Thermistor / Voltmeter

Assume that I had a circuit as such above. I was wondering, if I increased the temperature of the surroundings, what would a graph of the temperature/PD graph look like?

I know that Resistance decreases with temperature, as more electrons 'escape' from their atoms, so more charge carriers are available, but would the graph show a general decrease in PD as temperature increases?


  • 3
    \$\begingroup\$ Would Electrical Engineering be a better home for this question? \$\endgroup\$ – Qmechanic Apr 30 '16 at 21:40
  • 2
    \$\begingroup\$ The temperature curves of thermistors are technology dependent and can be found in the data sheets. Once you have that, you simply apply a resistor divider formula. \$\endgroup\$ – CuriousOne Apr 30 '16 at 21:42

There are a few formulas to model the behavior of an NTC. The most common (and simlest) one is the b-Formula:

$$R(T)=R_0\cdot \exp\left(b\cdot \left(\frac{1}{T}-\frac{1}{T_0})\right)\right)$$

T is given in Kelvin, and b is a parameter of the NTC type, typically in the order of 3000-5000. \$R_0\$ is the resistance at \$T_0=298.15K(=25°C)\$.

Putting this into the formula of a voltage divider, one gets this plots:

enter image description here

For the first curves, the normal resistor \$R_N\$has a value equal to \$R_0\$, for the two, it has a value of \$200R_0\$ or \$(1/200)R_0\$

So there are three conclusions:

  • The higher the b-value, the higher the sensivity (slope), but the smaller the temperature range.
  • The highest sensitivity is at the temperature T where \$R(T)=R_N\$, and it decreases with temperature difference from T.
  • Choosing an other value for \$R_N\$ allows to shift the usable range, but the sensitivy / range will change, too.
  • \$\begingroup\$ Nice answer. I recommend putting correct units on b (it is a temperature), as I find it adds a level of understanding. \$\endgroup\$ – Scott Seidman Aug 3 '16 at 13:39

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