Digital medical thermometers determine temperature by measuring the resistance o

Question

Digital medical thermometers determine temperature by measuring the resistance of a semiconductor device called a thermistor (which has = 0.0620/°C) when it is at the same temperature (in °C) as the patient. What is a patient's temperature if the thermistor's resistance at that temperature is 84.0% of its value at 37.0°C (normal body temperature)?

B) The negative value for may not be maintained for very low temperatures. Discuss why and whether this is the case here. (Hint: Resistance can't become negative.)

Explanation / Answer

alpha, coefficient of resistivity change alpha = -0.0620 / C
let the patients temperature be T
resistance at Temperature T = R
body temperature = TO = 37 C
Resistance at this temp = RO
now, R = 0.84Ro

also, R = Ro(1 + alpha*(T - To))
0.84 = 1 + alpha(T - To)
-0.16 = -0.062(T - 37)
T = 39.58 C

B. as alpha is -ve, so when temperatuer increases, resistance of the resistor drops
   consider
   reisstance of 0
   0 = 1 + alpha(T - 37)
   1 = 0.062(T - 37)
   T = 53.16
   so above 53.16 C, the resistance should become -ve, but its not possible physically
   so that mrans value of alpha will change a

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