Final answer:
Capacitive reactance is inversely proportional to frequency, meaning it decreases as frequency increases, and is calculated using the formula Xc = 1 / (2πfC). Capacitors impede lower frequencies more and allow higher frequencies to pass more easily.
Step-by-step explanation:
The relationship between capacitive reactance (Xc) and frequency (f) is that capacitive reactance is inversely proportional to frequency. This means as the frequency of the alternating current (AC) increases, the capacitive reactance decreases. The formula to calculate capacitive reactance is Xc = 1 / (2πfC), where π is pi (approximately 3.14159), f is the frequency in hertz, and C is the capacitance in farads. Capacitors impede current more at lower frequencies because there is more time to become charged and block the current. At higher frequencies, the reactance of the capacitor is smaller, allowing a larger current to flow through.
Capacitors and inductors react oppositely to frequency changes: while capacitors impede low frequencies more, inductors impede high frequencies more. This characteristic is critical in applications such as filters where capacitors may be used to remove low-frequency noise from signals, such as the 60 Hz hum in a sound system.