A thermistor is a solid-state device widely used in a variety of engineering app

Question

A thermistor is a solid-state device widely used in a variety of engineering applications. Its primary characteristic is that its electric resistance varies greatly with temperature. Its temperature dependence is given approximately by R = R0eB/T, where R is in ohms (), T is in kelvins, and R0 and B are constants that can be determined by measuring R at calibration points such as the ice point and the steam point. (a) If R = 7360 at the ice point and 153 at the steam point, find R0 and B.

(b) What is the resistance of the thermistor at T= 98.6°F?
3

(c) What is the rate of change of the resistance with temperature (dR/dT) at the ice point and the steam point?

(d) At which temperature is the thermistor most sensitive?

Explanation / Answer

(a) R = R0e/T => ln R = ln R0 + /T

At T = 273 K (ice point), R = 7360 and at T = 373 K (steam point), R = 153

ln(7360) = ln R0 + /273

ln(153) = ln R0 + /373

/273 - /373 = ln(7360) - ln(153)

= 3944 K

ln R0 = ln(7360) - 3944/273 = -5.543

R0 = exp (-5.543) = 0.003914

(b) T = 98.6 oF = 37 oC = 310 K

R = 0.003914 x exp(3944/310) = 1312

(c) R = R0e/T => dR/dT = (-R0/T2)e/T

At T = 273 K (ice point),

dR/dT = (-3944 x 0.003914/2732) x exp(3944/273) = -389 /K

At T = 373 K (steam point),

dR/dT = (-3944 x 0.003914/3732) x exp(3944/373) = -4.34 /K

(d) The thermistor is most sensitive when |dR/dT| is largest:

i.e. lower temperature

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