Question for the resistance of the wire

[bckcookie]

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!)

 

[CWatters]

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

 

[bckcookie]

I don't know what is the value of changing L and how to calculate it, please advise me!

 

[CWatters]

If the diameter is reduced the length will increase. Assume the volume of copper is constant.

 

[bckcookie]

I got it, thanks so much!