Define and give the formula for capacitive reactance.

• A. X_C = 1/(ωC); units in ohms, where ω = 2πf.
• B. X_C = ωL; where ω is angular frequency and L is inductance.
• C. X_C = R; resistance value independent of frequency.
• D. X_C = 1/(C) * ω; incorrect unit.

Answer: (A)

Capacitive reactance tells us how a capacitor opposes alternating current at a specific frequency. It is described by the formula X_C = 1/(ωC), where ω is the angular frequency (ω = 2πf). This shows the opposition gets smaller as either the frequency or the capacitance increases, so a capacitor looks less “blocked” to higher-frequency signals or larger capacitances. The units come out in ohms, which is consistent with how impedance is measured in AC circuits. In phasor form, a capacitor’s impedance is -jX_C, indicating a 90-degree phase shift between voltage and current.

Why this form is correct: the inverse relationship with both ω and C captures how a capacitor stores and releases charge over time, making it easier for higher-frequency currents to flow because the capacitor has less time to develop a large opposing voltage.

Other options don’t fit: inductive reactance uses ωL, not 1/(ωC); resistance R is not frequency-dependent; and multiplying ω by 1/C would give the wrong units and an incorrect relationship for reactance.