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Consider a coil connected to a battery and a tapping key.(figure below)

When the key K is pressed,the current starts growing through the coil and as a result, the magnetic field lines also start growing through it.This,in turn, produces induced  e.m.f. in the coil.The direction of the induced e.m.f. is such that it opposes the growth of current in the circuit.

On the other hand,when the key is released,the current in the circuit starts decaying.As a result of this, magnetic field lines linked with the coil also starts decreasing.The e.m.f. is produced in the coil so that it opposes the decay of current in the coil, an opposing induced e.m.f .is produced in the coil.

The phenomenon ,according to which an opposing induced e.m.f is produced in a coil as a result of change in current or magnetic flux linked with the coil,is called self induction.