Inductors in series
A series combination of inductors involves connecting multiple inductors end-to-end to share the same path for electric current, resulting in a single pathway. In a series configuration, the current through each inductor is the same, so the total voltage is the sum of the individual L.di/dt-drop across each inductor. An inductor with lower inductance will have a lower voltage drop across it.
Total inductance: The formula to calculate the total inductance (LT) in series is the sum of individual inductances (L1, L2, L3, …):
$$L_{T}=L_1+L_2+L_3+\cdots{}$$
Derivation of inductance:
$$V_{AB}=V_{L1}+V_{L2}+V_{L3}$$
$$L_T\cfrac{dI}{dt}=L_1\cfrac{dI}{dt}+L_2\cfrac{dI}{dt}+L_3\cfrac{dI}{dt}$$
$$\implies{}L_T=L_1+L_2+L_3$$
Equivalent Inductance: The equivalent inductance in a series combination is always greater than the highest individual resistance. Adding more resistances in series impedes the current more, increasing the overall resistance.
Series combinations of resistors are commonly used to increase the overall resistance in electronic circuits. For a constant current, the voltage drop increases with an increase in series resistance. For a constant voltage, the current reduces with increased series resistance.
Inductors in parallel
A parallel combination of inductance involves connecting the terminals of multiple inductances together at the same voltage level, essentially creating multiple pathways for electric current. In a parallel configuration, all inductances have the same voltage across them. Inductors with lesser inductances will allow more current to flow from them.
Total Inductance: The total inductance (Ltotal) of inductors in parallel is reciprocal of the sum of reciprocal of individual inductances (L1, L2, L3, …):
$$\cfrac{1}{L_{total}}=\cfrac{1}{L_1}+\cfrac{1}{L_2}+\cfrac{1}{L_3}+\cdots{}$$
Equivalent Inductance: The equivalent inductance in a parallel combination is always lesser than the smallest individual inductance. This is because connecting more parallel inductors effectively provides more paths for the current to flow, reducing inductances.
Parallel combinations of inductors are commonly used to decrease the overall inductance in electronic circuits.