Strain gauges are sensors commonly used on bridges to determine if there is too much stress on a particular area. For example, if the cables supporting the Golden Gate Bridge need to be replaced or reinforced.
The gauge is made up of a strip of conductive metal. Its electrical resistance will increase if the gauge is stretched (smaller cross-section and longer length), and decrease if the gauge is compressed (larger cross-section and shorter length). Knowing the relationship between strain and electrical resistance, i.e. gauge factor, allows us to measure the stress.
Classic strain gauges use a Wheatstone bridge circuit setup like shown above. Under normal stress, we might want a reference output voltage of 0V. Assuming R2 = R3 = R4 = 10 Ω, what would the electrical resistance of the strain gauge (R1) have to be for that to occur? If the cable stretches (thus stretching the metal on the gauge), is the output voltage then a positive or negative value (assuming top output lead is positive, and the left excitation lead is at a higher potential than the right)?