Question

In an inductor of inductance $L$, current passing is $I_0$. Derive an expression for energy stored in it. In what forms is this energy stored?

Answer 1

$E-L\frac{di}{dt}=iR$

$E=i^{2}Rdt+L$

${\int }_0^{t}E={\int }_0^t{i}^{2}Rdt+{\int }_0^{i}L$

${\int }_0^{t}E={\int }_0^t{i}^{2}Rdt+\frac{1}{2}L{i}^2$

$\frac{1}{2}L{i}^2$ is the energy stored in the inductor as the current iit increases from 0 to i .

As the energy is zero when the current is zero,

the energy in an inductor carrying a current i, is

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