A metallic strain gauge has gauge factor 2 and unstressed resistance 1 kΩ. It is bonded to material with elastic modulus 200 GN/m² and forms a quarter bridge with three fixed 1 kΩ resistors, excited at 4 V DC. Under stress 100 MN/m², find bridge-output magnitude in mV, to two decimal places.
The longitudinal strain is $\epsilon=\sigma/E=100\times10^6/(200\times10^9)=0.0005$. Gauge factor gives $\Delta R/R=2\epsilon=0.001$, so $\Delta R=1$ Ω. The small-change quarter-bridge output is $V_o\simeq V_s(\Delta R/R)/4=4(0.001)/4=0.001$ V = 1.00 mV. Exact bridge division gives 0.9995 mV, with the same rounded result.
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