$8.$ A strain gauge is normally setup in a bridge configuration in order to minimize the effect of temperature and other environmental factors. The bridge set up is shown in the figure below. The non$-$strained resistance of each gauge is $3$ k Ohm and the Gauge Factor is $2.(20$ points$)$

Note that this is not an LTSpice problem, and no simulation is called for.

With the gauges set on the flexing beam as shown here, the effect on the bridge will be as shown in the following circuit, where $\backslash ($ x $\backslash )$ is the strain.

Set the gain for the amplifier such that a stain $(\backslash (\backslash$varepsilon $\backslash ))$ of $\backslash (\backslash$pm $5\backslash$mathrm$\{$~m$\}\backslash$quad $\backslash )$ would result in a voltage into the ADC of $\backslash (\backslash$pm $1\mathrm{.}023\backslash )($half of its range$).$ Note the Vref can be used to offset this by $1\mathrm{.}023$ Volts or midrange of the ADC.

$9.$ What is the resolution of this system in $\backslash (\backslash$varepsilon $\backslash )$ per LSB and what would the formula be to compute $\backslash (\backslash$varepsilon $\backslash )$ based on the ADC's output number. $(10$ points$)$