Question

Define self-inductance of a coil. Obtain the expression for the energy stored in an inductor L connected across a source of emf.

Answer 1

Self inductance of a coil is equal to the magnitude of induced emf produced in the coil when rate of change of current through the coil is unity.
$\Phi =LI$
$e=-\frac{d\Phi }{dt}$
$e=-L\frac{dI}{dt}$

For the current I at an instant in a circuit, the rate of work done is $\frac{dW}{dt}=|e|I$ $=LI\frac{dI}{dt}$
Total work done in increasing the current from 0 to I is given by $W={\int }_0^{I}LIdIW=L{\left[\frac{I^2}{2}\right]}_0^{I}W=\frac{1}{2}L{I}^2$
This work done is stored as magnetic potential energy. $U=\frac{1}{2}L{I}^2$