Compare the reactance of a capacitor of 0.4 myu faraday at hz and 1 khz
Answers
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. But 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 impedance of the capacitor. This internal impedance is commonly known as Capacitive Reactance and is given the symbol XC in Ohms.
Unlike resistance which has a fixed value, for example, 100Ω, 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 capacitor’s, “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 capacitor’s complex impedance.
Complex impedance exists because the electrons in the form of an electrical charge on the capacitor plates, appear to 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 impedance 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
capacitive circuit capacitive reactance
Capacitive Reactance Formula
Where:
Xc = Capacitive Reactance in Ohms, (Ω)
π (pi) = 3.142 (decimal) or as 22÷7 (fraction)
ƒ = Frequency in Hertz, (Hz)
C = Capacitance in Farads, (F)
Capacitive Reactance Example No1
Calculate the capacitive reactance value of a 220nF capacitor at a frequency of 1kHz and again at a frequency of 20kHz.
At a frequency of 1kHz:
capacitive reactance equation
Again at a frequency of 20kHz:
reactance formula
where: ƒ = frequency in Hertz and C = capacitance in Farads
Therefore, it can be seen from above that as the frequency applied across the 220nF capacitor increases, from 1kHz to 20kHz, its reactance value, XC decreases, from approx 723Ω to just 36Ω and this is always true as capacitive reactance, XC is inversely proportional to frequency with the current passed by the capacitor for a given voltage being proportional to the frequency.
For any given value of capacitance, the reactance of a capacitor, XC expressed in ohms can be plotted against the frequency as shown below.