What is the principle behind a wire strain sensor (gage)?

A wire strain gage operates on the principle that a conductor’s electrical resistance changes when it is deformed. In other words, when the wire is stretched (or compressed), its length and cross-sectional area change, which causes a corresponding change in its resistance. Here’s how it works in more detail: 1. When the wire is subjected to mechanical strain, its length increases and its cross-sectional area decreases. This leads to an increase in electrical resistance according to the resistivity equation (R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area). 2. Conversely, if the wire is compressed, the length decreases and the cross-sectional area increases, leading to a decrease in resistance. 3. The sensitivity of the strain gage is characterized by its gauge factor (GF), defined as:   GF = (ΔR/R) / ε where ΔR/R is the fractional change in resistance and ε is the strain (change in length divided by the original length). This factor provides a direct relationship between the measured resistance change and the amount of strain. 4. Typically, the strain gage is arranged in a Wheatstone bridge circuit to accurately detect very small changes in resistance, which correspond to the mechanical strain experienced by the wire. Thus, by measuring the change in resistance, one can quantify the mechanical deformation (strain) of the material to which the gage is attached.