Finding the coefficients of a Resistance vs. Temp curve

In summary: In this case, the coefficients are not perfect factors of each other because the temperatures are not all the same. To solve for a and b, you would need to divide each equation by the coefficient of that equation and then solve for a and b.
  • #1
guyvsdcsniper
264
37
Homework Statement
Find Ro, a, and b.
Relevant Equations
R(T) = Ro (1 + aT + bT2 )
I am asked to find Ro, a, and b. Th problem states the values are determined by the measurements at the normal ice, steam and sulfur points. So I approached the problem by plugging the the temperature problems. For 0°C, Ro reduces to 7 ohms. Then for the other two non zero temperatures, it looks like I am left with a system of equations.

I am a bit stumbled because the values associated for a and b of both equations arent factors of each other, so canceling out seems a bit trickier. I don't really recall running across a problem like this before.

Am I approaching this problem correctly? If so what is a way to solve for a and b?
img_b9c76850568e-1-jpeg.jpg
 
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  • #2
You have three temperatures which means that you can write three equations, one at each temperature, and three unknowns. The first equation gives you (as you have already found) R0 = 7 Ω. Use that value in the other two equations which form a system of 2 equations and 2 unknowns a and b. Can you solve that?
 
  • #3
kuruman said:
You have three temperatures which means that you can write three equations, one at each temperature, and three unknowns. The first equation gives you (as you have already found) R0 = 7 Ω. Use that value in the other two equations which form a system of 2 equations and 2 unknowns a and b. Can you solve that?
I figured it out. I actually just finished a linear algebra course and they never gave us a problem like that where the coefficients weren't perfect factors of each other.

Very noob post. Sorry lol
 
  • #4
quittingthecult said:
I figured it out. I actually just finished a linear algebra course and they never gave us a problem like that where the coefficients weren't perfect factors of each other.
Yes, but don't berate yourself. You were led up the garden path. Mathematicians sometimes have a different view of the world from physicists.
 
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Related to Finding the coefficients of a Resistance vs. Temp curve

1. What is the purpose of finding the coefficients of a Resistance vs. Temp curve?

The coefficients of a Resistance vs. Temp curve allow us to determine the relationship between resistance and temperature for a particular material. This information is useful in understanding the behavior of the material and can be used to make predictions about its resistance at different temperatures.

2. How are the coefficients of a Resistance vs. Temp curve calculated?

The coefficients are typically calculated using regression analysis, which involves fitting a mathematical curve to a set of data points. This curve is then used to calculate the coefficients, which represent the slope and intercept of the curve.

3. What factors can affect the coefficients of a Resistance vs. Temp curve?

The coefficients can be affected by various factors, including the type of material, the purity of the material, and the measurement method used. Other factors such as environmental conditions and sample preparation can also have an impact on the coefficients.

4. How can the coefficients of a Resistance vs. Temp curve be used in practical applications?

The coefficients can be used to design and optimize electronic circuits, as well as in the development of temperature sensors and other devices that rely on the relationship between resistance and temperature. They can also be used in quality control and testing processes for materials.

5. Can the coefficients of a Resistance vs. Temp curve change over time?

Yes, the coefficients can change over time due to factors such as aging, material degradation, and changes in environmental conditions. It is important to regularly recalibrate and update the coefficients to ensure accurate measurements and predictions.

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