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**Coefficient of coupling (k):**

It is defined as the ratio of actual mutual inductance present between two coils to the maximum possible value.

If L1 and L2 are coefficients of self inductances of two coils having mutual inductance ‘M’ between them then the coefficient of coupling between these coils is given by: k = M/ √ (L_{1}L_{2})

OR

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.

k = Φ_{12}/Φ_{1}

where, Φ_{1} is the total flux produced by coil 1,

Φ_{12} is the flux (out of Φ_{1}) linking with coil 2

OR

It is a measure of the portion of flux produced by a coil linking another coil. It is defined as (K) the ratio of actual mutual inductance (M) present between the coils C1 and C2 to the maximum possible value of M. OR it is the fraction of the total flux produced by current in a coil that links the other coil

**Explanation of coefficient of coupling:** Mathematical expression for coefficient of coupling is

K = M / M_{max}

But, M_{max} = √ (L_{1}L_{2})

K = M / (√L_{1}L_{2})

The maximum value of K is 1 which represents the coupling of all flux produced by one coil with the other coil

Corresponding to K = 1 the value of mutual inductance will be maximum and it is given by, M_{max} = √ (L_{1}L_{2}) Corresponding to K = 1

The coupling between the two coils is said to be a tight coupling if K = 1 and the coupling is called as loose coupling if K is less than one.

The coefficient of coupling is also called as Magnetic coupling Coefficient.