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

Options

A. `Li^(2)`
B. `2Li^(2)`
C. `(Li^(2))/(4)`
D. `(Li^(2))/(2)`

Answer

D

Explanation

As we know `e=-(dvarphi)/(dt)=-L(di)/(dt)`
work done against back e.m.f. `e` in time `dt` and current `i` is
`dW=-eidet=L(di)/(dt)idt=Li di`
`impliesW=Lint_(0)^(i)di=(10)/(2)Li^(2)`