Correct Answer - Option 3 : 1.5 × 10
-4
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 = \(Δ L\) /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
Calculation:
With \(GF= \frac{{Δ R/R}}{{{\rm{\varepsilon \;}}}}\)
The strain can be calculated as:
\(ϵ= \frac{Δ R}{R}.\frac{1}{GF}\)
Given:
ΔR = 0.15 Ω, R = 250 Ω, and GF = 4
Putting on the respective values, we get:
\(ϵ= \frac{0.15}{250}.\frac{1}{4}\)
ϵ = 1.5 × 10-4
