Inductance is a fundamental property of an electrical component called an inductor, which opposes changes in current flow through it. It is typically represented by the symbol L and is measured in henries (H).

When current flows through an inductor, it generates a magnetic field around it. The strength of this magnetic field is directly proportional to the current flowing through the inductor and the number of turns in the coil. The inductance of the coil is a measure of the amount of magnetic flux generated per unit of current.

Equation

The formula for calculating the inductance of a coil is given by:

$$L_{coil} = \frac{ \mu_{r}  \mu_{0}  N^{2}  A}{l} = \frac{ \mu_{r} \mu_{0} N^{2} \pi r^2}{l}$$

Where:

L_coil = inductance of the coil in henries (H)

μ_r = relative permeability of the core (dimensionless)

μ₀ = permeability of free space = 4π×10^-7 H/m

N = number of turns

A = coil area (m²)

r = coil radius (m)

l = coil length (m)

This formula essentially states that the inductance is directly proportional to the square of the number of turns and the cross-sectional area of the coil, and inversely proportional to the length of the coil.

In practice, for simpler cases where the coil has a uniform winding density and is not affected by factors like the shape of the coil or the magnetic properties of a core material, this formula provides a good approximation for calculating the inductance. However, for more complex coil geometries or inductors with magnetic cores, additional factors need to be considered in the calculation.

Series and Parallel Inductance Calculator