What is Inductance? Complete Guide for Electrical Engineers

Before explaining inductance, let us recall what an inductor is. An inductor is a passive device that opposes sudden change in current through it by inducing an emf across it. Actually, an inductor is a coil of conducting wire. When current flows through an inductor, it produces a magnetic flux around it. Hence, this flux is proportional to the current causing it. Therefore, any change in the current causes a change in the magnetic flux. According to Faraday’s law of electromagnetic induction, this changing flux induces an emf across the inductor. Since the ultimate cause of that emf is the change in current through the inductor, the emf opposes any sudden change in current.

Definition of Inductance

Inductance is the ability to oppose the change in current through an inductor. Certainly, this opposition depends upon the value of the induced voltage across the inductor. Hence, the higher the rate of change of current through the inductor, the greater the induced voltage. This relation is linear. That means the induced voltage, or emf, across the inductor is directly proportional to the rate of change of the current through it. The constant of proportionality of this relation is the inductance of that inductor. So, we can write,

$v\propto \frac{di}{dt}\Rightarrow v=L\frac{di}{dt}$

Here, the letter L represents the inductance.

Unit of Inductance

From the above relation, we can also write,

$v=L\frac{di}{dt} \Rightarrow L = \frac{v}{\frac{di}{dt}}$

Now, v equals 1 volt, and $\frac{di}{dt}$ is 1 amp per second, the inductance will be 1 unit. We denote this unit of inductance by the term ‘henry,’ after the great scientist Joseph Henry.

$1\text{ henry (H)} = \frac{1\text{ volt}}{\text{1 amp per second}}$

Relation of Inductance with Flux

The total flux linkage with the inductor of N turns is $\psi=N\phi$. Now, according to Faraday’s law of electromagnetic induction,

$v=\frac{d\psi}{dt}=N\frac{d\phi}{dt}\cdot\cdot\cdot(1)$

Again, we have already derived that,

$v=L\frac{di}{dt}\cdot\cdot\cdot(2)$

So, from (1) and (2), we can write,

$N\frac{d\phi}{dt}=L\frac{di}{dt}\Rightarrow Nd\phi=Ldi\\\\\Rightarrow N\int d\phi=L\int di \Rightarrow N\phi=Li\\\\\Rightarrow L=\frac{N\phi}{i}\cdot\cdot\cdot (3)$

What affects inductance?

From equation (3), we can write,

$L=\frac{N\phi}{i}=\frac{NBA}{i}\;\;\left[\text{Where, } \phi=BA\right]$

Here, B is the flux density, and A is the cross-section of the coil (inductor).

$L=\frac{N\mu H A}{i}\;\;\left[\text{Where, }B=\mu H\right]$

Here, μ is the permeability of the medium surrounding the inductor. Again, we know that,

$Hl=Ni\Rightarrow H=\frac{Ni}{l}$

Therefore,

$L=\frac{N\mu NiA}{li}=\frac{\mu N^2A}{l}$

Therefore, we can finally write,

$L = \frac{\mu N^2 A}{l}$