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# Self Induction-Definition, Equation, and Uses

August 6, 2022
written by Adeel Abbas

The phenomenon in which a changing current in a coil induced an emf in itself is called self induction. Self inductance is the ability of a coil to resist changes in current in itself.

## Self-Induction

Consider a coil connected in series with a battery and a rheostat. Magnetic flux is produced through the coil due to the current in it.

When the current through the coil is changed by rheostat magnetic flux through the coil changes and an induced emf is produced in the coil itself. Such an emf is called self-induction emf. By faradays law emf induced in the coil is

ԑL= -N (Δϕ/ Δt)

### Self Induction Equation

Let the flux through one loop of the coil be ϕ then the total flux through N turns would be Nϕ.

As the magnetic flux through the coil is proportional to the current I then

Nϕ ∝ l

Nϕ=LI

Where L is the constant of proportionality called the Self induction. Putting the value of Nϕ from

ԑL= -N (Δϕ /Δt)

ԑL= -Δ (Li)/ Δt

ԑL=-L Δi/Δt

L=ԑL/ Δi/Δt

Self-induction emf in the coil is proportional to the time rate of change of current in the coil. The ratio of average emf to the change of current with time in the coil.

### Self-Induction Unit:

The SI unit for the self-inductance L is VsA-1 which is also called henry (H).

Henry: One henry is the self induction of the coil in which a rate of change of current of one ampere per second causes an induced emf of one volt in the coil itself.

### Factors upon which self induction depends:

Self-induction depends upon

• Number of turns of the coil
• The cross-sectional area of coils
• The core material

Self-induction can be increased by using a ferromagnetic (iron) core as compared to an air core.

## What is Back emf?

The –ve sign indicates that the induced emf must oppose the change that produced it according to Lenz’s law. That is why the self-induced emf is called Back emf.

If the current increases the induced emf will be opposite to that of the battery and if the current is decreasing the induced emf will be in the direction of the original current.

## What are Inductors?

Due to self-inductance coils of wire are known as inductors. Inductors are widely used in electronics and behave as resistors in alternating current.

## Uses of Self Inductance

The major function of an inductor is to store electrical energy in the form of a magnetic field. Inductors are used in the following:

• Inductors used as relays
• Sensors
• Transformers
• Chokes
• Tuning circuits
• Store energy in a device
• Induction motors
• Filters
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