Correct Answer - Option 3 : a and c are true
The piezo-resistive effect is a change in the electrical resistivity of a semiconductor or metal when mechanical strain is applied. Strain gauges are based on piezo-resistive effect.
The strain gauge has a low temperature coefficient of resistance. Due to temperature variation, errors can be minimized in this way. In most of the strain gauges, temperature compensation is provided.
The gauge factor is defined as the ratio of per unit change in resistance to per unit change in length. It is a measure of the sensitivity of the gauge.
Gauge factor, \({G_f} = \frac{{{\rm{\Delta }}R/R}}{{{\rm{\Delta }}L/L}}\)
\(\frac{{{\rm{\Delta }}R}}{R} = {G_f}\frac{{{\rm{\Delta }}L}}{L} = {G_f}\varepsilon \)
Where ε = strain = ΔL/L
The gauge factor can be written as:
= Resistance change due to change of length + Resistance change due to change in the area + Resistance change due to the piezoresistive effect
\({G_f} = \frac{{{\rm{\Delta }}R/R}}{{{\rm{\Delta }}L/L}} = 1 + 2v + \frac{{{\rm{\Delta }}\rho /\rho }}{\varepsilon }\)
If the change in the value of resistivity of a material when strained is neglected, the gauge factor is:
\({G_f} = 1 + 2v\)
The above equation is valid only when the Piezoresistive effect that changes in resistivity due to strain is almost neglected.
For wire-wound strain gauges, Piezoresistive effect is almost negligible.
The gauge factor in a strain gauge must be high. A large value of gauge factor indicates a large change in the value of resistance for a particular strain.
