GATE 2025 IN – Question 53
A metallic strain gauge of resistance $R_{SG}$ is connected as shown, with lead resistances $R_{L1},R_{L2},R_{L3}$. Gauge factor is 2 and nominal resistance $R_N=125\ \Omega$. A true tensile strain $2\times10^{-3}$ changes its resistance by $\Delta R$. The measured change is $\Delta R_{MEAS}=R_{EQ2}-R_{EQ1}$, where $R_{EQ1}$ is measured between terminals 1 and 2 and $R_{EQ2}$ between 2 and 3. If $R_{L1}=R_{L2}=5\ \Omega$ and $R_{L3}=4.95\ \Omega$, the inferred tensile strain is ______ $\times10^{-3}$ (rounded to two decimal places).
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Correct answer: 1.75 to 1.85
Explanation
The true resistance change is $\Delta R=GF\,R_N\epsilon=2(125)(0.002)=0.5\ \Omega$.
The terminal measurements give $R_{EQ2}-R_{EQ1}=\Delta R+R_{L3}-R_{L1}$ because $R_{L2}$ cancels.
Thus the measured change is $0.5+4.95-5=0.45\ \Omega$.
The inferred strain is $0.45/(2\times125)=0.0018=1.80\times10^{-3}$.
The requested coefficient is **1.80**.