A strain gauge measures the external force applied to a fine wire by causing a change in what property?

A strain gauge operates based on the principle that the electrical resistance of a material changes when it is mechanically deformed. When an external force is applied to the fine wire within the strain gauge, it causes the wire to stretch or compress, resulting in a change in its dimensions. This change in geometry alters the electrical resistance of the wire according to the gauge's design.

The relationship between mechanical deformation and resistance change is well-established; as the wire is deformed, the distance between the atoms in the wire changes, affecting how easily electrons can flow through it. This allows the strain gauge to provide a measurable electrical signal that corresponds to the amount of strain, which can then be related back to the external force applied.

This principle makes the change in resistance the key property that a strain gauge measures, enabling it to be used in various applications for force and stress analysis in engineering and structural monitoring.