From the above figure, first coil carries current i1 and its self inductance is L1. Along with its self inductance it has to face mutual induction due to rate of change of current i2 in the second coil. Same case happens in the second coil also. Dot convention is used to mark the polarity of the mutual induction. Suppose two coils are placed nearby. Coil 1 carries I1 current having N1 number of turn. Now the flux density created by the coil 1 is B1. Coil 2 with N2 number of turn gets linked with this flux from coil 1. So flux linkage in coil 2 is N2 . φ21 [φ21 is called leakage flux in coil 2 due to coil 1].
Consider φ21 is also changing with respect to time, so an EMF appears across coil 2. This EMF is called mutually induced EMF. Now it can be written from these equations, Again, coil 1 gets induced by flux from coil 2 due to current I2 in the coil 2. In same manner it can be written that for coil 1. However, using the reciprocity theorem which combines Ampere’s law and the Biot-Savart law, one may show that the constants are equal. i.e. M12 = M21 = M. M is the mutual inductance for both coil in Henry. The value of mutual inductance is a function of the self-inductances Suppose two coils are place nearby such that they are in mutual induction. L1 and L2 are co-efficient of self induction of them. M is the mutual inductance. Here, ƙ is called co-efficient of coupling and it is defined as the ratio of mutual inductance actually present between the two coils to the maximum possible value. If the flux due to first coil completely links with second coil, then ƙ = 1, then two coils are tightly coupled. Again if no linkage at all then ƙ = 0 and hence two coils are magnetically isolated. Merits and demerits of mutual inductance: Due to mutual inductance, transformer establishes its operating principle. But due to mutual inductance, in any circuit having inductors, has to face extra voltage drop.
How to find out Leq in a circuit having mutual inductance with dot convention Suppose two coils are in series with same place dot. Mutual inductance between them is positive. Suppose two coils are in series with opposite place dot. When a few numbers of inductors are in series with mutual inductances.