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Capacitive reactance of a capacitor

AC circuit with a capacitive reactance of the capacitor
Level 2 (without higher mathematics)
Level 2 requires school mathematics. Suitable for pupils.
Updated by Alexander Fufaev on

Video - Capacitive reactance of a capacitor briefly explained

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AC voltage applied to a capacitor
A time-dependent alternating voltage is applied to a capacitor.

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 \(C\):

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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.

Graph: AC voltage and current at capacitor
The minus sign in the capacitive reactance causes a phase shift between current and voltage at the capacitor.

The unit of capacitive reactance is Ohm:

Unit of capacitive reactance
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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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Example: Calculate reactance of the capacitor

You apply a voltage of \( 230 \, \mathrm{V} \) to a capacitor with a capacitance of \(10 \, \mathrm{nF} \). The voltage has a frequency of \(50 \, \mathrm{Hz} \). Insert the values into the formula 3:

Example calculation: Capacitive reactance
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To determine the rms current \(I_{\text{eff}}\) flowing through the capacitor, use the URI formula. Instead of using the ohmic resistance R, use the capacitive reactance \(X_{\text C}\). Rearrange the URI formula according for the current:

Formula: RMS current using capacitive resistance
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Insert the \(230 \, \mathrm{V} \) rms voltage and \( 318 \, \mathrm{k\Omega} \), then you get the rms current:

Example calculation: Determine rms current using capacitive reactance
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