Question

A bonded metal strain gauge has the following specfications:
Gauge factor = 2.0
Unstrained resistance = 120 $\Omega$ at $0^{\circ }C$
Maximum operating temperature = 150 ${}^{\circ }C$
Temperature coefficient of resistance = $(2\times {10}^{-5}{)}^{\circ }{C}^{-1}$
Maximum tensile and compressive strain = $2\times {10}^{-2}$

The temperature-induced resistance error at the maximum operating temperature expressed as the percentage of resistance change due to maximum tensile strain only, assuming self-heating effects to be negligible, is

• A. 0.0625
• B. 0.625
• C. 6.26
• D. 7.5

Answer 1

The correct option is D 7.5

Due to temperature, the resistance of the gauge changes to
$R_T=R_0(1+\alpha \Delta t)$

$=120(1+2\times {10}^{-5}\times 150)$

$=120(1+0.003)=120.36$

Change in resistance due to temperature variation is
$(\Delta R{)}_T=R_T-R_0$

$=120.36-120=0.36$

$\therefore \frac{(\Delta R{)}_T}{R}=\frac{0.36}{120}....\left(i\right)$

Resistance error due to the tensile strain only is
$\frac{\Delta R}{R}=Gϵ....\left(ii\right)$

Percentage of resistance change $=\frac{0.36/120}{G\times ϵ}\times 100$

$=\frac{0.36}{2\times 2\times {10}^{-2}\times 120}\times 100$

$=0.075\times 100=7.5$