Question

A thermistor is a temperature‐sensing element composed of a semiconductor material, which exhibits a large change in resistance proportional to a small change in temperature. A particular thermistor has a resistance of 5 kΩ at 25°C. Its resistance is 340 Ω at 100°C. Assuming a straight‐line relationship between these two values, at what temperature will the thermistor's resistance equal 1 kΩ?

Answer 1

The temperature at which the resistance is $1 k\Omega$ is $89.4^{\circ}C$

Explanation:

For the thermistor in this problem, the relationship between temperature and resistance is linear.

We have:

$R_1 = 5000 \Omega$ when the temperature is $T=25^{\circ}C$

$R_2=340 \Omega$ when the temperature is $T=100^{\circ}C$

Assuming a straight-line relationship, we can find the slope of the line:

$m=\frac{R_2-R_1}{T_2-T_1}=\frac{340-5000}{100-25}=-62.1 \Omega/^{\circ}C$

Now that we know the slope, we can extrapolate the temperature when the resistance is

$R_3 = 1 k\Omega = 1000 \Omega$

In fact, we can write:

$m=\frac{R_3-R_2}{T_3-T_2}$

And solving for $T_3$,

$m(T_3-T_2)=R_3-R_2\\T_3 = T_2 +\frac{R_3-R_2}{m}=100 + \frac{1000-340}{-62.1}=89.4^{\circ}C$

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