Capacitive Reactance of a Capacitor Simply Explained
Formula
What do the formula symbols mean?
Capacitive reactance
$$ \class{purple}{X_{\text C}} $$ Unit $$ \mathrm{\Omega} $$In the case of a DC circuit, the voltage frequency is \( f = 0 \). In this case, the capacitor has an infinite reactance and thus the capacitor does not conduct current.
Frequency
$$ f $$ Unit $$ \mathrm{Hz} = \frac{ 1 }{ \mathrm{s} } $$The alternating current flowing through the capacitor also changes direction at this frequency.
With the angular frequency \(\omega ~=~ 2\pi \, f\) the capacitive reactance can be written as: $$ X_{\text C} ~=~ \frac{1}{\omega \, C} $$
Capacitance
$$ C $$ Unit $$ \mathrm{F} = \frac{ \mathrm{C} }{ \mathrm{V} } $$Video
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 nonohmic 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 KondensatorKapazität \(C\):
\(\pi\) 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:
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 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: