Choosing the output node — when a series RC network is used as a low-pass filter, from which component should the output be taken to obtain low-pass behavior?

Introduction / Context:
First-order RC filters are formed by selecting which element develops the output. The same two components can implement either a high-pass or a low-pass, depending on where the output is taken. This question checks if you can identify the correct node for a low-pass configuration in a series RC network.

Given Data / Assumptions:

• Series RC branch driven by a source.
• Sinusoidal steady-state analysis.
• Ideal components and light loading (or buffered output).

Concept / Approach:
In a series RC, the resistor and capacitor form a voltage divider whose division ratio varies with frequency. The capacitor’s reactance is high at low frequency and low at high frequency. Taking the output across the capacitor provides more voltage at low frequencies and less at high frequencies, which is the definition of low-pass behavior. Conversely, taking the output across the resistor yields a high-pass response.

Step-by-Step Solution:

Verification / Alternative check:
At DC (omega = 0), |Z_C| is very large, so almost all the source voltage appears across the capacitor (Vout near Vin). At very high frequency, |Z_C| is very small, so most voltage is across the resistor and the capacitor output tends toward zero. This exactly matches a low-pass characteristic.

Why Other Options Are Wrong:

• Across the resistor is a high-pass configuration.
• “Either node is identical” is incorrect; the transfer function depends on the node.
• A parallel RC is not required; a series RC suffices for first-order low-pass.

Common Pitfalls:
Forgetting that “output across C = low-pass” and “output across R = high-pass” in the series RC topology.

Final Answer:
Correct — take the output across the capacitor.