(Solved): Q1- A Linear temperature sensor RX is connected in the circuit shown opposite, where Vin=12 ...

Q1- A Linear temperature sensor ${\mathbf{R}}_{\mathbf{X}}$ is connected in the circuit shown opposite, where ${\mathrm{V}}_{\text{in }}=12[\mathrm{V}]$. If the sensor resistance ${\mathbf{R}}_{\mathbf{S}}[?]$ varies with temperature $T\left[{}^{?}\mathrm{C}\right]$ according to the following equation: $R_S=0.5T+90$ a) Assign values to resistors $R_1,R_2$, and $R_3$ so that $V_0=0[\mathrm{V}]$ at $T={20?}^{?}\mathrm{C}]$ ? b) Derive the equation for $V_O[\mathbf{V}]$ as a function of the temperature ${T?}^{?}\mathrm{C}]$ ? c) Sketch $V_O[\mathrm{V}]$ versus ${\mathrm{T}?}^{?}\mathrm{C}]$ for $0?{T?}^{?}\mathrm{C}??100$ ? d) Determine the value of ${\mathbf{V}}_{\mathrm{o}}[\mathbf{V}]$ and the circuit sensitivity in units of $\left[\mathrm{mV}/{}^{?}\mathrm{C}\right]$ at temperature $\mathbf{T}={20?}^{?}\mathrm{C}?$ ? e) Use the results of part-d to calculate a linear approximation for ${\mathbf{V}}_{\mathrm{o}}[\mathbf{V}]$ ? f) Determine the \% relative error in the value of ${\mathbf{V}}_{\mathbf{O}}[\mathbf{V}]$ at $\mathbf{T}={80?}^{?}\mathrm{C}$, if the linear approximation calculated in part-e was used?