Final answer:
The capacitance needed for a certain reactance changes with frequency; larger capacitance is required at lower frequencies to achieve high reactance, which is used in Low Pass Filters, and reactance decreases at higher frequencies, allowing signals through as seen in High Pass Filters.
Step-by-step explanation:
Understanding Capacitor Reactance for Low and High Frequencies
The question pertains to the reactance of a capacitor at different frequencies and the subsequent implications for signal filtering in circuits. To calculate the capacitor's reactance (XC) needed at a specific frequency, the formula XC = 1/(2πfC) is used, where f is the frequency in hertz (Hz) and C is the capacitance in farads (F). This formula is derived from the capacitive reactance concept in AC circuits.
(a) To find the capacitance that produces a 100kΩ reactance at 120Hz, we rearrange the formula: C = 1/(2πfXC). Plugging in the values gives us C = 1/(2π × 120 × 100,000) = 1/(2π × 12,000,000) F.
(b) The reactance of the same capacitor at 1.00MHz would be found using the original formula XC = 1/(2πfC), plugging in the frequency of 1.00MHz.
(c) The implications of the answers to parts (a) and (b) shed light on how a capacitor's reactance varies inversely with frequency, impacting its ability to filter signals at both low and high frequencies. At low frequencies, a larger capacitance is required to achieve a high reactance, thereby blocking or impeding signals, which is useful for Low Pass Filters (LPF). At higher frequencies, the reactance decreases, allowing signals to pass through more easily, which is a characteristic desirable in High Pass Filters (HPF).