# Formula Inductive Reactance of a Coil Frequency Inductance

## Inductive reactance

`$$ \class{brown}{X_{\text L}} $$`Unit

`$$ \mathrm{\Omega} $$`

Inductive reactance is the complex component of the impedance (complex resistance). This reactance of the coil on the one hand inhibits the alternating current through the coil and on the other hand creates a phase shift between voltage \(U_{\text{L}}(t)\) and current \(I_{\text{L}}(t)\).

In the case of a DC circuit, the voltage frequency is \( f = 0 \). In this case, the induction coil has no reactance. Without an internal resistance, the coil would produce a short circuit when a DC voltage is applied to it.

## Frequency

`$$ f $$`Unit

`$$ \mathrm{Hz} = \frac{ 1 }{ \mathrm{s} } $$`

Frequency at which the AC voltage changes its polarity:

`$$ U_{\text{L}}(t) ~=~ U_0 \, \cos(2\pi\, f \, t) $$`The alternating current flowing through the coil also changes its direction at this frequency.

With the angular frequency \(\omega ~=~ 2\pi \, f\) the inductive reactance can be written as: `$$ X_{\text L} ~=~ \omega \, L $$`

## Inductance

`$$ L $$`Unit

`$$ \mathrm{H} $$`

Inductance is a characteristic quantity of a coil and describes how much magnetic flux it can enclose inside when a certain current flows through the coil. The higher the inductance \(L\), the greater the inductive reactance \( X_{\text L} \).