First slide

Inductance

Question

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 amp is passed through it. Find the time constant of the circuit when it is formed across an ideal battery.

Difficult

A

$τ = 0.2 \sec$
B

$τ = 0.32 \sec$
C

$τ = 0.5 \sec$
D

$τ = 1 \sec$

Solution

$M a g n e t i c f i e l d e n e r g y s t o r e d = U = \frac{1}{2} L i^{2}$
$32 = \frac{1}{2} L (4)^{2} or L = 4 Henry$
$Power dissipated as heat is P = i^{2} R$
$320 = 4^{2} R or R = 20 ohm$
$Time constant of circuit = τ = \frac{L}{R} = \frac{4}{20} = 0.2 \sec$

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