We know that, when a current flows through a coil, it produces a magnetic field and hence a magnetic flux, which can be linked with the coil itself. It is possible that emf is induced in a single isolated coil due to change of flux through the coil itself by means of varying the current through the same coil. This phenomenon is called self-induction. The induced emf is called ‘back emf’.
Thus, when the current in a coil is switched on, the (induced) back emf opposes the growth of current. Similarly, when the current is switched off, the back emf opposes the decay of the current.
Let us consider a coil of N turns carrying a current i. Let ϕB the magnetic flux linked with each turn of the coil. The total flux, linked with the coil, is proportional to the current i through the coil, and can be expressed as
Here L is a constant called the coefficient of self induction, or ‘self inductance’, of the coil. Physically, the self inductance plays the role of ‘inertia’ in electrical circuits. It is defined as the magnetic flux, linked with the coil, when a unit current is flowing through the coil itself.
When the current in the coil is varied, the flux linked with the coil also changes and an emf is induced in the coil. This is given by
The negative sign indicates that the self induced emf (or back emf) always opposes any change (increase or decrease) of current in the coil. From the above formula, we have
Hence the coefficient of self induction or self inductance of a coil is numerically also equal to the emf induced in coil when the rate of change of current, in the coil in unity.
The S.I unit of ‘L’ is 1 Henry = 1 H
