# Graph of Thermistor against Temperature

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?

Thanks.

• Would Electrical Engineering be a better home for this question? – Qmechanic Apr 30 '16 at 21:40
• 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. – 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:

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.
• Nice answer. I recommend putting correct units on b (it is a temperature), as I find it adds a level of understanding. – Scott Seidman Aug 3 '16 at 13:39