Why Does My Calculation of Ro Result in Zero for a Thermistor?

[lionely]

The resistance,R, of a thermistor varies with absolute temperature according to the following equation:

R= R₀ e^k/T


I was asked to find the constant k using the graph.

I put the equation given in the form

ln R= k/t + lnR₀

k would be the gradient. So I found the gradient from the graph and I got 2968.80

then I was asked to find Ro

so I used a point off the graph and the gradient

point (2.88,4.3)

4.3 = lnRo + (2968.80/2.88)

=> lnRo = -1.031 x 10⁶

then I took anti logs and got Ro = 0 . Which i think is wrong...

Guidance appreciated.

 

[TSny]

point (2.88,4.3)

Should the 2.88 be multiplied by 10 to some power?

4.3 = lnRo + (2968.80/2.88)

Do you really want to divide here?

 

[lionely]

Oh yeah the 2.88 should be 2.88 x 10^-3

and yeah wouldn't I divide? Isn't it k/T?

 

[TSny]

and yeah wouldn't I divide? Isn't it k/T?

k/T says to divide by T. But you're graphing 1/T, not T.

 

[lionely]

oh I see thank you.

 

[lionely]

I got Ro to be 0.014

 

[TSny]

That looks ok. But, I find the graph has a slope (gradient) closer to 2850. That would change the result for Ro somewhat.

 

[lionely]

Oh what did you use for your values to find the gradient? I used (3.52*10^-3 , 6.2)

(2.88 * 10^-3, 4.3)

 

[TSny]

When finding the gradient, it's best to pick two points on the line rather than picking two data points. The data points generally don't lie directly on the best fit line. Also, it's best to pick two points fairly far apart.

I picked the two points shown in the attached figure.

 

[lionely]

ohh okay thank you

 

[TSny]

Also, note that you cannot expect to get a gradient more precise than 3 significant figures for this graph.