# Self-inductance and Principle of transformer

### What is inductance?

Electromagnetic induction is the phenomenon of producing an electric current in a coil of wire with the help of a magnetic field. This phenomenon is used in devices like transformers and generators.

### Faraday’s Law of Electromagnetic Induction

1st Law: Whenever there is a change in the magnetic flux linked with a circuit an emf and hence current is induced in th circuit. The induced emf lasts as long as the change in flux persists 2nd Law: The magnitude of the induced emf is directly proportional to the rate of change of magnetic flux linked with the circuit.

### Factors Affecting Inductance

Electromagnetic induction depends on the following factors

• The number of turns in the coil: If the number of turns in the coil is large it will result in greater inductance
• The shape of the core: If the coil area is more then the inductance will be greater. The longer the length of the coil lesser will be the inductance.
• The material used in the core: The greater the magnetic permeability of the core the greater is the inductance

### What is Self Inductance?

The phenomenon in which an electromotive force (emf) is produced in the coil due to the change in the current flowing through the same coil is called Self Inductance. 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 magnetic flux Φ linked with the coil at any instant is directly proportional to the current I linked with the coil.

The magnetic flux, Φ = LI

Where L is the Self Inductance or coefficient of self conduction of the coil

If e is the magnitude of the emf induced in the coil then

e=dΦ/dt

e=d(LI)/dt

Thus e=L(dI/dt)

If dI/dt =1 ,then e=L

Therefore the emf induced in the coil is numerically equal to the Self Inductance of the coil when the rate of change of current through the coil is unity.

### What is Mutual Inductance?

The phenomenon in which change in the current flowing through the one coil produces an electromotive force (emf) in another coil is called Mutual Inductance. The emf (e) produced in the secondary coil is directly proportional to the change in current (dI/dt)  in the primary coil. The mutual inductance between a pair of coils is equal to 1 henry when 1 volt of emf is produced in the secondary coil when the current in the primary coil changes at a rate of 1 Ampere per second.

### Working Principle of Transformer

The transformer is a device that transfers electric energy from one circuit to another circuit. The electric energy transferred will have the same frequency. The working principle of the transformer is based on mutual inductance between the two coils that are linked by a common magnetic flux. The transformer has a primary and secondary winding. When the primary coil is connected to the source of alternating voltage the magnetic flux induced in the primary coil induces a magnetic flux in the secondary coil also.