Final answer:
A strain gauge is a sensor that converts mechanical deformation into a change in resistance. Its gauge factor, which describes how resistance changes relative to mechanical strain, is calculated using the change in resistance and the applied strain. For a resistance change of 10 ohms at 7000 micro-strain, the gauge factor is approximately 2.353.
Step-by-step explanation:
A sensor that converts mechanical entities such as stress or force into an equivalent resistance, is known as a strain gauge. The working principle of a strain gauge is based on the change of electrical resistance in conductive foils as they are deformed with the applied strain. When mechanical deformation occurs, such as stretching, the conductive foil's geometric dimensions change, leading to a change in its electrical resistance.
Specifically, the resistance of a strain gauge changes linearly with the strain applied to it. This property is quantitatively described by the gauge factor, which is defined as the ratio of fractional change in electrical resistance to the fractional change in length (strain). For a strain gauge with an initial resistance value of 170 ohms and a change of 10 ohms corresponding to 7000 micro-strain, the gauge factor can be calculated using the formula:
Gauge Factor (GF) = (∆R / R) / (∆L / L)
Where ∆R is the change in resistance, R is the initial resistance, ∆L is the change in length, and L is the initial length (strain in this case). Here, ∆R/R is 10/170 and ∆L/L is 7000 x 10⁻⁶ (micro-strain is 10⁻⁶ of strain). Thus:
GF = (10/170) / (7000 x 10⁻⁻⁶) ≈ 2.353
It's important to note that strain gauges are affected by temperature changes. Temperature compensation or adjustments are necessary to ensure accurate strain measurements.