Inductor

Inductance

Inductance (L), measured in henries (H) is the effect which results from the magnetic field around a current-carrying conductor. Current through the conductor creates a magnetic flux proportional to the current. A change in this current creates a change in magnetic flux that, in turn, generates an electromotive force (EMF) that acts to oppose this change in current. Inductance is a measure of the amount of EMF generated for a unit change in current.

Inductor formulae

Construction	Formula	Dimensions
Cylindrical coil	<math>L=\frac{\mu_0\mu_rN^2A}{l}</math>	L = inductance in henries (H) μ0 = permeability of free space = 4<math>\pi</math> × 10-7 H/m μr = Relative permeability of core material N = number of turns A = area of cross-section of the coil in square metres (m2) l = length of coil in metres (m)
Straight wire conductor	<math>L = l\left(\ln\frac{4l}{d}-1\right) \cdot 200 \times 10^{-9}</math>	L = inductance (H) l = length of conductor (m) d = diameter of conductor (m)
	<math>L = 5.08 \cdot l\left(\ln\frac{4l}{d}-1\right)</math>	L = inductance (nH) l = length of conductor (in) d = diameter of conductor (in)
Short air-core cylindrical coil	<math>L=\frac{r^2N^2}{9r+10l}</math>	L = inductance (µH) r = outer radius of coil (in) l = length of coil (in) N = number of turns
Multilayer air-core coil	<math>L = \frac{0.8r^2N^2}{6r+9l+10d}</math>	L = inductance (µH) r = mean radius of coil (in) l = physical length of coil winding (in) N = number of turns d = depth of coil (outer radius minus inner radius) (in)
Flat spiral air-core coil	<math>L=\frac{r^2N^2}{(2r+2.8d) \times 10^5}</math>	L = inductance (H) r = mean radius of coil (m) N = number of turns d = depth of coil (outer radius minus inner radius) (m)
	<math>L=\frac{r^2N^2}{8r+11d}</math>	L = inductance (µH) r = mean radius of coil (in) N = number of turns d = depth of coil (outer radius minus inner radius) (in)
Toroidal core (circular cross-section)	<math>L=\mu_0\mu_r\frac{N^2r^2}{D}</math>	L = inductance (H) μ0 = permeability free space = 4<math>\pi</math> × 10-7 H/m μr = relative permeability of core material N = number of turns r = radius of coil winding (m) D = overall diameter of toroid (m)