In calculus terms, we would say that the induced voltage across the inductor is the derivative of the current through the inductor: that is, proportional to the current’s rate of change concerning time.
The inductor, always opposing any change in current, will produce a voltage drop opposite to the change''s direction. With that in mind, how much voltage the inductor will produce depends on how rapidly the current through it is decreased. As described by Lenz’s Law, the induced voltage will be opposed to the change in current.
As current starts to flow, a voltage (e r) appears across R, and the voltage across the inductor is reduced by the same amount. The fact that the voltage across the inductor (L) is reduced means that the growth current (i,) is increased and consequently eg is increased.
The instantaneous voltage drop across an inductor is directly proportional to the rate of change of the current passing through the inductor. The mathematical relationship is given by v = L (di/dt). Inductors do not have a stable “ resistance ” as conductors do.
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