Definition: The **coefficient of coupling**, denoted by (k), represents the proportion of magnetic flux generated by the current in one coil that interlinks with the other coil.

Consider two coils, P and Q. When current flows through coil P, it generates magnetic flux that links with coil Q. However, not all of the flux produced by coil P may or may not be linked entirely with coil Q. Similarly when current passes through coil Q, it generates flux, which may or may not be entirely linked with coil P. This incomplete linking happens due to the flux leakage, represented by a fraction (k) known as the **Coefficient of Coupling.**

When *k*=1, it indicates that the flux generated by one coil fully links with the other coil, resulting in a state known as magnetically tightly coupled.

On the other hand, when *k*=0, it signifies that the flux from one coil doesn’t link with the other, indicating that the coils are magnetically isolated.

**FORMULA DERIVATION**

Consider two magnetic coils, P and Q. When current I_{1 }flows through coil P, The self-inductance (L1) and mutual inductance(M) of the coil is :

When current I_{2 }flows through coil Q, The self-inductance (L2) and mutual inductance(M) of the coil is :

By multiplying equations 2 and 3, we can calculate the coefficient of coupling.

Equation (3) above illustrates the relationship between the mutual inductance and self-inductance of the two coils.

**Solved Example on Coefficient of Coupling**

The self-inductance of the two coils is 75 and 120 mH, respectively. The mutual inductance of the coils is 50 mH. Calculate the coupling coefficient.

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