Determing Resistance of metal with temperature coefficient of resistance

AI Thread Summary
To determine the resistance of a metal using its temperature coefficient, the equations R_T = R_273(1+alpha(T)) and R_T = R_0(1+alpha(T)) are utilized, where R_T is the resistance at temperature T. The challenge lies in identifying the material's alpha value, as it is unknown. A graph was created to find alpha through the line's gradient, but the results for R_T at other temperatures were invalid. It is suggested to rewrite the equations in the form R_T = R_0(1+alpha(T - T0)) for clarity and to apply linear regression for accurate calculations, while remaining within the linear region of the graph. Accurate determination of alpha is crucial for reliable resistance calculations across varying temperatures.
eximius
Messages
29
Reaction score
0

Homework Statement

I'm trying to determine R_0 and alpha (temperature coefficient of resistance) from results I obtained through an experiment. We have been given the first equation and been told that R_T is the resistance at temperature T in kelvin. R_273 is the resistance at temperature 273K and alpha is a constant called the temperature coefficient of resistance. I don't know what the material is therefore I have no idea of what alpha should be.

Homework Equations


1)R_T = R_273(1+alpha(T))
2)R_T = R_0(1+alpha(T))

The Attempt at a Solution



I created the attached graph to try and determine alpha through the gradient of the line, but no matter how i try and derive alpha and/or R_0, I simply can't get an answer that's gives valid results for R_T at other temperatures.
 

Attachments

  • graph.png
    graph.png
    14.5 KB · Views: 849
Last edited:
Physics news on Phys.org
First, I think you want to write your equations in the form:

R_T = R_0(1+alpha(T - T0))

so when T = T0, then R_T = R_0

Then, I would re-arrange your equation into the standard form:

y = mx + b

And you can solve for alpha with linear regression or pick two good end-point. Metals get non-linear at cold temperatures (as your graph shows) so stay in the linear region.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top