Question

Obtain an expression for the energy associated with an inductor.

Answer 1

Emf induced in an inductor

$\epsilon =-L\frac{dI}{dt}$

Work done against emf is stored as energy

$dW=-\epsilon dq=LdI\left(\frac{dq}{dt}\right)$

$dW=LdI$

Work done is stored as energy

${\int }_o^{U}dU={\int }_o^{I}LIdI$

$U-0=L{\left[\frac{I^2}{2}\right]}_0^I$

$U=\frac{1}{2}L{I}^2$