Whats the relationship??

[squires]

Hi all,

I am a Heating engineer and I am trying to work out if there is a direct relationship between temperature and resistance of a thermistor, I only have 4 values for each element and when plotting them on a graph it appears to be an exponential curve showing that there is a direct relationship.
I would like to have a usable formula so that when a thermistor has reached a certain temp I know what the resistance should be therefore seeing whether it is faulty or not.

Here are the values T=temp R=resistance, so when T=20 R=12100; T=25 R=10000; T=80 R=1500; T=100 R=900.

I did do maths to a reasonably high level but it was so long ago that I am struggling to get my head round this.

Thanks in advance,

Carl.

 

[galactus]

Hi Squires. With the data you provided, I managed to perform a 'cubic regression' and got an R^2 of 1. This means is as good as it gets.

The equation is \(\displaystyle R=-.034545T^{3}+8.742424T^{2}-760.7273T+24093.94\)

If you sub in your values you provided for T, you will see the results are very close to the R values you provided. I reckon this may be a reasonable formula for inputting T and getting R.

I also done an exponential regression and got \(\displaystyle R=22864.38\cdot (0.96755)^{T}\)

The exponential is not as accurate as the cubic within your data range. Of course, cubics tend to be accurate within a certain domain, then they infinitely increase or decrease.

The cubic should work well if you work with the range T=20 to 100 or somewhere close.

 

[galactus]

There are no maxima or minima for this particular cubic. It decreases.

Here is a graph of the two. Note the cubic is below the x axis for values of T greater than approx. 112. Thus, R could be negative. Which, I would assume, is extraneous.

The exponential is monotonic and levels off on the x axis, thus R will never be negative.

Use which ever one, if either, you wish. Though, in the ling run, the exponential may be the best bet.

If you had more data points, that may help. Things like this tend to be more exponential than polynomial related.

 

[Deleted member 4993]

Need a little Physics here. Thermistors follow Steinhard's equation - which is:

1/T = A + B*ln(R) + C*(ln(R))³ R in W, T in ^oK

Now we can find A, B and C through standard algebra.
​

 

[galactus]

There ya' go !!!. Ol' SK know the correct formula. I am ashamed to admit, I have never heard of a thermistor. So, what do I know
Disregard my hackneyed posts

 

[Deleted member 4993]

Watch out Galactus - whom are you calling old - you whipper snapper.....

Anyway - I am a material scientist - I'm 'pposed to know those things.

For the problem at hand - a linear approximation between (1/T_abs) and ln(R) is very good (R² = 0.9999) - and it is on good "physics" grounding.

However, we must remember the range of the function (data set) T = 20 °C to T = 100 °C

Another warning about the data set - there is a large gap between T = 25 and T = 80

But then we all know - whatever we get, we got to make do with (very carefully)