# Inductive Reactance of a Coil

**Level 2**requires school mathematics. Suitable for pupils.

## Video - Inductive reactance of a coil briefly explained

Subscribe on YouTube 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 non-ohmic 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:

**Formula: Inductive reactance**

\(\pi\) is here a mathematical constant with the value \( \pi = 3.14 \). The unit of the inductive reactance is Ohm:

**Unit of inductive reactance**$$ \begin{align} \left[ X_{\text L} \right] ~=~ \mathrm{\Omega} \end{align} $$

By the way, the factor \( 2 \, \pi \, f \) in Eq. 1

is often combined to **angular frequency** \( \omega \):

**Formula: Inductive reactance using angular frequency**

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.