# Series and Parallel Inductors

An inductor is passive circuit element. Let us find out the equivalent inductance of **series connected and parallel connected inductors**.

## Series Connected Inductors

Let us consider n number of**inductors connected in series**as shown below.

Let us also consider that,
the inductance of inductor 1 and voltage drop across it are L_{1} and v_{1} rspectively,
the inductance of inductor 1 and voltage drop across it are L_{2} and v_{2} rspectively,
the inductance of inductor 1 and voltage drop across it are L_{3} and v_{3} rspectively,
the inductance of inductor 1 and voltage drop across it are L_{4} and v_{4} rspectively,
the inductance of inductor 1 and voltage drop across it are L_{n} and v_{n} rspectively.
Now, applying, Kirchhoff's Voltage Law, we get, total voltage drop (v) across the **series combination of the inductors**,

The votage drop across an inductor of inductance L can be expressed as, Where, i is the instanteous current through the inductor. As all inductors of the combinations are connected in series, here, the current through each of the inductors is same, and say also it is i. So, from above KVL equation, we get,

This equation can be rewritten as,
Where, L_{eq} is equivalent inductance of the **series combined inductors**. Hence,

## Parallel Connected Inductors

Let us consider n number of**inductors connected in parallel**as shown below. Let us also consider that, the inductance of inductor 1 and current through it are L

_{1}and i

_{1}rspectively, the inductance of inductor 1 and current through it are L

_{2}and i

_{2}rspectively, the inductance of inductor 1 and current through it are L

_{3}and i

_{3}rspectively, the inductance of inductor 1 and current through it are L

_{4}and i

_{4}rspectively, the inductance of inductor 1 and current through it are L

_{n}and i

_{n}rspectively.

Now, applying, Kirchhoff's Current Law, we get, total current (i) entering in the **parallel combination of the inductors**,
The current throgh an inductor of inductance L can be expressed as,

Where, v is the instanteous voltage across the inductor.
As all inductors of the combinations are connected in parallel, here, the voltage drop across each of the inductors is same, and say also it is v. So, from above KCL equation, we get,
This equation can be rewritten as,
Where, L_{eq} is equivalent inductance of the **parallel combined inductors**. Hence,

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