You would like to design and simulate a circuit for a piezoresistive differential pressure sensing element with a zero pressure resistance $\backslash ($ R$\_\{0\}=1\backslash$mathrm$\{$k$\}\backslash$Omega $\backslash )$ and a sensitivity of $\backslash (\backslash$Delta $\backslash$mathrm$\{$R$\}/\backslash$mathrm$\{$R$\}\_\{\backslash$mathrm$\{$o$\}\}=0\mathrm{.}001/\backslash$mathrm$\{$psi$\}\backslash ).$

a$)$ What is the expression relating the resistance to pressure?

b$)$ If you choose to bias the resistor at constant current of $1$ mA what is the output is V$/$psi$?$

c$)$ Is the output of the circuit in b$)$ linear with applied pressure?

d$)$ Design a circuit using a single sensing element, a $5$ V power supply, and passive components, that will provide $0$ V output at zero pressure.

e$)$ What is the output voltage of the circuit in d$)$ at $20$ psi applied pressure? Is the output of this circuit linear with applied pressure?