What is the physical role of self inductance?

Explanation

Physically, the self inductance plays the role of inertia. It is the electromagnetic analogue of mass in mechanics. So, work needs to be done against the back emf in establishing the current. This work done is stored as magnetic potential energy.
`W=U=(1)/(2)Ll^(2)" ...(i)"`
This is equivalent to (mechanical) kinetic energy of a particle of mass m,
`K=(1)/(2)mv^(2)" ...(ii)"`
In above equation, L is analogous to m (i.e, L is the electrical inertia and opposes growth and decay of current in the circuit).