GATE 2025 BM – Question 63
The Wheatstone bridge shown is initially balanced. Straining its cylindrical resistor Rstrain along length l produces |Vout|=10 mV for 1 V excitation. Its cross-sectional area is A. Estimate strain magnitude to two decimal places; the resistor has length l and cross-sectional area A.
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Correct answer: 0.01 to 0.10
Explanation
Let Rstrain=R(1+ε), using the stated fixed-area/resistivity model. The changed divider voltage differs from the unchanged one half by |ε/[2(2+ε)]| of the excitation. Setting this to 0.01 gives ε≈0.0408 for extension; the small-signal approximation gives ε≈4×0.01=0.04. Thus the strain magnitude is about 0.04. A Poisson-dependent gauge factor would require additional material information absent from the question; the official broad numerical range includes the intended estimate.