Question

In the circuit shown below, the op-amp is ideal (with saturation voltage $\pm 12V$) and the sensor is an P-type semiconductor strain gauge whose nominal resistance is $1000\Omega$ and gauge factor is 200. The output voltage of the circuit when strain gauge is subjected to 100 microstrain is_________V.

• A. -40
• B. -3
• C. -12
• D. -6

Answer 1

The correct option is C -12

Change in resistance of the strain gauge due to applied strain is:

$\Delta R=R\times G\times ϵ=1000\times 200\times 1000\times {10}^{-6}=200\Omega$

New resistance of gauge

$R_{new}=R+\Delta R=1200\Omega$


KCL at node A

$I_1+I_2+I_3=0$

$\frac{V_A-10}{100\Omega }+\frac{V_A}{100\Omega }+\frac{V_A-V_B}{100\Omega }=0$

$V_A[\frac{1}{100}+\frac{1}{100}+\frac{1}{100}]=\frac{10}{100}$

$V_A\left[\frac{3}{100\Omega }\right]=\frac{10}{100}$

$V_A=\frac{10}{3}V$

Apply KCL at node B,

$I_3=I_4$

$\frac{V_a-V_B}{100}=\frac{V_B-V_0}{1200}$

$\frac{\frac{10}{3}-0}{100}=\frac{0-V_0}{1200}$

$V_0=-40V$

$\text{Since,}{V}_0<-V_{\text{sat}},\text{hence}{V}_0=-12V$