# Inductor

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Related wiki pages: Electronic Theory, Capacitors, Resistors, Impedance

An inductor is a device that stores energy in a magnetic field. Inductors are short circuits to DC current, but their impedance rises as AC current passing through them has its frequency increased. Extremely high frequency currents see inductors as open circuits.

In some ways, inductors behave as the opposite of capacitors. This property is critically important to the circuit design of oscillators.

Fundamentally, inductors consist of a conductor, which is usually wrapped into a coil. Many inductors have an insulator inside the coil that has magnetic properties that raise the inductance. Such materials include powdered iron toroids and ferrite toroids.

## Inductance

Inductance (L), measured in henries (H) is the effect which results from the magnetic field around a current-carrying conductor. Current flowing 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.

## Inductive Reactance

The impedance of an inductor is given by the formula

$Z = j \omega L \,$

where $Z\,$ is the impedance, $\omega\,$ is $2 \pi f\,$, and $f\,$ is the frequency. $j\,$ is "operator j" from phasor analysis.

In practical terms this leads to:

$X_c = 2 \pi F L$ where:

• $X_c$ is capacitive reactance
• F is the frequency of operation in Hertz
• L is the inductance in Henries

## Inductor formulae

Construction Formula Dimensions
Cylindrical coil $L=\frac{\mu_0\mu_rN^2A}{l}$
• L = inductance in henries (H)
• μ0 = permeability of free space = 4$\pi$ × 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 $L = l\left(\ln\frac{4l}{d}-1\right) \cdot 200 \times 10^{-9}$
• L = inductance (H)
• l = length of conductor (m)
• d = diameter of conductor (m)
$L = 5.08 \cdot l\left(\ln\frac{4l}{d}-1\right)$
• L = inductance (nH)
• l = length of conductor (in)
• d = diameter of conductor (in)
Short air-core cylindrical coil $L=\frac{r^2N^2}{9r+10l}$
• L = inductance (µH)
• r = outer radius of coil (in)
• l = length of coil (in)
• N = number of turns
Multilayer air-core coil $L = \frac{0.8r^2N^2}{6r+9l+10d}$
• 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 $L=\frac{r^2N^2}{(2r+2.8d) \times 10^5}$
• L = inductance (H)
• r = mean radius of coil (m)
• N = number of turns
• d = depth of coil (outer radius minus inner radius) (m)
$L=\frac{r^2N^2}{8r+11d}$
• 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) $L=\mu_0\mu_r\frac{N^2r^2}{D}$
• L = inductance (H)
• μ0 = permeability free space = 4$\pi$ × 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)

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