Inductors in Series
When inductors are connected in series (end to end in a single path), their inductances add directly, similar to resistors in series. The total inductance is simply the sum of all individual inductances. This is because the same current flows through each inductor, and the total voltage is the sum of the voltages across each inductor.
This assumes there is no mutual inductance (magnetic coupling) between the inductors. If inductors are placed close together, mutual inductance can either increase or decrease the total inductance depending on the orientation of the magnetic fields.
Series Inductor Formulas
Series vs Parallel Inductors
| Property | Series | Parallel |
|---|---|---|
| Total Inductance | L₁ + L₂ + ... | 1/(1/L₁ + 1/L₂ + ...) |
| Current | Same through all | Divided among branches |
| Voltage | Sum of individual | Same across all |
| Total L | Always larger | Always smaller |
| Analogy | Like resistors in series | Like resistors in parallel |
Frequently Asked Questions
Does the order of inductors matter in series?
No, the order of inductors in a series connection does not affect the total inductance. Addition is commutative, so L1 + L2 = L2 + L1. However, the physical placement can matter if mutual inductance exists between nearby inductors.
What is inductive reactance?
Inductive reactance (XL) is the opposition to alternating current flow provided by an inductor. It increases with both frequency and inductance: XL = 2*pi*f*L. At DC (f = 0), an ideal inductor has zero reactance (acts as a short circuit). At high frequencies, reactance becomes very large.
What happens to energy storage in series inductors?
The total energy stored in series inductors carrying current I is E = (1/2)*L_total*I^2. Since L_total is larger for series connections, series inductors store more total energy than a single inductor for the same current. Each inductor stores energy proportional to its individual inductance.