Derive the mutual-inductance of 2-winding IT in terms of the physical parameters of the transformer.

To derive the mutual-inductance of 2 winding inductive turn in terms of the physical parameter of the transformer. Let L₁ and L₂ is the self-inductance of the primary and secondary winding.

Mutual inductance is defines the flux of the coil 2 linking with coil 1, λ₁₂. To the current flowing in coil 2.

Flux linkage of the coil from the 2 to the coil 1. Hence,

Similarly, mutual inductance of coil 1 to the coil 2,

Now assume that all flux produced by each coil links with the other coil. The implication of this is that there is no leakage flux.

The flux from coil 2 linking with coil 1 is equal to the flux from coil 2 linking with coil 2.