Coefficient Of Coupling

The fraction of magnetic flux produced by the current in one coil that links with the other coil is called coefficient of coupling between the two coils. It is denoted by (k).

Two coils are taken coil A and coil B, When current flows through one coil it produces flux; the whole flux may not link with the other coil coupled, and this is because of leakage flux by a fraction (k) known as Coefficient Of Coupling.

Coefficient of coupling fig
k=1 when the flux produced by one coil completely links with the other coil and is called magnetically tightly coupled.

k=0 when the flux produced by one coil does not link at all with the other coil and thus the coils are said to be magnetically isolated.

DERIVATION

Consider two magnetic coils A and B.
When current I1 flows through coil A.
Coefficient-of-coupling-eq1
Considering coil B in which current I2 flows
Coefficient-of-coupling-eq2
Multiplying equation (1) and (2)
Coefficient-of-coupling-eq3
The above equation (A) shows the relationship between mutual inductance and self inductance between two the coils.
                       

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