Inductor in series
when an inudctor is connected in series with the axis of one coil perpendicular to the axis of the other,there is no mutual inductance i.e M=0.Let us consider the inuctance of two coils as L1 andL2. When the current enters the dot end of coil L1 and leaves it must enter the second coil of L2 as its dotted end.In such case there will be the addition of fluxes of two coils.This type of series connection is known as series aiding.
If the connection to inductor L2 are reversed so that the current must enter its undotted end,there fluxes will oppose each other.This type of series connection is known as series opposing.we assume that the axis of the inductance coils are on the same straight line.
series Aiding:The total emf induced in each of the coils L1 and L2 is due to coil’s self inductance and the emf induced by the other coil.
so the total induced emf in the circuit is given by,
Therefore the total inductance of the circuit,L
series opposing:The mutually induced emf opposes the self induced emf in case of series opposing.
Inductors in parallel
we consider the two coils L1 and L2 connected in parallel.The supply currents divided into two components i1 and 12 flowing through two coils.
self-induced emf in coil A,
mutually induced emf in coil A due to change of currents in coil B,
m=mutual coefficient of inductance .
Resultant emf induced in coil A
similarly resultant emf induced in coil B
Resultant emf induced in both of the coils must be equal when both coils are connected in parallel.
If L is the equivalent inductance of the combination then induced emf,
when mutual flux helps the individual flux.
But when mutual flux opposes the individual flux.