RC high-pass behavior — as input frequency decreases, does the output voltage magnitude of a simple RC high-pass filter increase or decrease?
-
AIncorrect — the output decreases at low frequencies because the capacitor blocks slow changes.
-
BCorrect — the output increases as frequency decreases in a high-pass filter.
-
CHolds only when the load is purely inductive.
-
DUndetermined — must know the exact R and C values.
Answer
Correct Answer: Incorrect — the output decreases at low frequencies because the capacitor blocks slow changes.
Explanation
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:
Recognize the high-pass role: blocks DC and very slow variations.At low frequency: Xc is large → series impedance high → output across the resistor is small.At high frequency: Xc is small → signal passes → output increases toward input magnitude.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.