Series & Parallel Inductors

You may still be reeling from the strange complications of calculating series and parallel capacitors and voltage/current dividers. I am happy to report that there are no such issues with inductors.

To all intents and purposes, inductors can be treated in the same way as resistors!

Series Inductors

Series inductances are additive, just like resistances are.

\(L_{Total} = L_1 + L_2 + {…} + L_n \)

Since the same current passes through all series connected inductors, the voltage drop across any inductor is proportional to it’s own inductance compared to the total inductance.

\(V_{Ln} = V_{Total} \times \frac{L_n}{L_{Total}} \)

Parallel Inductors

Total parallel inductance can be calculated in the same fashion as for parallel resistors:

\(\frac{1}{L_{Total}} = \frac{1}{L_1} + \frac{1}{L_2} + {…} + \frac{1}{L_n} \\\) \(\text{or} \\\) \(L_{Total} = \frac{1}{\frac{1}{L_1} + \frac{1}{L_2} + {…} + \frac{1}{L_n}} \)

Also all the same short cut variations on the formula that worked for resistances also work for inductors:

For just two parallel inductors:

\(L_{Total} = \frac{L_1 \times L_2}{L_1 + L_2} \)

And for any number (n) of parallel inductors, all of the same value (x):

\(L_{Total} = \frac{L_{x}}{n} \)

Similarly, the current through any parallel branch is also calculated in a similar fashion to that of parallel resistors:

\(I_n = I_{Total} \times \frac{L_{Total} – L_n}{L_{Total}} \)