What is the formula for capacitive reactance, XC?

• A. ωC
• B. -1/ωC
• C. 1/ωC
• D. jωC

Answer: (B)

Capacitive reactance, denoted as ( X_C ), is defined as the opposition that a capacitor presents to the flow of alternating current (AC). The formula for capacitive reactance is given by:

[

X_C = \frac{1}{\omega C}

]

where ( \omega ) is the angular frequency in radians per second, and ( C ) is the capacitance in farads. This formula indicates that the capacitive reactance decreases with an increase in either frequency (( \omega )) or capacitance (( C )). In essence, a higher frequency or larger capacitor results in a lower opposition to AC flow, making it easier for the current to pass through.

The negative sign associated with the formula emphasizes that the phase of the current leads the phase of the voltage in a capacitive circuit, but it's important to note that the basic magnitude of reactance is given by the absolute value of ( X_C ), ignoring the negative sign when simply referencing capacitive reactance.

This understanding is essential for analyzing AC circuits, particularly in applications involving resonant circuits and filter designs. Recognizing that capacitive reactance is inversely proportional to frequency is critical when designing circuits that rely on specific frequency