First slide

Inductance

Question

Average energy stored in a pure inductance L when a current i flows through it, is

Easy

A

$L i^{2}$
B

$2 L i^{2}$
C

$\frac{L i^{2}}{4}$
D

$\frac{{Li}^{2}}{2}$

Solution

As we know, $e = - \frac{dϕ}{dt} = - L \frac{di}{dt}$
Work done against back e.m.f. e in time dt and current i is
$dW = - eidt = L \frac{di}{dt} idt = Lidi$
$\Rightarrow W = L \int_{0}^{i} idi = \frac{1}{2} {Li}^{2}$

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