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

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Multiple Choice

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

Explanation:
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.

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.

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