rightarrow \tau=\frac{4}{20}$
$\Rightarrow \tau=0.2 \, s$