Resistance of a copper wire

In summary, the conversation discussed the calculation of resistance and drift velocity for a 10-g piece of copper formed into a wire with a radius of 1.0 mm at 50°C. The resistivity of copper at 50°C was found to be 1.899*10^-8 Ωm. The conversation then explored how to determine the length of the wire using the density of copper, which led to a final calculation of 2.152*10^-4 ohms for the wire's resistance. The high current of 5577 amps was noted, potentially causing the wire to melt if not properly cooled.
  • #1
pilotguy
12
0

Homework Statement



A 10-g piece of copper is to be formed into a wire of radius 1.0 mm at a temperature of 50°
C. What is the resistance of this wire? (Hint: you will need to look up the density of copper.) If a potential of 12 V is put across this wire, what is the drift velocity?

Homework Equations



J=I/A=nqvd
R=ρ(L/A)
ρ=ρ0(1+[itex]\alpha[/itex](T-T0)
ρ0=1.7*10^-8 at 20°C

The Attempt at a Solution



The resistivity of copper at 50°C is:
ρ=ρ0(1+[itex]\alpha[/itex](T-20) where [itex]\alpha[/itex]=3.9*10^-3 1/°C
Substituting values, ρ=1.899*10^-8 Ωm

I hit a brick wall here, though. I don't know how to get from density of copper to length of the wire for R=ρ(L/A)

Any advice?
 
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  • #2
What can you calculate from the density and mass of the piece of copper? How does that relate to A and L?
 
  • #3
Hmm. Density of Cu=8.96 g/cm^3

(8.96g/cm^3 * 1 / 10g)^-1=1.119 cm^3 Ohh, that gives you a volume! D'oh!

V=1.119 cm^3
1.119=pi*r^2*L
L=1.119/(pi*.1^2)
L=35.605 cm

So, R=rho(L/A)
R=(1.899*10^-8)(.0356)/(3.142*10^-6)
R=2.152*10^-4 ohms

Does this sound right?
 
  • #4
Except that gives a current of 5577 amps for the second part. What am I missing?
 
  • #5
Everything looks ok to me except for your conversion of L from cm to m.
 
  • #6
Yeah, I noticed that. I tried it with the correct conversion (.356 m) and 5577 amps was what I found for current. Isn't that really high though?
 
  • #7
I think it's ok. The resistance of the wire is very small, so the current will be very high. In fact, the current would quickly heat the wire and it could melt if there's not sufficient heat transfer to the environment.
 

1. How does temperature affect the resistance of a copper wire?

As the temperature of a copper wire increases, its resistance also increases. This is because the atoms in the wire vibrate more at higher temperatures, making it more difficult for electrons to pass through and increasing the overall resistance.

2. What factors determine the resistance of a copper wire?

The resistance of a copper wire is determined by its length, cross-sectional area, and the material's resistivity. The longer the wire, the higher the resistance, while a larger cross-sectional area and lower resistivity will result in lower resistance.

3. How does the thickness of a copper wire affect its resistance?

The thickness of a copper wire, also known as its gauge, has an inverse relationship with its resistance. A thicker wire will have a lower resistance compared to a thinner wire of the same length and material.

4. Why is copper commonly used in electrical wires?

Copper is commonly used in electrical wires due to its low resistivity and high conductivity. This allows for the efficient flow of electricity through the wire with minimal loss of energy due to resistance.

5. Can the resistance of a copper wire be changed?

Yes, the resistance of a copper wire can be changed by altering its length, cross-sectional area, or temperature. Additionally, the use of different materials or alloys can also affect the resistance of a copper wire.

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