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Physics-

General

Easy

Question

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

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

The correct answer is: $fraction numerator 2 i to the power of 2 end exponent over denominator 2 end fraction$

As we know $e equals negative fraction numerator d ϕ over denominator d t end fraction equals negative L fraction numerator d i over denominator d t end fraction$
Work done against back e.m.f. $e$ in time $d t$ and current $i$ is
$d W equals negative e i d t equals L fraction numerator d i over denominator d t end fraction i d t equals L i blank d i blank rightwards double arrow W equals L not stretchy integral subscript 0 end subscript superscript i end superscript i blank d i equals fraction numerator 1 over denominator 2 end fraction L i to the power of 2 end exponent$

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