Define an inductor. Derive equation of energy `U=1/2LI^2` stored in inductor.

Explanation

In a circuit, a component which has self inductance is called an inductor. Symbol for an inductor in a circuit is the one shown in figure.

This self-induced emf is also called the back emf as it opposes any change in the current in a circuit. So, work needs to be done against the back emf (e) in establishing the current. This work done is stored as magnetic potential energy.
For the current I at an instant in a circuit, the rate of work done is,
`(dW)/(dt)=|epsilon|I=LI(dI)/(dt)`
`therefore` dW=LIdI
Total amount of work done in establishing the current I is,
`W=int_0^1 dW=int_0^1 LIdI=1/2LI^2`
Thus, the electrical energy required to build up the current I is,
`U=1/2LI^2`
This expression reminds us of `mv^2//2` for the (mechanical) kinetic energy of a particle of mass m, and shows that L is analogous to m (i.e., L is electrical inertia and opposes growth and decay of current in the circuit).