CO-EFFICIENT OF COUPLING

When current flows through one coil, it produces flux (f₁). The whole of this flux may not be linking with the other coil coupled to it, as shown in Figure 5.32. It may be reduced because of leakage flux f_l by a fraction k known as co-efficient of coupling.

Fig. 5.32  Magnetic circuit for co-efficient of coupling

Thus, the fraction of magnetic flux produced by the current in one coil that links with the other is known as co-efficient of coupling (k) between the two coils. If the flux produced by one coil completely links with the other, then the value of k is 1 and the coils are said to be magnetically tightly coupled. However, if the flux produced by one coil does not link at all with the other, then the value of k is zero and the coils are said to be magnetically isolated.

5.22.1  Mathematical Expression

Consider the magnetic circuit shown in Figure 5.32. When current I₁ flows through coil 1,

(Θɸ₁₂ = kɸ₁)

Now, considering coil 2 carrying current I₂;

(Θɸ₂₁ = kɸ₂)

Multiplying Equations (5.3) and (5.4), we get

or

or

The abovementioned expression gives a relation between mutual inductance between the two coils and their respective self-inductances.

Expression (5.5) can also be written as