Explain why the reactance offered by an inductor increases with increasing frequency of an alternating voltage.

Explanation

An inductor opposes flow of current through it by developing a back emf according to Lenz.s law. The induced voltage has a polarity so as to maintain the current at its present value. If the current is decreasing the polarity of the induced emf will be so as to increase the current and vice-versa.
Since, the induced emf is proportional to the rate of change of current it will provide greater reactance to the flow of current if the rate of change is faster means if the frequency is higher the reactance of an inductor, therefore, is proportional to the frequency.
Mathematically the reactance offered by the inductor is given by `X_L=2pivL`