# Why is the resistivity of a copper cable much higher than copper?

I was looking at the data sheet for a copper cable and noticed the conductor resistance to be specified at around 5 mOhm/m. This is magnitudes higher than pure copper, which has a resistance in the order of 10 nOhm*m (from Wikipedia). Why is the resistivity so much higher?

• Watch out not to confuse resistance and resistivity in your question. By the way, what is your source for those numbers? – Steeven Oct 23 '15 at 8:47

The resistivity of a metal gives the resistance it will have based on the cross-sectional area and the length of the conductor.

$$\rho = \frac {AR}{L}$$

This means that resitivity is in SI units of $\Omega\text{ m}$. Neither of your quoted figures are in such units. Copper has a resistivity around $1.68 \times 10^{-8} \Omega \text{ m}$.

Unlike the bulk metal, a wire or conductor is manufactured with a constant cross section. If you pull the cross section away, you can characterize it with resistance per length, or $\frac{\Omega}{\text{m}}$.

In fact, assuming the wire above is copper, we can calculate the size based on linear resistance figure given.

$$\rho = \frac{AR}{L}$$ $$A = \frac{\rho} {\frac{R}{L}}$$ $$A = \frac{1.68 \times 10^{-8}\Omega \text{ m}}{5 \times 10^{-3}\Omega \text{ m}^{-1}}$$ $$A = 3.36\times 10^{-6}\text{m}^2 = 3.36\text{mm}^2$$

That cross section happens to be quite close to that of 12 gauge (AWG) wire.

• I had noted the wrong unit for pure copper, but you got it all right in your answer :) – akid Oct 24 '15 at 18:28
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