If the frequency doubles, what happens to the capacitive reactance X_C = 1/(ω C)?

• A. Doubles
• B. Halves
• C. Stays the same
• D. Becomes zero

Answer: (B)

Capacitive reactance is inversely related to how fast the voltage changes, so it goes down as frequency goes up. The formula is X_C = 1/(ω C), with ω = 2π f. If the frequency doubles, ω doubles, giving X_C' = 1/(2ω C) = (1/2) X_C. So the reactance becomes half. This also highlights that at very high frequencies, X_C gets very small, tending toward zero only in the theoretical limit of infinite frequency.