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Coefficient of Coupling

When two coils are placed near each other, all the flux produced by one coil does not link with the other coil, as assumed in Art only certain portion say, K)of flux produced by one coil links with the other coil, K being less than unity, K is called the coefficient of coupling.

Flux created in coil A due to current of i1 amperes, 1 N1i1  Wb
                                                                                  l / μoμra

Flux linking with coil B, 2 = K1 = KN1i1  Wb
                                                      l / μoμra

Coefficient of mutual induce, M = KN1N2
                                               l / μoμra
Coefficient of self inductance of coil  A, L1 = N11 =  N12
                                                                 i1       l / μoμra 

Coefficient of self inductance of coil B, L2 = N22  =   N22
                                                                                       i2          l / μoμra 

Multiplying expressions and taking square root we get

Comparing expressions and we get

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