# 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.**

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 I_{1 }flows through coil A.

Considering coil B in which current I_{2} flows

Multiplying equation (1) and (2)

The above equation (A) shows the relationship between mutual inductance and self inductance between two the coils.

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