Question

A metallic strain gauge has a resistance of $120\Omega$ & a gauge factor of 2. It is installed on a aluminium structure which has a yield point stress of $0.2GN/m^2$ & Young's modulus of $68.7GN/m^2$. The change in resistance (in $\Omega$) of the gauge that would be caused by loading the material to yield point is

• A. 0.1
• B. 0.6
• C. 0.7
• D. 0.3

Answer 1

The correct option is C 0.7

$R=120\Omega$
$G_f=2$
$S=\text{stress}=0.2\left(GN/m^2\right)$
$Y=68.7\left(GN/m^2\right)$

$Y=\frac{\text{Stress}}{\text{Strain}}$

$\text{Strain}\left(\epsilon \right)=\frac{0.2\times {10}^9}{68.7\times {10}^9}=2.91\times {10}^{-3}$

$\frac{\Delta R}{R}=G_f\epsilon$

$\Delta R=2\times 2.91\times {10}^{-3}\times 120=0.6984\Omega$

$\Delta R\cong 0.7\Omega$