Question

A bonded metal strain gauge has the following specifications
$\text{Gauge factor}=2.0$

$\text{Unstrained Resistance}=100\Omega$

$\text{Maximum tensile and compressive strain}=100\text{microstrain}$

Two strain gauges, with the specifications given above mounted on a structural memebr in a push - pull configuration are connected in a bridge along with two standard resistances, whose output is fed to a differential amplifier using two buffers as shown in the figure. The magnitude of the output voltage $V_o$ per unit microstrain is ___ $mV.$

• A. $10$
• B. $0.01$
• C. $0.1$
• D. $1$

Answer 1

The correct option is D $1$

Since the output of the bridge circuit is first fed to the buffer amplifier hence their is no loading on output.

So, output off differential amplifier is given by,

$V_o=\frac{100R}{R}(V_1-V_2)=100(V_1-V_2)$

$V_1=V_i\times \left[\frac{R}{R+R}\right]=\frac{V_i}{2}$

$V_2=V_i\times \left[\frac{R-\Delta R}{R-\Delta R+R+\Delta R}\right]=V_i\times \frac{R-\Delta R}{2R}$

$=\frac{V_i}{2}[1-\frac{\Delta R}{R}]=\frac{V_i}{2}[1-(G\times \epsilon \left)\right]$

$\therefore V_0=100[\frac{V_i}{2}-\frac{V_i}{2}(1-G\times \epsilon \left)\right]$

$=100(\frac{V_i}{2}\times G\times \epsilon )=\frac{100\times 10\times 2\times 1\times {10}^{-6}}{2}=1mV$