**Inductor in series**

When an inductor 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 input of two coils L1 and L2. When the current enters the dot end of coil L1 and leaves, it must enter the second coil of coil L2 as its dotted end. In such a case, there will be the addition of flux from two coils. This type of series connection is known as **series aiding**.

If the connection to inductor L2 is reversed so that the current must enter its undotted end, the fluxes will oppose each other. This type of series connection is known as **series opposing. **We assume that the axes 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 the coil’s self-inductance and the emf induced by the other coil.

similarly,

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 the case of series opposing.

**Inductors in parallel**

We consider the two coils L1 and L2 connected in parallel. The supply currents are divided into two components i1 and 12 flowing through two coils.

we have,

i=i1+i2

self-induced emf in coil A,

mutually induced emf in coil A due to a change of currents in coil B,

where

m=mutual coefficient of inductance.

Resultant emf induced in coil A

similarly, resultant emf induced in coil B

The 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,

since,

substituting

and

we get,

when mutual flux helps the individual flux.

But when mutual flux opposes the individual flux.

**References**

- https://www.allaboutcircuits.com/textbook/direct-current/chpt-15/series-and-parallel-inductors/
- https://www.electronics-tutorials.ws/inductor/series-inductors.html
- https://wiraelectrical.com/inductors-in-series-and-parallel-formula/