Question $3$:

A strain gauge has a nominal resistance of $R_{\text{s}\text{t}\text{r}\text{a}\text{i}\text{n}}=350$ ohms and a gauge factor $S_g=1\mathrm{.}8.$ The gage factor relates the change in resistance to the axial strain ${}_x$ by the following equation

$S_g=\frac{\frac{R}{R_{\text{s}\text{t}\text{r}\text{a}\text{i}\text{n}}}}{{}_x}$

Where $R$ is the change in strain gauge resistance. It is required to design a measuring system such that the output voltage $V_0=3V$ at an axial strain ${}_x=0\mathrm{.}05.$ The maximum permissible current through the strain gauge is $20$ mA $.$ Also show in your design how to improve the sensitivity and linearity of the proposed system.