Correct Answer - Option 2 :

\(\frac{{\Delta R/R}}{{\Delta L/L}}\)
Gauge Factor:

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 = \(\frac{{\Delta L}}{{L}}\)

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.