What are the applications of self and mutually induced emf?

Self induced EMF opposes the applied voltage due to the changing current (AC). The common name for this device is an “inductor”. They are used in an innumerable number of circuits in power and electronics for many different purposes.

The very common use of this device is to limit the current through a discharge lamp like fluorescent tubes. Mercury and sodium vapour lamps when the lamp is on. This device is called a ballast or choke. It (chokes the current). The ballast or choke performs another function too. When the starter interrupts the current through the tube the rapidly collapsing magnetic field produces a very high voltage that ignites the tube.