# Karşılıklı Endüktans / Mutual Inductance

Mutual Inducing is the magnetic effect of two different coils on each other when the voltage induces.

In the previous lesson, we found that an inductor creates an induced pacifier in itself as a result of the magnetic field changing around their rotation. When this emk is induced in the same circuit where the current changes, this effect is called Self-induction, i.e. self-induction, (L).

However, when the emk is induced into an adjacent coil located within the same magnetic field, it is said that the emk is induced magnetically, inductively or by mutual induction, symbol (M). Then, when two or more coils are magnetically connected together by a common magnetic flux, they have mutual inducing properties.

Mutual Inducing is the basic principle of operation of the transformer, engines, generators and other electrical components that interact with another magnetic field. We can define the mutual inducing as the current flowing in a coil that induces a voltage in an adjacent coil.

However, mutual inducing can also be a bad thing, as the induct of "leakage" or "leakage" from a coil can interfere with the operation of another adjacent component through electromagnetic induction. Therefore, in cases where mutual induction is undesirable, layers of protection or grounding can be resorted to.

The amount of mutual inductation that connects one coil to another depends very much on the relative position of the two coils. If one coil is placed next to the other coil with a small physical distance, almost all of the magnetic battery produced by the first coil will interact with the coil rotations of the second coil, producing a relatively large impetus.

Similarly, if the two coils are further apart or at different angles, the amount of magnetic flux induced from the first coil to the second will be weaker, producing a much smaller induced absorb and therefore a much smaller mutual induced value. Therefore, the effect of mutual inducing depends on the relative position or range (S) of the two coils.

The mutual inducing between the two coils can be greatly increased by placing them on a common ferromameric nucleus or by increasing the number of rotations of both coils, as can be found in a transformer.

If the two coils are tightly wrapped on a common ferromageticr core, it is said that there is a union coupling between them, since any loss from the flux leakage will be extremely small. Then, assuming an excellent flux connection between the two coils, it can be given as the mutual inducing that exists between them.

Where:

μ_{o} Is the permeability of the free space (4.π.10^{-7})

μr is the relative permeability of the Ferromomanetic nucleus.

N is the number of rounds of coil turns.

A is in the section area in m^{2.}

l Coil length in meters

## Mutual Inducing

Here the current flowing in the first coil, L_{1}, some of these magnetic field lines pass through the coil two, establishing a magnetic field around itself, L_{2} gives us mutual inducing. The first coil has a rotational current of I_{1} and_{N 1,} while the coil has two_{N 2} turns. Therefore, the M_{12} mutual inductation of the two coils, which are available according to the coil one, depends on their position relative to each other and is given as follows:

Similarly, the flux that connects the first coil is exactly the same as the flux that binds the second coil, L_{1}, when a current flows around the second coil, L_{2}, when the same current flows around the coil above, then the mutual inductive of the coil one related to the two of the coils is defined as M_{21.} This mutual inducing is true regardless of the size, number of turns, relative position or orientation of the two coils. Therefore, we can write the mutual inductation between the two coils as M_{12} = M_{21} = M.

Then we can see that the self-induced characterizes an inductor as a single circuit element, while the mutual inducing means some kind of magnetic connection between the two inductors or coils, depending on their distance and arrangement. The inducing of each coil is given as follows:

By cross-multiplying the above two equations, the mutual inductax M between the two coils can be expressed in the self-inductace of each coil.

by simplifying this expression, we can reach a simpler and more common expression:

However, for the equation above,_{} we assume that there are two coils, zero flux leakage between L 1 and L_{2} and 100% magnetic coupling. In reality, there will always be some loss due to leakage and location, so the magnetic connection between the two coils can never reach or exceed 100%, but in some special inductive coils it may be very close to this value.

If part of the total magnetic battery is connected to two coils, this amount of flux connection can be defined as a fraction of the total possible flux connection between the coils. This fraction value is called the link coefficient and is given the letter **k.**

## Coupling Coefficient

In general, the amount of inductive coupling between the two coils is expressed as a fractional number between 0 and 1 instead of a percentage (%); where 0 specifies zero inductive coupling and 1 specifies full or maximum inductive coupling.

In other words, if k = 1, the two coils are perfectly acuple, while the k > is 0.5, the two coils are tightly acupnised and < 0,5 ise iki bobinin gevşek akuple olduğu söylenir. Then, the above equation, which assumes a perfect match, can be modified to take into account this match coefficient (k) and is given as follows:

All flux lines of a coil will cut all rotations of the second coil, that is, the coupling coefficient, k, equals 1, so that the two coils are tightly connected to each other, the resulting mutual inductace should be equal to the geometric mean of the two separate inductees of the coils.

Also, when the inducings of the two coils are the same and equal, when L_{1}is equal to L_{2,}the mutual inductive between the two coils will be equal to the value of a single coil, since the square root of the two equal values is the same.

## Mutual Inducing Question Example 1

The two inductors, whose self-inducts are given as 75mH and 55mH respectively, are positioned side by side on a common magnetic core, so that 75% of the flux lines from the first coil cut the second coil. Calculate the total mutual inductee that exists between the two coils.

## Mutual Inducing Question Example 2

When the two coils, whose induceds were 5H and 4H respectively, were properly wrapped in a non-magnetic nucleus, their mutual inducing was found to be 1.5H. Calculate the coupling coefficient between them.

In the next tutorial on inductors, we will look at connecting inductors in Series and the effect of this combination on mutual inducing, total induced and their induced voltages on circuits.