Q$1)$ The system shown in fig$1$ is used to monitor the temperature of a chamber.

The temperature is measured through a sensor with a resistance $R_S$ that varies linearly with temperature. As temperature varies from $50$ to $100C,$ the sensor impedance varies from $450$ to $500.$ Neglect loading between stages one and two and let

s

$V_S=15$ volts.

i$)$ Find $R_1$ so that maximum power dissipated by sensor will not exceed $9$ mW $(3$ points$)$

ii$)$ Find values of $R_2,R_3$ and $V_1$ so that $V_{\text{o}\text{u}\text{t}}$ will be $0$ volt when temperature is $50C$ and $5$ volts when temperature reaches $100C.(3$ points$)$

iii$)$ Find the rate of change of the output voltage with respect to impedance Rs $(2$ points$)$