Question for the resistance of the wire

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Homework Help Overview

The discussion revolves around calculating the resistance of a copper wire based on its dimensions and temperature. The original poster presents a problem involving a copper rod and its transformation into a wire, seeking assistance with their calculations and understanding of resistivity and resistance.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate the resistivity of copper and the resistance of a wire derived from a rod, but expresses uncertainty about their steps. Some participants question the assumptions regarding the length of the wire after it is drawn out and the implications of volume conservation.

Discussion Status

Participants are actively engaging with the problem, with some providing clarifications on the relationship between diameter, length, and volume. There is a recognition of the need to adjust calculations based on changing dimensions, but no consensus has been reached on the correct approach yet.

Contextual Notes

There is an assumption that the volume of the copper remains constant during the transformation from rod to wire, which is a point of discussion among participants. The original poster is also navigating the implications of temperature on resistance without fully resolving the calculations.

bckcookie
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I think about many times for few days, but I still can't find out the correct answer! Maybe my steps are somethings wrong, please advise me! Thanks!

A copper rod, 0.4m long and 4.0mm in diameter, has a resistance of 550μΩ at 20℃. Calculate the resistivity of copper at that temperature. If the rod is drawn out into a wire having a uniform diameter of 0.8mm, calculate the resistance of the wire when its temperature is 60℃. Assume the resistivity to be unchanged and the temperature coefficient of resistance of copper to be 0.00426/℃.Correct answer : 0.0173 x 10^-6 ohm m, 0.398ohm

My steps as follows:

the resistivity of copper : 0.0173 x 10^-6 ohm m ( I've got it, no problem!)

the resistance of the wire :

Area : π x [(0.8/2)x10^-3]^2

R0 = Pl/A =[ 0.0173 x 10^-6 x 0.4] / 3.14 x 1.6 x 10^-7 =0.01377ohm

R1 /R2= (1+0.00426x20) / (1+0.00426x60)

R1/0.01377ohm = 0.8652

R1 = 0.1184ohm (wrong answer!)
 
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bckcookie said:
R0 = Pl/A =[ 0.0173 x 10^-6 x 0.4] / 3.14 x 1.6 x 10^-7 =0.01377ohm

The equation R0 = ρL/A is correct but you forgot about L changing when you substituted the numbers.

L is no longer 0.4m
 
I don't know what is the value of changing L and how to calculate it, please advise me!
 
Last edited:
If the diameter is reduced the length will increase. Assume the volume of copper is constant.
 
I got it, thanks so much!
 

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