# Formula Capacitive Reactance of a Capacitor Capacitive reactance Frequency Capacitance

## Capacitive reactance

`$$ X_{\text C} $$`Unit

`$$ \mathrm{\Omega} $$`

Capcitive reactance is the complex part of the capacitor impedance (complex resistance). This capacitance reactance, on the one hand, allows the alternating current to flow through the capacitor and, on the other hand, it creates a phase shift between voltage \(U_{\text{C}}(t)\) and current \(I_{\text{C}}(t)\).

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

`$$ \mathrm{Hz} = \frac{ 1 }{ \mathrm{s} } $$`

Frequency at which the AC voltage applied to the capacitor changes its polarity:

`$$ U_{\text{C}}(t) ~=~ U_0 \, \cos(2\pi\, f \, t) $$`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

`$$ \mathrm{F} = \frac{ \mathrm{C} }{ \mathrm{V} } $$`

It is a characteristic quantity of the capacitor and tells how many charges must be brought onto the capacitor to charge the capacitor to the voltage \( 1 \, \text{V} \).