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 anchor$$ \begin{align} \class{purple}{X_{\text C}} ~=~ -\frac{1}{2\pi \, f \, \class{purple}{C}} \end{align} $$

\(\pi\) 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.

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

Formula anchor$$ \begin{align} |X_{\text C}| ~=~ \frac{1}{2\,\pi \, f \, C} \end{align} $$

+ Perfect for high school and undergraduate physics students + Contains over 500 illustrated formulas on just 140 pages + Contains tables with examples and measured constants + Easy for everyone because without vectors and integrals