A resistance strain gauge has gauge factor G = 2 mounted on a specimen under stress of 1050 kg/cm². If the gauge resistance is 1000 Ω, estimate the change in resistance ΔR (assume steel with E ≈ 2 × 10^6 kg/cm²).
Electronics and Communication Engineering
Measurements and Instrumentation
Difficulty: Medium
Choose an option
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A2 Ω
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B3 Ω
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C4 Ω
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D1 Ω
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E0.5 Ω
Answer
Correct Answer: 1 Ω
Explanation
Introduction / Context:Strain gauges convert mechanical strain into a resistance change. The core relation is ΔR/R = G * ε, where ε is axial strain and G is the gauge factor. To get ε from stress σ, Hooke's law ε = σ / E is used for linear elastic behavior.
Given Data / Assumptions:
- Gauge factor G = 2.
- Stress σ = 1050 kg/cm².
- Gauge resistance R = 1000 Ω.
- Assume material modulus E ≈ 2 × 10^6 kg/cm² (typical steel order of magnitude).
Concept / Approach:Compute strain ε from σ and E, then apply ΔR = R * G * ε. This is the standard small-strain, linear-elastic estimation widely used in experimental stress analysis.
Step-by-Step Solution:
ε = σ / E = 1050 / (2 × 10^6) = 5.25 × 10^-4ΔR/R = G * ε = 2 * 5.25 × 10^-4 = 1.05 × 10^-3ΔR = R * (ΔR/R) = 1000 × 1.05 × 10^-3 ≈ 1.05 Ω ≈ 1 ΩVerification / Alternative check:
Using E = 2.1 × 10^6 kg/cm² gives ΔR ≈ 1.0 Ω; either way the closest option is 1 Ω.Why Other Options Are Wrong:
2–4 Ω would require roughly double to quadruple the computed strain; 0.5 Ω is about half the computed change.Common Pitfalls:
Forgetting to convert stress to strain using E; misapplying gauge factor relation.Final Answer:
1 Ω