Why does the inductor not allow sudden change in current?

Hint:In order to answer this question we have to apply the concept of induced EMF. In case of inductor the formula for the voltage that develops across the inductor is \[V{\text{ }} = {\text{ }}L{\text{ }}x{\text{ }}\left( {\dfrac{{di}}{{dt}}} \right).\]

Complete step by step solution:
We can say that when electrical energy is passed to an inductor, it stores energy in the form of magnetic energy and is used in most power electronic circuits. An inductor's major feature is that it impedes or rejects any change in the amount of current flowing through it. When the current passing through the inductor changes, it either gains or loses charge in order to equalize the current passing through it. The inductor is also known as a choke, reactor, or simply a coil.

Due to self-induced EMF within the circuit caused by the magnetic field, inductors will not permit any rapid change in current. Here, \[V{\text{ }} = {\text{ }}L{\text{ }} \times {\text{ }}\left( {\dfrac{{di}}{{dt}}} \right).\] is the voltage formed across the inductor.

An unexpected change in current indicates that $di$ has changed for time $dt$ equal to zero. As a result, the voltage value is infinite. There is no such thing as infinite voltage. As a result, a rapid reversal in current is not permitted by an inductor.

Note: The students make mistakes while understanding the concept of the inductor. They make explain without formula of voltage but it makes easier for them to use \[V{\text{ }} = {\text{ }}L{\text{ }} \times {\text{ }}\left( {\dfrac{{di}}{{dt}}} \right).\] for explanation. This will give a clear idea about why the inductor does not allow the sudden change in current.