Question

A strain gauage having nominal resistance $1k\Omega$ and gauge factor of $2.1$ is connected to an ideal op-amp circuit through lead wire. Lead wire, 100m long is made up of some metal which is having temperature co-efficient of $0.004{/}^{\circ }C$ and resistance varies at $0.5\Omega /mat{0}^{\circ }C.$

If the applied strain is ${10}^{-3}m/m$ then the output of op-amp at ${40}^{\circ }C$ is ___.

• A. 9V
• B. 4V
• C. 3V
• D. 1V

Answer 1

The correct option is A 9V

Change in resistance due to applied strain,

$\Delta R=G_f.\epsilon .R=2.1\times {10}^{-3}\times 1k\Omega =2.1\Omega$

$\text{Lead wire resistance at}{0}^{\circ }C=0.05\Omega /m\times (100+100)\Omega$

$=100\Omega$

$at{40}^{\circ }C.,R_{Lead}=100\Omega (1+0.004\times 40)$

$=116\Omega$

$\therefore \text{Total feedback resistance},R_f=(116\Omega +1k\Omega +2.1\Omega )$

$1.1181k\Omega$

$\therefore V_0=-\frac{R_f}{R_i}\times V_i=\frac{-1.1181k}{0.6k}\times -5V$

$\Rightarrow V_0=9.3175V$

As $V_0>9V$ (Saturation) hence op-amp will be saturated to 9V.

$\therefore V_0=9V$