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Capacitive Reactance

In the RC Network tutorial we saw that when a DC voltage is applied to a capacitor, the capacitor itself draws a charging current from the supply and charges up to a value equal to the applied voltage. Likewise, when the supply voltage is reduced the charge stored in the capacitor also reduces and the capacitor discharges.

In an AC circuit in which the applied voltage signal is continually changing from a positive to a negative polarity at a rate determined by the frequency of the supply, as in the case of a sine wave voltage, for example. The capacitor is either being charged or discharged on a continuous basis at a rate determined by the frequency. As the capacitor ...view middle of the document...

Capacitive Reactance has the electrical symbol "Xc" and has units measured in Ohms the same as resistance, ( R ). It is calculated using the following formula:

Capacitive Reactance

Capacitive Reactance Formula

• Where:

• Xc = Capacitive Reactance in Ohms, (Ω)

• π (pi) = 3.142 or 22/7

• ƒ = Frequency in Hertz, (Hz)

• C = Capacitance in Farads, (F)

Example No1

Calculate the capacitive reactance of a 220nF capacitor at a frequency of 1kHz and again at 20kHz.

At a frequency of 1kHz,

Again at a frequency of 20kHz,

where: ƒ = frequency in Hertz and C = capacitance in Farads

It can be seen that as the frequency applied to our 220nF capacitor increases from 1kHz to 20kHz, its reactance decreases from approx 723Ωs to just 36Ωs. For any given value of capacitance the reactance of a capacitor can be plotted against the frequency as shown below.

Capacitive Reactance against Frequency

By re-arranging the reactance formula above, we can also find at what frequency a capacitor will have a particular capacitive reactance ( XC ) value.

Example No1 - At which frequency would a 2.2uF Capacitor have a reactance value of 200Ωs?

Or we can find the value of the capacitor in Farads by knowing the applied frequency and its reactance value at that frequency.

Example No2 - What will be the value of a Capacitor in farads when it has a capacitive reactance of 200Ω and is connected to a 50Hz supply.

We can see from the above examples that a capacitor when connected to a variable frequency supply, acts a bit like a "frequency controlled variable resistor". At very low frequencies, such as 1Hz our 220nF capacitor has a high capacitive reactance value of approx 723KΩs (giving the effect of an open circuit). At very high frequencies such as 1Mhz the capacitor has a low capacitive reactance value of just 0.7 ohms (giving the effect of a short circuit). At zero frequency or steady state DC the capacitor has infinite reactance looking more like an "open-circuit" between the plates and blocking any flow of current through it.

Voltage Divider Revision

We remember from our tutorial about Resistors in Series that different voltages...

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