Show that energy stored in an inductor L, when a current is f established through it, is 1/2( LI ^2).

Explanation

Energy stored in an inductor : Let a source of emfis connected to an inductor of inductance L,
Initially at time t=0, current flowing through inductor =0
Let at any instant, I = Current flowing through the inductor.
`(dI)/(dt) =` Rate of growth of current through inductor at given instant.
So `e=L (dI)/(dt)=` Induced enmfproduced in the inductor ...(i)
If l is the current supplied by the source of emffor time dt then
Small amount of work done by source of emf = dw = e I dt
`dW =(L(dI)/(dt))dt" "` [Using eq. (i)]
`dW=LI dI`
Total work done in increasing the çurrent from 0 to Iis given by
`int dW = overset(I)underset(0)int LI dI`
`W=L |(I^(2))/(2)|_(0)^(I)`
`W=(I)/(2) LI^(2)`
This work done gets stored in the inductor in the form of energy.
`W=U =(1)/(2) LI^(2)`
Energy stored in the inductor `U=(1)/(2) LI^(2)`