Which of the following statements are true?

a. Strain gauges are based on piezo-resistive effect.

b. The strain gauges should have high resistance coefficient.

c. The gauge factor is defined as the ratio of per unit change in resistance to per unit change in length.

d. Strain gauge should have low value of gauge factor to result high sensitivity.This question was previously asked in

MPSC Assistant Engineer EE Mains 2019 - Paper 1

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.

ST 1: Logical reasoning

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