Inductive Reactance of a Coil
Important Formula
What do the formula symbols mean?
Inductive reactance
$$ \class{brown}{X_{\text L}} $$ Unit $$ \mathrm{\Omega} $$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 $$ \mathrm{Hz} = \frac{ 1 }{ \mathrm{s} } $$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
$$ \class{brown}{L} $$ Unit $$ \mathrm{H} = \frac{ \mathrm{Vs} }{ \mathrm{A} } $$If we apply an AC voltage \( U_{\text L}(t) \) to a coil of inductance \( L \) , then an AC current \( I_{\text L}(t) \) flows through the coil. The alternating voltage changes polarity with the frequency \(f\). With this frequency, the alternating current also changes its direction.
A coil to which an alternating voltage is applied has a complex nonohmic resistance which is called inductive reactance. This resistance is usually abbreviated as \( X_{\text L} \).
You can easily calculate the inductive reactance. You need the AC frequency \( f \) and the inductance \( L \) of the coil:
\(\pi\) is here a mathematical constant with the value \( \pi = 3.14 \). The unit of the inductive reactance is Ohm:
By the way, the factor \( 2 \, \pi \, f \) in Eq. 1
is often combined to angular frequency \( \omega \):

If you use a very large AC frequency, then the inductive reactance will also be very large and the coil will barely let the current through.

If, on the other hand, the AC voltage frequency is very small or even zero, that is if a DC voltage is applied, then the inductive reactance also becomes zero. The coil allows an arbitrarily high current to pass, which corresponds to a short circuit.
As you can see from Eq. 1
or 2
, you can also use the inductance \( L \) to adjust the reactance of the coil.