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10.16: Energy Stored in an Inductance

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 \(\dot i\), there will be a back EMF \(L\dot i\). The rate of doing work against this back EMF is then \(Li\dot i\). The work done in time \(dt\text{ is }Li \dot i \,dt = Li\,di \) where \(di\) is the increase in current in time \(dt\). The total work done when the current is increased from 0 to \(I\) is

\[\label{10.16.1}L\int_0^I i\,di = \frac{1}{2}LI^2,\]

and this is the energy stored in the inductance. (Verify the dimensions.)

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