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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. Series Connected Inductors

Let us also consider that, the inductance of inductor 1 and voltage drop across it are L1 and v1 rspectively, the inductance of inductor 1 and voltage drop across it are L2 and v2 rspectively, the inductance of inductor 1 and voltage drop across it are L3 and v3 rspectively, the inductance of inductor 1 and voltage drop across it are L4 and v4 rspectively, the inductance of inductor 1 and voltage drop across it are Ln and vn 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, Leq is equivalent inductance of the series combined inductors. Hence, equivalent inductance of series inductors

Equivalent inductance of series connecetd inductors is simply arithmetic sum of the inductance of individual inductors.

Parallel Connected Inductors

Let us consider n number of inductors connected in parallel as shown below. Parallel Connected Inductors Let us also consider that, the inductance of inductor 1 and current through it are L1 and i1 rspectively, the inductance of inductor 1 and current through it are L2 and i2 rspectively, the inductance of inductor 1 and current through it are L3 and i3 rspectively, the inductance of inductor 1 and current through it are L4 and i4 rspectively, the inductance of inductor 1 and current through it are Ln and in 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, Leq is equivalent inductance of the parallel combined inductors. Hence, equivalent inductance of parallel inductors

Reciprocal of equivalent inductance of parallel connecetd inductors is simply arithmetic sum of the reciprocal of inductance of individual inductors.



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