Mutual Inductance

Mutual inductance is seen in the case of two coils that are in proximity to each other. The proximity between these coils tends to affect the magnetic field in other coils resulting in a flux linkage. Let us formally define mutual inductance

Mutual Inductance can be defined as a property of a coil due to its magnetic field which affects the properties like current and voltage in other coils known as secondary coils.

Let us see the effect of mutual inductance in series connection and parallel connection of inductors.

Mutual Inductance in Series Conductor

In a series configuration of inductors, the flux of one inductor links the nearby inductors in proximity therefore, mutual inductance is introduced to take into consideration that magnetic field. Here is a diagram showing the mutual inductance in the case of inductors in series.

In this series configuration, due to the same current flowing through both the inductors, we can say that current enters both the inductors at the same time denoted by the dot. The current flowing in inductor 1 (L₁) will produce a voltage across inductor 2 and the current flowing in inductor 2 (L₂) will induce a voltage in inductor 1.

Note that this will induce a voltage in the direction of the self-induced voltage. This is why the inductance due to the mutual interaction will be added to the self-inductance to calculate the equivalent expression.

Therefore, the voltage across L₁ and L₂ are

For inductor 1

V₁ = L₁ .di / dt + M.di /dt

For inductor 2

V₂ = L₂ .di / dt + M.di /dt

Also if we consider the total inductance of the system as L_eq then, we can write

V₁ + V₂ = L_eq . di /dt

L₁ .di /dt + M. di /dt + L₂. di /dt + M.di /dt = L_eq. di /dt

L₁ + L₂ + 2 M = L_eq

Note that if the polarity of mutually induced emf is opposite from the self-induced emf the 2M will be subtracted instead of adding.

Mutual Inductance in Parallel Conductor

In a parallel configuration of inductors, the flux of one inductor links the nearby inductors in proximity therefore, mutual inductance is introduced to take into consideration that magnetic field. Here is a diagram showing the mutual inductance in the case of inductors in parallel.

In this parallel configuration, due to the same voltage across both the inductors, we can say that current enters both the inductors at the same time denoted by the dot. The current flowing in inductor 1 (L₁) will produce a voltage across inductor 2 and the current flowing in inductor 2 (L₂) will induce a voltage in inductor 1.

Note that this will induce a voltage in the direction of the self-induced voltage. This is why the inductance due to the mutual interaction will be added to the self-inductance to calculate the equivalent expression.

The total inductance in this case will be

L_eq = ( L₁ L₂ – M² ) / (L₁ + L₂ + 2 M )

Note that if the polarity of mutually induced emf is opposite from the self-induced emf the 2M will be subtracted instead of adding.

Inductors are an important device used in electronics engineering for circuit designing and analysis. There are different configurations in which we can place an inductor two of the most important of which are series and parallel. In this article, we will study series and parallel inductor.

We will see the inductance, current, and flux linkage in each type of circuit. We will also see the total inductance in each case and discuss the concept of mutual inductance. Later, we will study the applications of each type of circuit. We will also see some examples to enhance the understanding of the concepts. The article concludes with some frequently asked questions that readers can refer to.