Inductors in Series

Inductors in series: total inductance

For inductors in series with no magnetic coupling, total inductance is the sum: Ltotal = L1 + L2 + ... + Ln. When mutual inductance M exists between coils, it becomes L = L1 + L2 ± 2M — sign depends on whether windings add or oppose flux. The coupling coefficient is k = M / √(L1·L2), with 0 ≤ k ≤ 1 (k=1 means perfect coupling, as in an ideal transformer). Energy stored: E = ½·L·I². In AC, inductive reactance XL = 2π·f·L grows with frequency, so series inductors block high-frequency signals. Example: 10 mH + 22 mH with no mutual coupling → 32 mH.

Applications: filters, chokes and antennas

Series inductors appear in LC band-pass filters at radio frequencies, RF chokes blocking AC while passing DC, fluorescent lamp ballasts (being phased out by LEDs), loop antennas, and audio output transformers in valve amplifiers. Switching power supplies use series inductors in buck/boost topologies to smooth current.

FAQ

What if two coils are close together? They may couple magnetically. Place them perpendicular, far apart, or use shielded inductors (toroidal cores) to minimize M.

Does the order matter? No — series total is the same regardless of position. Only the mutual coupling between adjacent coils changes.

How is this different from resistors? Series resistors and inductors both add. But inductors also store energy in a magnetic field and oppose current changes (Lenz's law).