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 supply frequency.

As the capacitor charges or discharges, a current flows through it which is restricted by the internal resistance of the capacitor. This internal resistance is commonly known as **Capacitive Reactance** and is given the symbol X_{C} in Ohms.

Unlike resistance which has a fixed value, for example, 100Ωs, 1kΩ, 10kΩ etc, (this is because resistance obeys Ohms Law), **Capacitive Reactance** varies with the applied frequency so any variation in supply frequency will have a big effect on the capacitors, “capacitive reactance” value.

As the frequency applied to the capacitor increases, its effect is to decrease its reactance (measured in ohms). Likewise as the frequency across the capacitor decreases its reactance value increases. This variation is called the capacitors **complex impedance**.

Complex impedance exists because the electrons in the form of an electrical charge on the capacitor plates, pass from one plate to the other more rapidly with respect to the varying frequency.

As the frequency increases, the capacitor passes more charge across the plates in a given time resulting in a greater current flow through the capacitor appearing as if the internal resistance of the capacitor has decreased. Therefore, a capacitor connected to a circuit that changes over a given range of frequencies can be said to be “Frequency Dependant”.

**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 Formula |

- Where:
- Xc = Capacitive Reactance in Ohms, (Ω)
- π (pi) = 3.142 (decimal) or 22÷7 (fraction)
- ƒ = Frequency in Hertz, (Hz)
- C = Capacitance in Farads, (F)

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

Therefore, it can be seen from above 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.

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

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.

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 723.3KΩs (giving the effect of an open circuit).

At very high frequencies such as 1Mhz the capacitor has a low capacitive reactance value of just 0.72Ω (giving the effect of a short circuit). So at zero frequency or steady state DC our 220nF capacitor has infinite reactance looking more like an “open-circuit” between the plates and blocking any flow of current through it.

We remember from our tutorial about Resistors in Series that different voltages can appear across each resistor depending upon the value of the resistance and that a voltage divider circuit has the ability to divide its supply voltage by the ratio of R2/(R1+R2). Therefore, when R1 = R2 the output voltage will be half the value of the input voltage. Likewise, any value of R2 greater or less than R1 will result in a proportional change to the output voltage. Consider the circuit below.

We now know that a capacitors reactance, Xc (its complex impedance) value changes with respect to the applied frequency. If we now changed resistor R2 above for a capacitor, the voltage drop across the two components would change as the frequency changed because the reactance of the capacitor affects its impedance.

The impedance of resistor R1 does not change with frequency. Resistors are of fixed values and are unaffected by frequency change. Then the voltage across resistor R1 and therefore the output voltage is determined by the capacitive reactance of the capacitor at a given frequency. This then results in a frequency-dependent RC voltage divider circuit. With this idea in mind, passive **Low Pass Filters** and **High Pass Filters** can be constructed by replacing one of the voltage divider resistors with a suitable capacitor as shown.

The property of **Capacitive Reactance**, makes capacitors ideal for use in AC filter circuits or in DC power supply smoothing circuits to reduce the effects of any unwanted Ripple Voltage as the capacitor applies an short circuit signal path to any unwanted frequency signals on the output terminals.

So, we can summarize the behaviour of a capacitor in a variable frequency circuit as being a sort of frequency controlled resistor that has a high capacitive reactance value (open circuit condition) at very low frequencies and low capacitive reactance value (short circuit condition) at very high frequencies as shown in the graph above.

It is important to remember these two conditions and in our next tutorial about the Passive Low Pass Filter, we will look at the use of **Capacitive reactance** to block any unwanted high frequency signals while allowing only low frequency signals to pass.

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very good and informative site..keep going and include more topics..

These are wonderful tutorials. Any chance you could create downloadable pdfs so they can be read off-line for personal sue only?

Hello Jerry, I have created a pdf eBook available to download from the front page

Interesting and informative, helps me to understand better.

The link to the pdf eBook gives an HTTP 404 error and I was unable to find the pdf eBook on the front page.

Is this pdf eBook still available for download? If it is please indicate download location.

Thanks.

Hello Franz. That’s very strange. I have checked and download the eBook without errors and other people have also download it today. Please try again. If you still have problems email me at: wayne@electronics-tutorials.ws

This was very helpful and informative. I am currently studying Digital Fundamentals and have taking a boebot class along with a class on DC. Im sorta taking a crash course on AC because I am doing a project that has to involve using trig, so i will be using sin wave to see what is happening to the NOTE A at 330 hz. This was helpful for me to understand some basic terminology. I will explore more threads in your website. thanks!

the information are so good at this page am enjoying with electronics

its great ….. so easy to understand ….. but also give some conceptuational questions i need them …..

Now It’s very easy to understand

me concepts, THANKS.. .

ALL INFORMATION ARE TRUE AND UNDERSTABLE TO READ….

Stop shouting ! But I agree with you 🙂

Thank you

i have a RC discharging circuit

the specification of capacitor is V= 2Volts

C= 1000uF

ESR= .131 ohm

and the resistance attached to the capacitor is 1 ohm

My question is while calculating maximum instantaneous current in the circuit should we take ESR value of the capacitor???

AND what will be the maximum current ??

The equivalent series resistance (ESR) of a capacitor is its ac resistance reflecting both the series resistance (Rs) and the parallel resistance (Rp) at a given frequency making it frequency sensitive. ESR is a measure of how much the capacitor deviates from a mathematically pure capacitance. Ideally, the ESR of a capacitor should be zero.

However, ESR develops a voltage drop and power loss across the resistive part of the capacitor impedance which results in a temperature rise within the capacitor, and it is this dissipation which limits the capacitor’s I^2R rating. In your case about 30W. Then yes ESR needs to be taken into account.

VERY GOOD..

IFORMATIVE.