# What is Self Inductance : Theory, Factors & Its Applications

In any circuit, when the switch is closed, the source of emf like the battery will start pushing the electrons in the whole circuit. So the flow of current will be increased to create the magnetic flux using the circuit. This flux will create an induced emf within the circuit to generate a flux to restrict the increasing flux. The induced emf direction is opposite to the battery so the flow of current will be increased gradually rather than an instantaneous one. This induced emf is known as self-inductance otherwise back emf. This article discusses an overview of self-inductance.

## What is Self Inductance?

Definition: When the current-carrying coil has the property of self-inductance, then it resists the change in the current flow is known as self-inductance. This mainly occurs when the self-induced e.m.f is generated within the coil. In other words, it can be defined as when the voltage induction occurs within a current-carrying wire.

When the current increases or decreases, the self-induced e.m.f will resist the current. Basically, the path of the induced e.m.f is reverse to the voltage applied, if the current is rising. Similarly, the path of the induced e.m.f is in a similar direction to the applied voltage, if the flow of current is reducing,

The above coil property mainly occurs when the flow of current changes which is the AC but not for the steady current or DC. Self-inductance resists the flow of current always, so it is a kind of electromagnetic induction and the SI unit of self-inductance is Henry.

### Self Inductance Theory

Once the current flow throughout a coil, then a magnetic field can be induced, so this extends externally from the wire and this can be connected through other circuits. The magnetic field can be imagined like concentric loops of magnetic flux that enclose the wire. The larger ones connect through others from the additional loops of the coil that enables self-coupling in the coil.

Once the flow of current within the coil alters, then the voltage can be induced various loops of the coil.

In terms of quantifying the effect of the inductance, the basic Self Inductance formula below quantifies the effect.

VL=−Ndϕdt

From the above equation,

‘VL’ is an induced voltage

‘N’ is the no. of turns within the coil

‘dφ/dt’ is the magnetic flux rate of change within Webers / Second

The voltage which is induced within an inductor can also be derived in terms of the inductance & the rate of current change.

VL= −Ldidt

Self-induction is one type of method which operates the single coils as well as chokes. A choke is applicable in RF circuits as it resists the RF signal and allows Dc or steady current to supply.

#### Dimension

The unit of self-inductance is H (Henry), so the dimension of self-inductance is ML2T -2A-2

Where ‘A’ is the cross-section area of the coil

The induced e.m.f production within a circuit can occur because the modify within a magnetic flux in its adjacent circuit is known as mutual induction.

We know that E = ½ LI2

From the above equation, L = 2E/I2

L = E/I2

= ML2T-2/A2 = ML2T-2A-2

### The Relation between Self Inductance and Mutual Inductance

Assume the no. of coils in the primary winding is ‘N1’, the length is ‘L’ and the cross-section area is ‘A’. Once the flow of current through this is ‘I’, then the flux connected to it can be

Φ = Magnetic Field * Effective Area

Φ = μoN1I/l × N1A

The primary coil’s self-inductance can be derived as

L1= ϕ1/I

L1=μN12A/l

Likewise, for the secondary coil

L2 = μN22A/l

Once the current ‘I’ supplies throughout ‘P’, then the flux connected coil ‘S’ is

ϕs = (μoN1I/l)×N2A

Two coils mutual inductance is

M = ϕs/I

From both the equations od

√L1L2 = μoN1N2A/l

By contrasting this through mutual inductance method we can get

M = √L1L2

### Factors

There are different factors affecting the self-inductance coil that includes the following.

• Turns in the coil
• Inductor coil area
• Coil length
• The material of the coil

#### Turns in the Coil

The coil’s inductance mainly depends on the turns of the coil. So they are proportional with each other like N ∝ L
The inductance value is high when the turns within the coil are high. Similarly, the inductance value is low when the turns within the coil are low.

#### Inductor Coil Area

Once the area of the inductor increases then the coil’s inductance will be increased (L∝ N). If the coil area is high, then it generates no. of magnetic flux lines, so magnetic flux can be formed. Therefore the inductance is high.

#### Coil Length

When the magnetic flux induced in a long coil, then it is less than the flux induced within a short coil. When the magnetic flux which is induced is reduced, then the coil’s inductance will be reduced. So the coil induction is inversely proportional to the coil’s inductance (L∝ 1/l)

#### The Material of the Coil

The material’s permeability with the wrapped coil will have an effect on the inductance and induced e. m.f. The high permeability materials can generate less inductance.

L ∝ μ0.

We know μ = μ0μr, then L∝ 1 / μr

#### Example of Self Inductance

Consider an inductor including copper wire with 500 turns, and it generates 10 milli Wb of the magnetic flux once 10 amps of DC current flow through it. Calculate the self-inductance of the wire.

By using the main relation of L & I, the inductance of the coil can be determined.

L = (N Φ)/I

Given that, N = 500 turns

Φ = 10 mille Weber = 0.001 Wb.

I = 10 amps

So inductance L = (500 x 0.01) / 10

= 500 Milli Henry

### Applications

The applications of self-inductance include the following.

• Tuning circuits
• Inductors used as relays
• Sensors