What is the resistance of a 3.1 m length of copper wire 1.7 mm in diameter?

Question

anonymous · Answer

$$R=\frac{ \rho L }{ A }$$

anonymous · Answer

$$\rho = resistivity, L=length, A=area$$

anonymous · Answer

To find the resistance of a piece of copper wire, we need to consider the equation$$R = \rho \frac{ L }{ A }$$  Where R is resistance measured in Ohms, "rho" is resistivity of copper measured in ohm-meters, L is length measured in meters, and A is area measured in square meters.  If we use 1.70 x 10^-8 as the resistivity then we can determine the resistance.

Next order of business however should be to determine the area of the conductor.  Knowing the diameter is 1.7 mm the radius would be half this value being 0.85 mm or 8.5 x 10^-4 meters.  Then for a circular cross-sectional area:$$A=\pi r ^{2}$$
Using 8.5x10^-4 as the radius and substituting into the equation we find the area to be$$A = \pi r ^{2} = 3.14\times 0.00085^{2} = 2.27e ^{-6} m ^{2}$$
Now returning to our resistivity equation and substituting:$$R = \rho \frac{ L }{ A } = 1.70e ^{-8}\times \frac{ 3.1 }{ 2.27e ^{-6} } = 0.023 Ohms $$
This is the final answer.

anonymous · Answer

As an addendum to Science Guy's post the symbol for ohm is $$\Omega $$

anonymous · Answer

thank you for your help