Question

A metal wire strain gauge having an unstrained resistance of $120\Omega$ and a gauge factor of $2.1$ is bonded onto a steel grinder so that it experiences a tensile stress of ${10}^{8}Pa.$ If Young's Modulus for steel is $2\times {10}^{11}Pa.$. The strained resistance of the gauge is _____ $\Omega$

• A. 120.12
• B. 0.126
• C. 120
• D. 1.26

Answer 1

The correct option is A 120.12

$R_0=120\Omega$

$G=2.1$

$\text{Stress}={10}^{8}Pa$

$E=2\times {10}^{11}Pa$

$\because strain=\frac{\text{stress}}{E}=\frac{{10}^8}{2\times {10}^{11}}=500\mu \text{strain}$

$\therefore \Delta R=R_0\times G\times \epsilon$

$=120\times 2.1\times 500\times {10}^{-6}$

$=0.126\Omega$

$R=R_0+\Delta R=120.12\Omega$