# Mutual Inductance

## Mutual Inductance

Inductance can be defined as the electromotive force generated to oppose the change in current in particular time duration. According to Faraday’s law, unit of Inductance:

$$Induc\tan ce\,\,=\,\,\frac{Volt\,\operatorname{Sec}ond}{Ampere}\,\,=\,\,Henry$$.

There are two types of Inductance are there:

• Self-Inductance
• Mutual Inductance.

What is a Mutual Inductance?

Mutual Inductance between the two coils is defined as the property of the coil due to which it opposes the change of current in the other coil or neighbouring coil. When the current in the neighbouring coil is changing the flux set up in the coil and because of this changing flux emf is induced in the coil called mutual induced emf and the phenomenon is called as Mutual Inductance. The relation is,

Magnetic Flux (φ) = Current (I)

φ = M x I

Where,

M = Mutual Inductance of the two coils/ Co-efficient of the Mutual Inductance of the two coils.

The rate of change of magnetic flux in the coil is:

$$e\,\,=\,\,-\,\frac{d\phi }{dt}\,\,=\,\,-\,\frac{d(M\times I)}{dt}$$,

$$e\,\,=\,\,-\,M\frac{dI}{dt}$$,

∴ $$Mutual\,\,Induc\tan ce\,(M)\,\,=\,\,-\,\frac{e}{\left( \frac{dI}{dt} \right)}$$.