Mutual Inductance and its coefficient
Mutual Inductance
In Article – Statically Induced E.M.F. (Figure given below) we have that any change of current in coil A is always accompanied by the production of mutually-induced e.m.f. in coil B. Mutual inductance may, therefore, be defined as the ability of one coil (or circuit) to produce an e.m.f. in a nearby coil by induction when the current in the first coil changes. This action being reciprocal, the second coil can also induce an e.m.f. in the first when current in the second coil changes. This ability of reciprocal induction is measured in terms of the coefficient of mutual induction M.
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Coefficient of Mutual Inductance (M) :
It can also be defined in three ways as given below :
(i) First Method for M
Let there be two magnetically-coupled coils having N1 and N2 turns respectively (Figure given above). Coefficient of mutual inductance between the two coils is defined as the weber-turns in one coil due to one ampere current in the other.
Let a current I1 ampere when flowing in the first coil produce a flux Φ1 webers in it. It is supposed that whole of this flux links with the turns of the second coil. Then, flux-linkages i.e., webers-turns in the second coil for unit current in the first coil are N2 Φ1/I1. Hence, by definition
If weber-turns in second coil due to one ampere current in the
first coil i.e. N2 Φ1/I1 = 1 then, as 
seen from above, M = 1H.
Hence,
Two coils are said to have a mutual inductance of 1 henry is one ampere current when flowing in one coil produces flux-linkages of one Wb-turn in the other.
Read article – Statically Induced E.M.F.
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