RC high-pass behavior — as input frequency decreases, does the output voltage magnitude of a simple RC high-pass filter increase or decrease?

Introduction / Context:
High-pass filters are ubiquitous in coupling networks, audio systems, and sensor interfaces. Their defining characteristic is that they pass high-frequency content while attenuating low-frequency components and DC. This question probes your qualitative understanding of how output changes with frequency.

Given Data / Assumptions:

• Single-pole RC high-pass filter (series capacitor, shunt resistor or equivalent topology).
• Sinusoidal steady-state behavior.
• No significant load interaction beyond the intended resistor.

Concept / Approach:
In a high-pass RC network, the capacitor’s reactance Xc = 1 / (omega * C) is large at low frequencies and small at high frequencies. The transfer function magnitude |H(jomega)| increases with frequency, approaching unity at very high frequency and approaching zero at very low frequency. Therefore, as frequency decreases, output voltage magnitude falls, not rises.

Step-by-Step Solution:

Verification / Alternative check:
Check the -3 dB cutoff f_c = 1 / (2 * pi * R * C). Below f_c, output rolls off at about -20 dB/decade (first order). Above f_c, output asymptotically approaches full scale.

Why Other Options Are Wrong:

• “Output increases as frequency decreases” contradicts high-pass behavior.
• “Only when load is inductive” is irrelevant to the basic trend; standard topology already determines the response.
• “Undetermined” is not correct; the qualitative direction is known without exact values.

Common Pitfalls:
Mixing up high-pass with low-pass or overlooking the role of the series capacitor as a frequency-dependent coupling element.

Final Answer:
Incorrect — the output of an RC high-pass decreases as frequency decreases.