A Strain Gauge with gauge factor of 2 is fastened to a metallic member subjected to a stress of 1000 $kg/cm^2$. The modulus of elasticity of the metal is $2 × 10^6 kg/cm^3$. Calculate the percentage change in the resistance of the strain gauge. What is the value of Poisson’s ratio?

Mumbai University > Electronics Engineering > Sem3 > Electronic Instruments and Measurements

Marks: 5M

Year: Dec 2013

Given –

Gauge Factor $G_f$=2

Stress =$1000 kg/cm^2 $

Modulus of elasticity=ε= $2×10^6 kg/cm^3$

Formulae –

Modulus of elasticity=ε=Stress/Strain

Change in Resistance=$∆R=G_f×Strain$

Poisson^' sratio=$μ=\frac{G_f-1}2$

Solution –

Before we calculate the change in resistance, we have to deduce the value of strain. Strain is given by the ratio of stress and modulus of elasticity,

$$Strain=\frac{Stress}ε \\ =\frac{1000}{2×10^6 } \\ =500×10^{-6} \\ Strain=500 μm/m$$

Now, change in resistance is given by,

$$∆R=G_f×Strain \\ =2×500 μ \\ ∆R=1 ×10^{-3}$$

Change in resistance in percentage,

$$∆R=1 ×10^{-3}×100=0.1\%$$

Therefore, change in resistance is 0.1%.

Further, Poisson’s ratio is given by,

$$μ=(G_f-1)/2 \\ μ=(2-1)/2 \\ μ=0.5$$

With this value, it is evident that the metal has a Poisson’s ratio in the upper limit which is 0.5. Generally, Poisson’s ratio always falls between 0 and 0.5. For gold, it is between 0.42 and 0.44; for copper, it is 0.33; and for steel, it is between 0.27 and 0.30.

For the given figures, the change in resistance is 0.1% and the Poisson’s ratio is 0.5 or 1/2.