# Capacitive reactance of a capacitor

Level 2 (suitable for students)
Level 2 requires school mathematics. Suitable for pupils.
Updated by Alexander Fufaev on

## Video - Capacitive reactance of a capacitor briefly explained

If we apply an AC voltage $$U_{\text C}(t)$$ to a capacitor of capacitance $$C$$, then an AC current $$I_{\text C}(t)$$ flows through the capacitor. The alternating voltage changes polarity with the frequency $$f$$. With this frequency, the alternating current also changes its direction.

A capacitor to which an alternating voltage is applied has a complex non-ohmic resistance which is called capacitive reactance $$X_{\text C}(t)$$.

Du kannst den kapazitiven Blindwiderstand ganz einfach berechnen. Du brauchst dafür lediglich die Wechselspannungsfrequenz $$f$$ und die Kondensator-Kapazität $$C$$:

Formula: Capacitive reactance
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$$\pi$$ is a mathematical constant with the value $$\pi = 3.14$$. The minus sign in the formula states, that the alternating voltage at a capacitor lags behind the alternating current.

The unit of capacitive reactance is Ohm:

Unit of capacitive reactance

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

Formula: Capacitive reactance using angular frequency
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• If you use a very large AC frequency, then the capacitive reactance becomes very small and the capacitor easily lets the current through.

• If, on the other hand, the AC voltage frequency is very low or even zero, i.e. if a DC voltage is applied, then the capacitive reactance becomes infinitely large. The capacitor does not allow any current to pass.

As you can see from Eq. 1 or 2, you can also use the capacitance $$C$$ to adjust the reactance $$X_{\text C}$$ of the capacitor.

When we work with rms values of voltage and current, we are usually only interested in the magnitude $$|X_{\text C}|$$ of the capacitive reactance:

Formula: Magnitude of the capacitive reactance
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