Which statement correctly describes how X_L and X_C change as angular frequency ω increases?

Which statement correctly describes how X_L and X_C change as angular frequency ω increases?

• A. X_L decreases with frequency; X_C increases; at high ω the circuit becomes capacitive
• B. X_L increases with frequency; X_C decreases with frequency; at high ω the circuit becomes inductive
• C. X_L constant; X_C constant; resonance occurs when L equals C
• D. X_L decreases; X_C decreases; at high ω the circuit becomes nonreactive

Answer: (B)

Inductive reactance grows with frequency while capacitive reactance falls. Specifically, X_L = ωL increases as ω increases, and X_C = 1/(ωC) decreases as ω increases. In a circuit where these two reactances oppose each other, the net reactance is X = X_L − X_C. At high frequencies, X_L dominates (it becomes large while X_C becomes small), so the net reactance is positive and the circuit behaves inductively. The other statements misstate how each reactance depends on frequency or when resonance occurs, so the best description is that X_L increases with frequency, X_C decreases with frequency, and the high-frequency behavior is inductive.

Inductive reactance grows with frequency while capacitive reactance falls. Specifically, X_L = ωL increases as ω increases, and X_C = 1/(ωC) decreases as ω increases. In a circuit where these two reactances oppose each other, the net reactance is X = X_L − X_C. At high frequencies, X_L dominates (it becomes large while X_C becomes small), so the net reactance is positive and the circuit behaves inductively. The other statements misstate how each reactance depends on frequency or when resonance occurs, so the best description is that X_L increases with frequency, X_C decreases with frequency, and the high-frequency behavior is inductive.