Series and Parallel Inductor 

An inductance is passive circuit component. allow us to resolve the equivalent inductance of series connected and parallel connected inductors.

Series Connected Inductors

Let us contemplate n variety of inductors connected nonparallel as shown below. Series Connected Inductors allow us to conjointly contemplate that,

the inductance of inductance one and dip across it square measure L1 and v1 respectively,
the inductance of inductance one and dip across it square measure L2 and v2 respectively,
the inductance of inductance one and dip across it square measure L3 and v3 respectively,
the inductance of inductance one and dip across it square measure L4 and v4 respectively,
the inductance of inductance one and dip across it square measure Ln and  V respectively.
                      v=l1( di/dt)+l2(di/dt)+l3(di/dt)+------

Now, applying, Kirchhoff's Voltage Law, we get, total dip (v) across the series combination of the inductors, The voltage drop across AN inductance of inductance L may be expressed as, Where, i is that the instantaneous current through the inductance. As all inductors of the mixtures square measure connected nonparallel, here, the present through every one of the inductors is same, and say conjointly it's i. So, from higher than KVL equation, we get, This equation may be rewritten as, Where, Leq is equivalent inductance of the series combined inductors. Hence, equivalent inductance of series inductors
            the inductance of series connected inductors is solely arithmetic total of the inductance of individual inductors.

Parallel Connected Inductors

Let us contemplate n variety of inductors connected in parallel as shown below. Parallel Connected Inductors allow us to conjointly contemplate that,

  the inductance of inductance one and current through it square measure L1 and i1 respectively,
the inductance of inductance one and current through it square measure L2 and i2 respectively,
the inductance of inductance one and current through it square measure L3 and i3 respectively,
the inductance of inductance one and current through it square measure L4 and i4 respectively,
the inductance of inductance one and current through it square measure Ln and in respectively.
         
           i1+i2+i3+i4+------------------

Now, applying, Kirchhoff's Current Law, we get, total current (i) coming into within the parallel combination of the inductors, the present through AN inductance of inductance L may be expressed as, Where, v is that the instantaneous voltage across the inductance. As all inductors of the mixtures square measure connected in parallel, here, the dip across every one of the inductors is same, and say conjointly it's v. So, from higher than KCL equation, we get, This equation may be rewritten as, Where, Leq is equivalent inductance of the parallel combined inductors. Hence, equivalent inductance of parallel inductors

Mutually Connected Inductors nonparallel

When inductors area unit connected along nonparallel in order that the field of 1 links with the opposite, the impact of coefficient either will increase or decreases the whole inductance relying upon the number of magnetic coupling. The impact of this coefficient depends upon the space apart of the coils and their orientation to every alternative.

Mutually connected series inductors are often classed as either “Aiding” or “Opposing” the whole inductance. If the magnetic flux created by this flows through the coils in the same direction then the coils area unit aforesaid to be Cumulatively Coupled. If this flows through the coils in opposite directions then the coils area unit aforesaid to be Differentially Coupled as shown below.