22.4 Capacitive Reactance (cont'd)

In a DC circuit, there is no current through a capacitor -- or through this simple circuit that contains a capacitor.

However, in an AC circuit, there will be a current through this simple capacitor circuit. The capacitor will start to build up a charge, and countervoltage, and then the AC voltage will change and the capacitor will discharge and start to build up an opposite charge.

In a simple resistor circuit, we defined the resistance R by

V = I R

We would like to do something with a similar form for this capacitor circuit. In a similar fashion, we can write


where VC is the maximum voltage across the capacitor and I is the maximum current through the circuit. XC is called the "capacitive reactance"; it is analogous to resistance and is also measured in ohms (). The amount of current through this circuit -- and, hence, the value of the capacitive reactance -- depends upon the frequency of the AC power supply. A low-frequency AC voltage will quickly charge up the capacitor so much that there will be very little current. Of course, a DC voltage is the limiting case or the ultimate low frequency and then there is no current at all. A high-frequency AC voltage will only begin to charge the capacitor before it reverses direction and discharges the capacitor so there will be a larger current. That is, the capacitive reactance will be large for low frequencies and small for high frequencies. The capacitive reactance is given by

Unlike the case for a resistor, the voltage and current in this simple capacitor circuit are not in phase. That is, they do not have their maximum values at the same time and they do not go to zero at the same time.

We describe this situation for a capacitor by saying the current leads the voltage. That means the current reaches a maximum value before the voltage reaches its maximum value.

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Inductive Reactance

(c) Doug Davis, 2002; all rights reserved