# Resistance of a copper wire

1. Jun 26, 2012

### pilotguy

1. The problem statement, all variables and given/known data

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?
2. Relevant equations

J=I/A=nqvd
R=ρ(L/A)
ρ=ρ0(1+$\alpha$(T-T0)
ρ0=1.7*10^-8 at 20°C
3. The attempt at a solution

The resistivity of copper at 50°C is:
ρ=ρ0(1+$\alpha$(T-20) where $\alpha$=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)

2. Jun 26, 2012

### TSny

What can you calculate from the density and mass of the piece of copper? How does that relate to A and L?

3. Jun 26, 2012

### pilotguy

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. Jun 26, 2012

### pilotguy

Except that gives a current of 5577 amps for the second part. What am I missing?

5. Jun 26, 2012

### TSny

Everything looks ok to me except for your conversion of L from cm to m.

6. Jun 26, 2012

### pilotguy

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. Jun 26, 2012

### TSny

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.