Determing Resistance of metal with temperature coefficient of resistance

In summary, the conversation discusses the process of determining R_0 and alpha (temperature coefficient of resistance) from experimental results. The equations used are R_T = R_273(1+alpha(T)) and R_T = R_0(1+alpha(T)). The individual has attempted to use a graph to find alpha, but has not been successful. Suggestions are given for finding alpha through linear regression or by selecting two good end-points. It is noted that metals can exhibit non-linear behavior at low temperatures.
  • #1
eximius
29
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

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  • #2
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.
 

1. What is the temperature coefficient of resistance?

The temperature coefficient of resistance (TCR) is a measure of how much an object's resistance changes with a change in temperature. It is typically expressed in units of ohms per degree Celsius (Ω/°C) or ohms per degree Kelvin (Ω/K).

2. How does temperature affect the resistance of a metal?

As the temperature of a metal increases, the average kinetic energy of its atoms also increases. This causes the atoms to vibrate more, which in turn increases the collisions between electrons and the atoms. These collisions make it more difficult for the electrons to flow, resulting in an increase in resistance.

3. How is the resistance-temperature relationship represented mathematically?

The resistance-temperature relationship can be represented by the equation R = R0[1 + α(T - T0)], where R is the resistance at a given temperature, R0 is the resistance at a reference temperature T0, and α is the temperature coefficient of resistance.

4. How can the temperature coefficient of resistance be determined experimentally?

To determine the temperature coefficient of resistance, you can conduct an experiment where the resistance of a metal is measured at different temperatures. The TCR can then be calculated by dividing the change in resistance by the change in temperature.

5. What are the practical applications of understanding the resistance-temperature relationship?

Understanding the resistance-temperature relationship is important in designing and using electronic devices. It allows for the prediction and compensation of changes in resistance due to temperature, which can help maintain the proper functioning of electronic components. This knowledge is also used in the design of thermistors, which are temperature-sensitive resistors used in temperature measurement and control systems.

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