You have a temperature sensor but you have no technical info

You have a temperature sensor, but you have no technical information about the sensor. Therefore, you conduct an experiment in which you measure the sensor\'s response immediately after it is placed into a container of boiling water at 100degree C. The plot shows the response. Assuming a first-order sensor, estimate the time constant and static sensitivity. Determine largest frequency content (in Hz) that the sensor can measure with a dynamic error magnitude within 10%. (If you don\'t have an answer for (a), then use a time constant of 0.5 seconds] Using the estimates in (a), determine the sensor\'s steady-state output response in volts for the input 85 + 10 sin (4 pi t) degree C. [If you don\'t have an answer for (a), then use a time constant of 0.5 seconds and a static sensitivity of 0.1 V/degree C]

Solution

a. First order sensor equation between volage and time is V=2(1-e^^-t/k)+1.4

where k is time constant.

time constant k=time taken to reach 0.673 of (2-1.4)v from 1.4v=0.37v

time taken for reaching (1.4+0.37)v is 0.5 sec. Hence k=0.2 sec.

hence equation becomes V=2(1-e^-2t)+1.4.

static sensitivity =(2-1.8)/(2.5-0.5)=0.1v/sec.