An Introduction to Inductance and Self-Inductance
The coil: structure and self-induction
What is a coil?
A coil (or inductor) is an electrodynamic component consisting of a conductive wire wound into turns, usually around a core (air, soft iron, ferrite). Its electrical symbol represents a series of loops. Its characteristic quantity is the self-inductance L, expressed in henry (H).
Self-flux and self-induction
When a current i(t) flows through the coil, it creates a magnetic field B which, through the N turns, generates a self-flux: φ = L * i
As soon as i varies, this flux also varies, and Faraday’s law dictates the appearance of an induced electromotive force that opposes the change in current that produced it. This is the phenomenon of self-induction, characteristic of any inductive circuit.
Voltage-current relationship
In the ‘receiver’ convention, the voltage across an ideal coil is given by:
u(t) = L * di/dt
L depends solely on the geometry of the winding. For a solenoid with N turns, cross-sectional area S and length l, filled with a material of permeability μ:
L = μ * N² * S / l
Orders of magnitude
| Component | Typical inductance |
|---|---|
| Small electronic coil | 1 uH to 1 mH |
| Mains filter coil | a few mH |
| Transformer winding | several H |
Common pitfall
Do not confuse L (a constant, determined by the geometry) with u (a variable, which depends on di/dt and not on i). A coil through which a strong CONSTANT current flows has zero voltage across its terminals, whereas a weak current that varies very rapidly can generate an enormous voltage.