First slide

Time -Varying current in L-R circuit

Question

An induction coil stores 32 joules of magnetic energy and dissipates energy as heat at the rate of 320 watt when a current of 4 amp is passed through it. Find the time constant of the circuit when the coil is joined across a battery.

Moderate

A

0.2 sec
B

0.1 sec
C

0.3 sec
D

0.4 sec

Solution

$U = \frac{1}{2} {LI}^{2}; 32 = \frac{1}{2} \times L \times 4^{2} ∴ L = 4 H$
$and I^{2} R = 320 \Rightarrow (4)^{2} R = 320 ∴ R = 20 Ω$
$T = L / R = \frac{4}{20} = 0.2 \sec$

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