Where to measure — RC differentiator output node: In a standard passive RC differentiator, is the output correctly taken across the capacitor, or across the resistor?

Introduction / Context:
Knowing where to take the output in basic RC networks avoids functional mistakes. In the differentiator configuration, the location of the output determines whether the circuit emphasizes edges (high-pass behavior) or averages signals (low-pass behavior). This item checks whether the output of an RC differentiator is taken across the capacitor or across the resistor.

Given Data / Assumptions:

• Passive differentiator: series capacitor, resistor to ground.
• Linear small-signal analysis; no loading that would fundamentally alter behavior.
• Objective: produce spikes at edges (differentiate).

Concept / Approach:
For differentiation, the output is taken across the resistor. A series capacitor blocks DC and passes fast-changing components as current pulses into the resistor; the resistor then converts these current pulses into voltage spikes (v_out = i * R). If, instead, one measures across the capacitor, the circuit behaves as a high-pass coupling network across the dielectric but does not provide the classic resistor-referenced spike output of a differentiator. Therefore, the statement “output of an RC differentiator is taken across the capacitor” is incorrect for the standard configuration.

Step-by-Step Solution:

Verification / Alternative check:
Textbook diagrams and lab demonstrations consistently show v_out measured across the resistor in the basic RC differentiator. Oscilloscope waveforms confirm positive and negative spikes corresponding to input edges.

Why Other Options Are Wrong:

• Correct: Misidentifies the output node.
• Frequency- or polarity-conditional options: The topology determines the correct node regardless of frequency or capacitor polarity (for non-polarized parts).

Common Pitfalls:
Confusing the differentiator with the RC integrator (output across the capacitor) due to their dual nature; mixing schematic conventions that place probes differently.

Final Answer:
Incorrect.