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?
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ACorrect
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BIncorrect
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CCorrect only at very low frequencies
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DDepends on coupling capacitor polarity
Answer
Correct Answer: Incorrect
Explanation
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:
Identify topology: input → C_series → node → R_to_ground.Take output at the node across R: v_out = i_C * R = C * dv_in/dt * R → spikes at edges.If output were across C, the behavior would not match the standard differentiator definition.Hence, the correct output node is across the resistor, not the capacitor.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.