Mutual Induction and Mutual Inductance with Dot Convention

Definition of Mutual induction

Mutual induction is defined as the phenomenon where a coil gets an induced EMF due to a changing current in a nearby coil, causing the flux of one coil to link with the other.

Definition of Mutual Inductance

Mutual inductance is defined as the ratio of the induced EMF in one coil to the rate of change of current in a nearby coil, indicating their potential for flux linkage.

Mutual Induction

Whenever there is a time varying current in a coil, the time varying flux will link with the coil itself and will cause self induced emf across the coil. This emf is viewed as a voltage drop across the coil or inductor. But it is not practical that a coil gets linked only with its own changing flux. When a time varying current flows in another coil placed nearby the first one then the flux produced by the second coil may also link the first one. This varying flux linkage from the second coil will also induce emf across the first coil. This phenomenon is called mutual induction and the emf induced in one coil due to time varying current flowing in any other coil is called mutually induced emf. If the first coil is also connected to the time varying source, the net emf of the first coil is the resultant of self induced and mutually induced emf.

Coefficient of Mutual Induction or Mutual Inductance

Let us consider one coil of self inductance L₁ and another coil of self inductance L₂. Now we will also consider that there is a low reluctance magnetic core which couples these both coils in such a way that entire flux created by one coil will link the other coil. That means there will be no leakage of flux in the system.

First, we apply a time-varying current to coil 1 while keeping coil 2 open-circuited. The voltage induced across coil 1 will be the self-induced EMF.
Now we will keep the first coil open and apply time varying current in coil 2. Now the flux produced by coil 2 will link coil 1 through the magnetic core and as a result, the emf induced in the coil 1 will be
Here, M is the coefficient of mutual induction or in short mutual inductance. Now without disturbing the source at coil 2, we connect a time varying current source across the coil 1. In that situation, there will be a self induced emf across the coil 1 due to its own current and also mutually induced emf across the coil 1 for the current in coil 2. So the resultant emf induced in the coil 1 is
Mutually induced emf may be either additive or subtractive depending on the polarity of the coil. The expression of M is

This expression is justified only when entire flux created by one coil will link another coil but practically it not always possible to link entire flux of one coil to another. The value of actual mutual inductance depends on the actual amount of flux of one coil links another. Here k is a coefficient which must be multiplied with M to derive actual value of mutual inductance.

Dot Convention

As we have already told that whether the mutually induced emf would be additive or subtractive depends on the relative polarity of the mutually coupled coils. The relative polarity of two or more mutually coupled coils is denoted by dot convention. It is represented with a dot mark at either end of a coil. If at an instant, current is entering a coil through dotted end then mutually induced emf on the other coil will have the positive polarity at the dotted end of the later. It can be said in a different way that if the current is leaving a coil through the dotted end then mutually induced emf on the other coil will have the negative polarity at the dotted end of the later.