Resistance change under temperature

In summary, the resistance of the aluminum rod at 120 degrees Celsius, taking into account changes in both the resistivity and dimensions of the rod, is calculated to be 1.238 ohms. However, there is a possibility of error and it is recommended to verify the approach and use the necessary constants, such as the thermal expansion coefficients and resistivity dependence on temperature, for a more accurate calculation. Additionally, there may be tools available to simplify the process, such as converting to LaTex.
  • #1

Pengwuino

Gold Member
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Ok so we got an aluminum rod that has a resistance of 1.234 ohms at 20 degrees Celsius. I need to calculate the resistance of the rod at 120 degrees by accounting for hte changes in both the resistivity and the dimensions of the rod.

I calculated the resistance would be 1.238 ohms.

Can someone verify this for me?
 
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  • #2
Pengwuino said:
Ok so we got an aluminum rod that has a resistance of 1.234 ohms at 20 degrees Celsius. I need to calculate the resistance of the rod at 120 degrees by accounting for hte changes in both the resistivity and the dimensions of the rod.

I calculated the resistance would be 1.238 ohms.

Can someone verify this for me?

There is a chance someone would verify your approach if you stated how you did the problem and provided the needed constants such as the thermal expansion coefficients and the resistivity dependence on temperature.
 
  • #3
ok here we go, at 20 degrees C...

expansion coeffecient: 24 * 10-6 C^-1 (yah my book says 24, not 2.4)
resistivity coefficient: 3.9 * 10-3 C^-1

Is there a simpler way to use that latex programming? I could show my work but it seems like it would take an hour to type up the formulas correctly.
 
  • #4
Pengwuino said:
ok here we go, at 20 degrees C...

expansion coeffecient: 24 * 10-6 C^-1 (yah my book says 24, not 2.4)
resistivity coefficient: 3.9 * 10-3 C^-1

Is there a simpler way to use that latex programming? I could show my work but it seems like it would take an hour to type up the formulas correctly.

So the new length and cross sections of the rod for a temperature change of 100 degrees C are

[tex]L = L_0(1+24*10^{-4})[/tex]

[tex]A = A_0(1+24*10^{-4})^2[/tex]

and the new resistivity is

[tex]\rho = \rho_0(1+3.9*10^{-1})[/tex]

The new resistance is

[tex]R = \frac{\rho_0(1+3.9*10^{-1})*L_0}{A_0(1+24*10^{-4})}[/tex]

[tex]R = R_0\frac{(1+3.9*10^{-1})}{(1+24*10^{-4})}[/tex]

[tex]R = 1.238\Omega*1.387 = 1.717\Omega[/tex]

One of us did it wrong. I think some people have tools for converting to LaTex. I don't have one, and it is a bit tedious.
 
  • #5
We did it in radically different ways too... someone throw me something that will allow me to do it in less then 5 hours and ill show you lol.

I was looking at it conceptually and thought ok, put a arbitrary number in for A and you can figure out how long a piece of wire would be (I used a wire of 1mm each side so its 1mm^2) and figured the wire would be some 45 meters long or so. I then plugged the length into the length expansion formula and got like a .1 meter expansion and then i plugged in the length into resistance formula using the new p from the resistance-temperature dependence and the resistance change was very small so i figured 2 very small changes should result in a much smaller change and thought my answer could very well be right.

If i just plugged in A = 0.00001m^2 and did all teh calculations correctly, would i still get the right answer (kind of a cheating way of checking your answer?)?

Added: ah crap, i just plugged in 0.001m as the side value (so 1x10^-6m^2) and got 1.717 ohms... crap, wonder where i went wrong.

Ah double crap! I didnt account for the expansion in both directions. Crap crap crap, i hate my life... good thing i did this a day in advance :D
 
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  • #6
Any combination of area, length, and resistivity that gives you the original resistance will work. You can make up any starting numbers you want as long as rho*L/A is 1.238 ohms. My calculation shows that all those numbers are replaced in the end by the original resistance.
 
  • #7
Yah i think leaving A alone screwed me up because it along with the resistivity coefficient just dissappeared in my equation.
 

What is resistance change under temperature?

Resistance change under temperature refers to the phenomenon where the resistance of a material changes as the temperature changes. In most materials, an increase in temperature leads to an increase in resistance.

Why does resistance change under temperature?

Resistance change under temperature is due to the movement of atoms in the material. As the temperature increases, the atoms vibrate more and collide with each other, causing an increase in resistance.

What is the relationship between resistance and temperature?

The relationship between resistance and temperature can vary depending on the material. In most cases, resistance increases with temperature, but in some materials, such as semiconductors, resistance decreases with temperature.

How does resistance under temperature affect electronic devices?

The change in resistance under temperature can affect the performance of electronic devices. It can lead to overheating, which can damage components and cause malfunction. Therefore, it is important to consider the temperature coefficient of resistance when designing and using electronic devices.

How is resistance under temperature measured and calculated?

Resistance under temperature can be measured using a thermometer and an ohmmeter. The temperature coefficient of resistance (TCR) is used to calculate the change in resistance for a certain change in temperature. This can be done using the formula: ΔR = R₀(1 + αΔT), where R₀ is the resistance at the initial temperature, α is the TCR, and ΔT is the change in temperature.

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