Obtain an expression for energy stored in an inductor connected to a source voltage.

Explanation

When a current grows through an inductor, the induced emf opposite its growth and as such it has to do some work . Let the current flowing through the circuit at any instant t be i.
The rate of growth of current at the time `=(di)/(dt)`
The induced emf set up in the inductor `E=L (di)/(dt)`
The work done by the current in increasing from zero to its maximum value `I,W int_(0)^(1) dW`.
But dW = Ei dt, Note : power = `("work")/("time")`
i.e., dW = `L((di)/(dt))idt= Li di`.
Hence `W=int_(0)^(1)Lidi=L((i^2)/(2))_0^1 or W=1/2LI^2`.
This amount of work done is stored in the form of magnetic energy . We note that the self inductance is the electrical inertia which opposes the growth or decay of current in the circuit.