Question

A strain gauge has gauge factor 2.1 and nominal resistance \(120\ \Omega\). If it is subjected to a strain of \(1000\ \mu\varepsilon\), the change in resistance is

• A. \(0.126\ \Omega\)
• B. \(0.252\ \Omega\)
• C. \(0.504\ \Omega\)
• D. \(1.20\ \Omega\)

Hint:

Use this straightforward multiplication formula for strain gauges: \(\Delta R = R \times G_F \times \text{Strain}\). Substituting the values yields \(120 \times 2.1 \times 0.001 = 0.252\ \Omega\).

Answer 1

The Correct Option is B

Concept: A resistance strain gauge operates on the principle that the electrical resistance of a conductor changes when it undergoes mechanical strain. The sensitivity of a strain gauge is defined by its Gauge Factor (\(G_F\)), which is the ratio of the fractional change in electrical resistance to the mechanical strain (\(\varepsilon\)): \[ G_F = \frac{\Delta R / R}{\varepsilon} \] where:
• \(\Delta R\) is the change in resistance of the strain gauge.
• \(R\) is the nominal or initial unstrained gauge resistance.
• \(\varepsilon\) is the mechanical strain, defined as \(\frac{\Delta L}{L}\).

Step 1: Identify the given values and convert units. The parameters provided are:
• Gauge Factor (\(G_F\)) = 2.1
• Nominal Resistance (\(R\)) = \(120\ \Omega\)
• Strain (\(\varepsilon\)) = \(1000\ \mu\varepsilon = 1000 \times 10^{-6}\)

Step 2: Rearrange the gauge factor equation to find the change in resistance (\(\Delta R\)). \[ \frac{\Delta R}{R} = G_F \cdot \varepsilon \quad \Rightarrow \quad \Delta R = G_F \cdot \varepsilon \cdot R \] Substitute the values into the equation: \[ \Delta R = 2.1 \times (1000 \times 10^{-6}) \times 120 \] Simplify the expression by combining terms: \[ 1000 \times 10^{-6} = 10^{-3} = 0.001 \] \[ \Delta R = 2.1 \times 120 \times 0.001 \] First evaluate the product of 2.1 and 120: \[ 2.1 \times 120 = 252 \] Now scale this result by 0.001: \[ \Delta R = 252 \times 0.001 = 0.252\ \Omega \] Hence, the total change in resistance is exactly \(0.252\ \Omega\), matching option (B).