# Homework Help: Thermistors - Voltage across a resistor compared with temperature

1. Mar 13, 2005

### Noj

I have physics courseowkr due tomorrow on sensors. Mine is on thermistors. I have got results of voltage across a resistor and this is compared with temperature. I don't know what my results tell me though and so I can't really hand in the coursework. Does anyone know anything about thermistors that can help me?!?! Many thanks,

Noj

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2. Mar 13, 2005

### xanthym

Try graphing the results at the site below using a Best-Fit Polynomial of degree 2. When graphing, use measured temperature in DEGREES KELVIN (add 273 to degC readings) on the x-axis (horizontal) and measured Voltage (in Volts) on the y-axis (vertical). Then read the Best-Fit equation from the output box below the graph. Of course, also screen capture the graph and label the 2 axes by hand for your report. (You can average your 2 data sets together into 1 graph.)
http://www.arachnoid.com/polysolve/

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Last edited: Mar 13, 2005
3. Mar 13, 2005

### xanthym

The URL below presents a "best-fit" curve thru your data using Degree-2 Polynomial Regression techniques. The graphed data is the average of your 2 data sets. Vertical axis ("y") is measured Voltage (in Volts), and Horizontal axis ("x") is measured Temperature (in Degrees Kelvin which is degC + 273). Note that the portion of the curve from about 330 degK to 365 degK is almost linear. This region would be best suited for operation of your thermistor device. In the box below the curve is the best-fit Degree-2 Polynomial ("quadratic") equation which shows the approx relationship between measured Temperature and Voltage. In this equation, "x" is Temperature (in degKelvin), and "y" is Voltage (in Volts) with the values of "a", "b", and "c" given there. (However, this equation is only valid within the range of Temperatures used in your experiment.) This equation might be utilized to better understand your device's operation. These results for your measurements are just one example of what can be done with experimental data.
Data Graph ---> http://img32.exs.cx/img32/9397/thermistorexp6os.jpg

Data was graphed at this Web Site:
http://science.kennesaw.edu/~plaval/applets/QRegression.html [Broken]

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Last edited by a moderator: May 1, 2017
4. Mar 13, 2005

### Noj

As you can see I'm up bright and early!! I just wanted to tell you that you are really the kindest person I have ever met. Just a few small points,

why have you used Degrees Kelvin??

you also mentioned that other things are possible with the data and I was just wandering if you could let me know?

I really am struggling on this project, if I can get an extension I would try to grasp it much better than i have, Thank you again for your kindness,

Noj

5. Mar 13, 2005

### xanthym

Degrees Kelvin is the standard method of using Temperature in theoretical studies and in equations. For instance, later in Chemistry, you'll use the equation {P*V=n*R*T}, where T is temperature in Degrees Kelvin.

Other possibilties for considering the data include trying to transform the data into a straight-line linear form, calculating the curve slopes at various points to determine Temperature-Voltage sensitivities under differing conditions, and determining statistical characteristics of the curve fit like the "variance" or "confidence intervals". Most of these items would require more measurement data or would take too much time at this stage. It's probably best to just focus on what you've done so far.

Remember that the reference below has lots of useful material for introductory or background info for you report.
http://www.thermometrics.com/assets/images/ntcnotes.pdf [Broken]

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Last edited by a moderator: May 1, 2017
6. Mar 13, 2005

### Noj

I did try to find useful information in the link but it doesn't focus on voltage against temperature information and so I can't see what I can get out of it. Have you had a look at it? I am currently writing about the need for a low current and not using a temperature outside of the maximum range for the thermistor. I have until 2pm today to write it up but to be honest I can't seem to say everything there is to say and what the relevence of the equation is that you gave me in my other thread on this matter. I will use the graient to work out the sensitivity of the sensor but what does the value I get mean and should I use the graph with degrees kelvin or the graph simply from the excel values. Your humble servant,

Noj

7. Mar 14, 2005

### xanthym

Concerning the reference document, the portion of interest is called "Linear Voltage Divider", and it presents Figure 14 (Voltage versus Temperature graph) which looks very much like your data!! You'll need to scroll all the way into the document (use the Figure number #14 to guide you). This document also provides descriptions of various thermistor applications.

You can use your Excel graph for the main data presentation. The best-fit curve graph and the best-fit equation are "extras" you can utilize (in addition to the Excel graph) to show an additional method for studying the data. Unfortunately, there's not a lot of "physical significance" to describe for the best-fit curve equation (at this point) because we haven't had time for the detailed thermistor physics. Just consider the equation as "quantifying" the relationship you measured between Voltage and Temperature in your experiment.

The slope of Voltage versus Temperature (units of Volts/degKelvin or Volts/degC depending on which graph you use) indicates how fast the Voltage is changing with respect to changes in Temperature. The larger the value, the greater the thermistor sensitivity. Note that the slope and thus the sensitivity can be different at different temperatures. Obviously, one would like to use the thermistor at temperatures for which it's fairly sensitive.

The equation below (which was stated before) is a THEORETICAL description of what the Voltage versus Temperature relationship should be for the basic voltage divider circuit. It's for your information, or you can also present it in your report for further background info. (It's a combination of some equations in the reference document.) Again, when you graph this equation, it has a similar general appearance to your data.

$$:(1): \ \ \ \ V \ = \ V_{s} \frac {R} {R + R_{0}e^{C(T - T_{0})} }$$

http://img191.exs.cx/img191/6674/thermistorexp4zk.jpg

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Last edited: Mar 14, 2005