REACTANCE AND FREQUENCY

Capacitive reactance behaves in many ways like a mirror image of inductive reactance. In another sense, however, X_C is an extension of X_L into negative values—below zero—with its own peculiar set of characteristics. If the frequency of an ac source is given in hertz as f and the capacitance of a capacitor in farads is given as C, then the capacitive reactance is
X_C=-1/(2πfC) = -(2πfC)^-1 ≈ -(6.2832fC)^-1
This same formula applies if the frequency is in megahertz (MHz) and the capacitance is in microfarads (μF). Remember that if the frequency is in millions, the capacitance must be in millionths. This formula also would apply for frequencies in kilohertz (kHz) and millifarads (mF), but for some reason, you’ll almost never see millifarads used in practice. Even millifarads are large units for capacitance; components of more than 1,000 μF (which would be 1 mF) are rarely found in real-world electrical systems.
Capacitive reactance varies inversely with the frequency. This means that the function X_C versus f appears as a curve when graphed, and this curve “blows up negatively” as the frequency nears zero. Capacitive reactance also varies inversely with the actual value of capacitance given a fixed frequency. The function of X_C versus C also appears as a curve that “blows up negatively” as the capacitance approaches zero. The negative of X_C is inversely proportional to frequency, as well as to capacitance. Relative graphs of these functions are shown in Fig. 1.

Fig. 1. Capacitive reactance is inversely proportional to the negative of the capacitance, as well as to the negative of the frequency.