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Reactance of a Capacitor

The instantaneous value p(t) of the power consumed by a capacitor is the product of the instantaneous current and voltage. Because these two variables are separated in phase by 90° in a capacitor, however, the power consumption characteristic has a frequency that is double that of the voltage and current themselves, as shown by the green curve in the diagram below. This characteristic comprises regions in which the voltage and current are in the same direction, causing the capacitor to act as a load, and regions of equally long duration where the voltage and current oppose each other so that the capacitor acts as a source of power (like a battery). 

CAPACITOR IN ALTERNATING CURRENT AC CIRCUITS !

The diagram represents consumption of energy as a positive value and regions where energy is being supplied as a negative value. In other words, the electrical energy alternates between capacitor-like and battery-like modes. With a resistive load, the power consumed is termed active power (in which case electrical energy is simply converted into heat energy), whereas for a capacitor the consumption is described in terms of reactive power. Instead of an ohmic resistance, the capacitor is said to have a reactance XC defined as the quotient of the rms voltage U and rms current I

CAPACITOR IN ALTERNATING CURRENT AC CIRCUITS !

The unit of reactance is the same as for an ohmic resistance, the ohm.

As indicated earlier, a capacitor's ability to "conduct" alternating current increases as the frequency rises and the capacitance increases. The formula for capacitive reactance is:

CAPACITOR IN ALTERNATING CURRENT AC CIRCUITS !

In qualitative terms:

Capacitive reactance decreases as the frequency and capacitance increase.

Example: at a mains frequency of f = 50 Hz, a 1 µF capacitor has a reactance of 

CAPACITOR IN ALTERNATING CURRENT AC CIRCUITS !

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