Electrical resistance strain gauge principle: when a fine conductor in a bonded strain gauge is elastically stretched, its length increases and diameter decreases. The combined dimensional changes result in what net change in electrical resistance?

Introduction / Context:
Strain gauges convert mechanical deformation into an electrical signal via resistance change. Understanding why resistance changes—and in which direction—is essential for designing Wheatstone bridge circuits, interpreting gauge factors, and avoiding sign errors in instrumentation.

Given Data / Assumptions:

• Elastic tensile strain is applied (no plastic deformation).
• Conductor length increases while cross-sectional area decreases.
• Resistivity may change slightly with strain but geometry dominates the sign.

Concept / Approach:
Resistance R = rho * L / A, where rho is resistivity, L is length, and A is area. Under tensile strain: L increases (raises R) and A decreases (also raises R). The piezoresistive change in rho can contribute but, for metallic gauges, the geometrical effects are primary and lead to a net increase in R under tension. The gauge factor GF approximately equals (ΔR/R)/ε and is typically around 2 for metal foil gauges.

Step-by-Step Solution:
Apply small tensile strain ε: L → L(1 + ε).Assuming volume constancy for small elastic strain: A decreases roughly by (1 - νε) where ν is Poisson’s ratio.Compute qualitative effect: R = rho * L / A increases because L↑ and A↓.Include minor rho changes: metallic gauges still show net ΔR > 0.

Verification / Alternative check:
Experimental calibration yields positive ΔR for tensile strain for common constantan or karma alloy gauges; compression yields negative ΔR of similar magnitude per unit strain.

Why Other Options Are Wrong:
No change: Contradicts R = rho*L/A behavior.Decrease/exponential decrease: Opposite sign; geometry dominates toward increase.Periodic fluctuation: Not characteristic of static elastic strain.

Common Pitfalls:
Ignoring Poisson effects; miswiring the Wheatstone bridge so that tension appears as a decrease in output; neglecting temperature compensation which can mask true strain signals.

Final Answer:
Increase