RC response to a square wave A resistor in series with a capacitor, with the output taken across the capacitor and driven by a square-wave source, behaves as which signal-shaping circuit?

Introduction / Context:
Simple RC networks perform useful signal shaping. When a square wave is applied, taking the output across different elements of the RC series network yields classic approximations of integration or differentiation, widely used in timing, smoothing, and edge-shaping circuits.

Given Data / Assumptions:

• Series connection: source → R → C → return.
• Output is measured across the capacitor.
• Square-wave input with frequency such that RC provides smoothing (RC larger than the input edge time).

Concept / Approach:
Taking output across the capacitor produces a low-pass behavior: high-frequency components are attenuated while low-frequency components pass. For a square wave, which contains strong high-frequency harmonics, the RC low-pass averages the waveform, approximating integration over time.

Step-by-Step Solution:
Identify network: series RC with output across C → low-pass.Square wave has fundamental plus many odd harmonics.Low-pass action attenuates harmonics, smoothing transitions.Resulting output resembles the time integral of the input: an integrator.

Verification / Alternative check:
Swapping the output to the resistor creates a high-pass response that emphasizes edges and approximates differentiation, confirming the complementary behavior of the same RC network.

Why Other Options Are Wrong:
Differentiator: occurs when output is taken across the resistor in a series RC under suitable conditions.Multiplier and divider: these are arithmetic terms; passive RC networks do not multiply signals in the time-domain sense.

Common Pitfalls:
Assuming any RC does both functions regardless of where the output is taken; placement determines behavior.Ignoring that practical integrators need RC chosen relative to the signal spectrum to approximate true integration.

Final Answer:
An integrator