CAPACITORS AND AC

Suppose that the power source connected to a capacitor is changed from dc to ac. Imagine that you can adjust the frequency of this ac from a low initial value of a few hertz up to hundreds of hertz, then to many kilohertz, and finally to many megahertz or gigahertz. At first, the voltage between the plates follows along with the voltage of the power source as the source polarity reverses over and over. However, the set of plates has a certain amount of capacitance. The plates can charge up fast if they are small and if the space between them is large, but they can’t charge instantaneously. As you increase the frequency of the ac source, there comes a point at which the plates do not get charged up very much before the source polarity reverses. The set of plates becomes sluggish. The charge does not have time to get established with each ac cycle. At high ac frequencies, the voltage between the plates has trouble following the current that is charging and discharging them. Just as the plates begin to get a good charge, the ac current passes its peak and starts to discharge them, pulling electrons out of the negative plate and pumping electrons into the positive plate. As the frequency is raised, the set of plates starts to act more and more like a short circuit. Eventually, if you keep on increasing the frequency, the period of the wave is much shorter than the charging-discharging time, and current flows in and out of the plates in the same way as it would flow if the plates were shorted out.
Capacitive reactance is a quantitative measure of the opposition that the set of plates offers to ac. It is measured in ohms, just like inductive reactance and just like resistance. However, by convention, it is assigned negative values rather than positive ones. Capacitive reactance, denoted X_C in mathematical formulas, can vary from near zero (when the plates are huge and close together and/or the frequency is very high) to a few negative ohms to many negative kilohms or megohms. Capacitive reactance varies with frequency. It gets larger negatively as the frequency goes down and smaller negatively as the frequency goes up.
This is the opposite of what happens with inductive reactance, which gets larger (positively) as the frequency goes up. Sometimes capacitive reactance is talked about in terms of its absolute value, with the minus sign removed. Then you might say that X_C increases as the frequency decreases or that X_C diminishes as the frequency is raised. However, it is best if you learn to work with negative X_C values from the start.