(5) A platinum resistance sensor is to be used to measure temperatures between 0 and 200 °C. Given that the resistance R, in Q as a function of the input

temperature T °C is given by: R_T=R_0\mleft(1+\alpha T+\beta T^2\mright)^^20^^20where^^20R_0=100\Omega,a=3.91\times10^{-3}and^^20\beta=-5.77\times10^{-7}; (a) Find the maximum non-linearity as percentage of FS. (b) A temperature sensor was inserted into a resistive bridge with DC excitation of V, = 2.5 V as shown in the figure below. i. Assuming the maximum allowed current is through the sensor 1 mA, what would be the value of R4 such that the bridge is balanced when the input temperature is zero? Approximate the result to the next higher standard resistance value. ii. Find the resistance ratio R3/R2 and express the output voltage ETh as a function of RT. iii. Plot the bridge output voltage ETh versus the input temperature T over the specified input temperature range. Estimate the maximum non-linearity in the bridge output as percentage of output voltage FS and compare it to the value you found in (a).