Fault effect on time constant — in an RC integrator or differentiator, which component fault most directly decreases the effective time constant τ = R * C (thus collapsing the time-based behavior)?

Introduction / Context:
The time constant of a simple RC stage is τ = R * C. Faults that effectively reduce R or C will reduce τ and undermine the intended timing/shape of the response. Identifying which failures drive τ downward helps with troubleshooting pulse-shaping networks.

Given Data / Assumptions:

• Simple first-order RC network used as an integrator or differentiator.
• Time constant τ = R * C for the effective series R and capacitance.
• We consider the dominant effect of common faults.

Concept / Approach:
A shorted capacitor effectively makes C → 0 in the time-constant product, collapsing τ toward zero and destroying the intended time-based behavior (the node becomes a near-short for AC transients in many topologies). By contrast, an open resistor removes the current path entirely (no defined exponential); an open capacitor removes C from the circuit (again no defined RC exponential). Increased leakage (finite parallel resistance) modifies the effective network but does not predictably “decrease τ” in the intended series path sense; instead it distorts the response and DC bias.

Step-by-Step Solution:

Verification / Alternative check:
Lab observation: with a shorted capacitor, edge responses vanish into immediate jumps limited only by wiring; with an open capacitor, the node stops integrating/differentiating entirely rather than becoming “faster.”

Why Other Options Are Wrong:

• Open resistor / open capacitor: break the RC function entirely; τ is not meaningfully reduced but rather undefined.
• Leaky capacitor: adds a parallel resistance that skews behavior, not a simple τ reduction.
• Shorted resistor bypassing the capacitor: not listed in original options, but such a bypass also collapses behavior; the classic textbook answer is the shorted capacitor.

Common Pitfalls:
Assuming any fault that “speeds up” a response means τ simply decreased; some faults destroy the RC mechanism instead of altering τ cleanly.

Final Answer:
Shorted capacitor.