Electrical Engineering ⇒ Topic : Expressions for Mutual Inductance

Expressions for Mutual Inductance

The mutual inductance between two coils can be determined by one of the following three methods :

(1) First Method. If the magnitude of mutually induced e.m.f. (e_m) in one coil for the given rate of change of current in the other is known, then M between the two coils can be determined from the following relation

(2) Second Method. Let there be two magnetically coupled coils A and B having N₁ and N₂ turns respectively (See Fig. a). Suppose a current I₁ flowing in coil A produces a mutual flux 1_2.Note that mutual flux 1₂ is that part of the flux created by coil A which links the coil B.

Thus, mutual inductance between two coils is equal to the flux linkages of one coil (N₂Φ₁₂) due to one ampere in the other coil. If N₂ Φ₁₂= 1 Wb-turn and /₁ = 1 A, then, M = 1H.

Hence mutual inductance between two coils is 1 henry if a current of 1 A flowing in one coil produces flux linkages of 1 Wb-turn in the other

(3) Third Method. The mutual inductance between the two coils can be determined in terms of physical dimensions of the magnetic circuit. Fig. (a) shows two magnetically coupled coils A and B having N₁ and N₂ turns respectively. Suppose l and 'a' are the length and area of cross-section of the magnetic circuit respectively. Let μ_r, be the relative permeability of the material of which the magnetic circuit is composed.

                                                                           figure (a)

                                                                                                                                     ............  (iv)

The mutual inductance can be found by using relation (iii) or (iv). Note that mutual inductance is inversely proportional to the reluctance of the magnetic circuit. The smaller the reluctance of the magnetic circuit, the greater is the mutual inductance and vice-versa