In a basic RC filter where a series capacitor feeds a resistor to ground and the output is taken across the resistor, what overall filter action results?

Introduction:
First-order RC networks are widely used as simple frequency-selective filters. This question assesses recognition of the transfer function when the output is taken across the resistor in a series C-R network.

Given Data / Assumptions:

• Series capacitor followed by resistor to ground.
• Output node is across the resistor.
• Linear components, small-signal AC.

Concept / Approach:
A capacitor has reactance Xc = 1 / (2 * pi * f * C). At low frequency, Xc is large and blocks signal; at high frequency, Xc is small and passes signal. With output across R, the voltage divider Vout = Vin * (R / (R + 1/(jomegaC))) increases with frequency, producing high-pass behavior.

Step-by-Step Solution:
1) Model as a frequency-dependent divider: Zc in series with R.2) For f near 0, |Zc| is large, most voltage is across capacitor, Vout across R is small.3) As f rises, |Zc| falls, more voltage appears across R.4) Therefore the circuit passes high frequencies and attenuates low frequencies.

Verification / Alternative check:
The magnitude response rises at 20 dB per decade below cutoff and flattens to unity above cutoff, with cutoff frequency fc = 1 / (2 * pi * R * C).

Why Other Options Are Wrong:
Low-pass: would occur if output were across the capacitor, not the resistor.
Bandpass: needs at least two reactive elements to create both low and high cutoffs.
Band-stop: attenuates a mid-band; not a first-order RC behavior in this topology.
All-pass: requires phase equalization with flat magnitude, not provided by this RC.

Common Pitfalls:
Confusing output node placement, or thinking any RC is low-pass by default. Placement of the output defines whether the network is low-pass or high-pass.

Final Answer:
high-pass