10.16: Energy Stored in an Inductance
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During the growth of the current in an inductor, at a time when the current is i and the rate of increase of current is ˙i, there will be a back EMF L˙i. The rate of doing work against this back EMF is then Li˙i. The work done in time dt is Li˙idt=Lidi where di is the increase in current in time dt. The total work done when the current is increased from 0 to I is
L∫I0idi=12LI2,
and this is the energy stored in the inductance. (Verify the dimensions.)