# Inductive Reactance of a Coil

Level 2 (without higher mathematics)
Level 2 requires school mathematics. Suitable for pupils.
Updated by Alexander Fufaev on

## Video - Inductive reactance of a coil briefly explained

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 anchor

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

Unit of inductive reactance
Formula anchor

By the way, the factor $$2 \, \pi \, f$$ in Eq. 1 is often combined to angular frequency $$\omega$$:

Formula: Inductive reactance using angular frequency
Formula anchor
• 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.