Question

Show that the energy required to build up the current I in a coil of inductance L is `1/2 LI^2`.

Answer 1

The work done against the back/induced emf is stored as magnetic potential energy.

The rate of work done, when a current i is passing through the coil, is:

`(dW)/dt = |epsilon|I = (L (dI)/dt)I`

∴ W = ∫dW

= `int_0^1`LIdl

= `1/2 LI^2`