A metallic strain gauge has resistance 200 Ω, Young’s modulus 80 GPa and Poisson’s ratio 0.42. It experiences longitudinal strain 50×10⁻⁶. Neglect piezoresistivity. Find its resistance change in mΩ to one decimal place.
Without a resistivity change, the geometric gauge factor is 1+2ν=1.84, from increased length and reduced cross-sectional area. Therefore ΔR=R(1+2ν)ε=200×1.84×50×10⁻⁶=.0184 Ω. Converting to milliohms gives 18.4 mΩ. Young’s modulus is unnecessary because strain is already supplied.
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