Question

A resistance strain gauge is used to measure the stress of steel which is stressed to 1200 kg/cm². If the gauge factor is 2.5 and Young’s modulus of steel is 2 x 10⁶ kg/cm², the percentage change in resistance of the gauge is
1. 0.05%
2. 0.10%
3. 0.15%
4. 0.25%

Answer 1

Correct Answer - Option 3 : 0.15%

Concept: 

Gauge factor (GF) or strain factor of a strain gauge is the ratio of relative change in electrical resistance (R) to the mechanical strain (ε).

\(GF = \frac{{Δ R/R}}{{Δ L/L}}\)

\(GF= \frac{{Δ R/R}}{{{\rm{\varepsilon \;}}}}\)

Where,

ε = Strain = \(\frac{Δ L}{L}\)

ΔL= Absolute change in length

L = Original length

ΔR = Change in strain gauge resistance due to axial strain and lateral strain

R = Unstrained resistance of strain gauge

Also, Young's modulus is defined as the ratio of stress to strain, i.e.

\(Y=\frac{Stress}{Strain}\)

Calculation:

For the given values of Y and Stress, we obtain the strain (ϵ):

\(\epsilon =\frac{Stress}{Y}=\frac{1200}{2\times 10^6}=6\times 10^{-4}\)

Since \(GF= \frac{{Δ R/R}}{{{\rm{\varepsilon \;}}}}\), the change in resistance will be:

\(\frac{\Delta R}{R}= G.F.\times \epsilon\)

\(\frac{\Delta R}{R}= 2.5\times 6\times 10^{-4}\)

\(\frac{\Delta R}{R}= 15\times 10^{-4}\)

Now, the percentage of change will be:

\(\frac{\Delta R}{R}\times 100= 0.15\%\)