Final answer:
The correct statement for large ω in an RLC circuit is A. Vout/Vin is proportional to 1/ω. This is because, at high frequencies, the inductive reactance dominates, causing the output voltage to drop with increasing frequency.
Step-by-step explanation:
The student's question involves the behavior of circuits with resistors (R), inductors (L), and capacitors (C) at high frequencies. The correct answer to which statement is true in the limit of large ω (frequency) for an RLC circuit is the one that reflects the behavior of the output voltage (Vout) relative to the input voltage (Vin) based on the reactance of inductors and capacitors at high frequency.
Inductive reactance (XL) increases with frequency, as XL = 2πfL. Capacitive reactance (Xc) decreases with frequency, as Xc = 1/(2πfC). When ω is much greater than 1/RC and 1/√(LC), the capacitive reactance becomes very small, and the inductive reactance becomes very large, resulting in a circuit behavior where Vout/Vin is proportional to 1/ω because the output voltage drops with increasing frequency due to the dominate inductive reactance.
Therefore, the correct statement for a large ω in an RLC circuit is A. Vout/Vin is proportional to 1/ω, as this accurately reflects the high frequency behavior of such circuits where the inductor's opposition to the change in current is significant.