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 RoeBIT, where R is in ohms (2), T is in kelvins, and Ro 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 = 6888 at the ice point and 133 at the steam point, find Ro and B Ro= B= (b) what is the resistance of the thermistor at T= 98.6°F? (c) What is the rate of change of the resistance with temperature (dR/dT) at the ice point and the steam point? ice point steam point (d) At which temperature is the thermistor most sensitive? n/K O higher temperature lower temperature

Explanation / Answer

Given,

Resistance, R = 6888 at ice point, 133 at steam point

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

At T = 273 K (ice point), R = 6888 and at T = 373 K (steam point), R = 133

ln(6888) = ln R0 + /273

ln(133) = ln R0 + /373

/273 - /373 = ln(6888) - ln(133)

= 4019.19 K

ln R0 = ln(6888) - 4019.19/273 = -5.88

R0 = exp (-5.88) = 0.00278

(b) T = 98.6 °F = 37 oC = 310 K

R = 0.00278 x exp(4019.19/310) = 1187.76

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

At T = 273 K (ice point),

dR/dT = (-4019.19 x 0.00278/2732) x exp(4019.19/273) = -371.26 /K

At T = 373 K (steam point),

dR/dT = (-4019.19 x 0.00278/3732) x exp(4019.19/373) = -3.84 /K

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

lower temperature

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