Lag network (RC low-pass) — does the output voltage lag the input in phase?

Introduction / Context:Lag networks (often realized as RC low-pass filters with output taken across the capacitor) are used for phase lag and amplitude attenuation at higher frequencies. This question checks phase intuition for such networks.

Given Data / Assumptions:

• A passive RC network configured so that output is across the capacitor (classic lag configuration).
• Sinusoidal steady-state operation at frequency ω.

Concept / Approach:For an RC low-pass, the capacitor current leads the capacitor voltage by 90 degrees, but the capacitor voltage lags the input because the resistor introduces a voltage division with frequency-dependent phase. Thus, Vout (across C) lags Vin for ω > 0.

Step-by-Step Solution:

Verification / Alternative check:Phasor diagram: input phasor equals the vector sum of resistor and capacitor voltage phasors; the capacitor voltage trails the current by 90 degrees, placing it behind the input phasor in angle.

Why Other Options Are Wrong:

• “False” would imply the output does not lag; that contradicts both H(jω) angle and basic RC phasor relations when output is taken across C.

Common Pitfalls:Confusing lag vs lead networks. If output is taken across the resistor (RC high-pass), the output leads the input at many frequencies (lead network). The placement of the output node determines phase behavior.

Final Answer:True