Strain Gauges

Physics: Cambridge International A Level, topic 12.1.11

Strain gauges are used to measure the strain of different materials by measuring changes in their resistance.

A strain gauge consists of a thin metal wire that is sealed into a thin layer by a flexible, insulating material.
The strain gauge is then connected to a circuit in order to make measurements.

The voltage and current of the circuit are measured both when the strain gauge is stretched and unstretched.
The change in resistance of the strain gauge is then given by the equation:
$\Delta R = \frac{\large \rho\Delta L}{\large A}$
Where $L$ is the change in length of the wire, $\rho$ is the resistivity of the material and $A$ is the cross-sectional area of the wire.
The change in cross-sectional area as the strain gauge (and wire) is stretched is assumed to be constant.

Test yourself on Strain Gauges

What is the correct relationship between the change in resistance of the strain gauge and the strain of the wire?
What is the correct equation for strain?