Question 104 of 190

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

A$0.4$B$0.2$C$0.125$D$0.8$

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Answer: (B) $0.2$

Energy stored in an inductor, $U=\dfrac{1}{2}L{I}^{2}$
$\Rightarrow 64=\dfrac{1}{2}L(8{)}^{2}\Rightarrow L=2H$
and power dissipated in a resistor, $P={I}^{2}R$
$\Rightarrow 640=(8{)}^{2}R\Rightarrow R=10\Omega$
Time constant of the $LRDC$ circuit is,
$\tau =\dfrac{L}{R}=\dfrac{2}{10}=0.2s$