Induction - Self Induction and Mutual Induction

What is Induction or Inductance?

Electromagnetic Induction law was given by Faraday which states that by varying the magnetic flux electromotive force is induced in the circuit. From Faraday’s law of electromagnetic induction, the concept of induction is derived. Inductance can be defined as the electromotive force generated to oppose the change in current in particular time duration.

According to Faraday’s Law:

Electro motive force = – L \( \frac {\Delta I}{\Delta t}\)

Unit of Inductance = \( \frac {Volt ~Second }{Ampere}\)=Henry

Types of Inductance

Two types of inductance are there:

  • Self Induction
  • Mutual Induction

Induction

What is Self Induction?

When there is a change in current or magnetic flux of the coil, an opposed induced electromotive force is produced. This phenomenon is termed as Self Induction. When the current starts flowing through the coil at any instant, it is found that that the magnetic flux becomes directly proportional to the current passing through the circuit. The relation is given as:

\( \phi \)= I

\( \phi \) = L I

Where L is termed as self-inductance of the coil or the coefficient of self-inductance. The self-inductance depends on the cross-sectional area, the permeability of the material or the number of turns in the coil.

The rate of change of magnetic flux in the coil is given as,

e = – \( \frac {d \phi}{dt} \) = – \( \frac {d (LI) }{dt} \)

or e = – L \( \frac {dI}{dt} \)

What is Mutual Induction?

We take two coils, and they are placed close to each other.  The two coils are P- coil (Primary coil) and S- coil (Secondary coil). To the P-coil, a battery, and a key is connected wherein the S-coil a galvanometer is connected across it. When there is a change in the current or magnetic flux linked with two coils an opposing electromotive force is produced across each coil, and this phenomenon is termed as Mutual Induction. The relation is given as:

\( \phi \) = I

\( \phi \) = M I

Where M is termed as the mutual inductance of the two coils or the coefficient of the mutual inductance of the two coils.

The rate of change of magnetic flux in the coil is given as,

e = – \( \frac {d \phi}{dt} \) = – \( \frac {d (MI)}{dt}\)

e = – M \( \frac {dI}{dt} \)

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Practise This Question

A mutual inductor consists of two coils X and Y as shown in fig. In which one-quarter of the magnetic flux produced by X links with Y, giving a mutual inductance M. What will be the mutual inductance when Y is used as the primary?