Question

High-voltage power lines are a familiar sight throughout the country. the aluminum (resistivity = 2.82 x 10-8Ï m) wire used for some of these lines has a cross-sectional area of 4.1 x 10-4 m2. what is the resistance of 8.2 kilometers of this wire?

Answer 1

The formula that relates the resistance R of a wire with the resistivity
`\rho` of the material of the wire is

`R= (\rho L)/(A)`
where L is the length of the wire (in our problem,
`L=8.2 km=8200 m`) and A is the cross sectional area (in our problem,
`A=4.1 \cdot 10^(-4) m^2`).
For the aluminim wire (
`\rho =2.82 \cdot 10^(-8) \Omega \cdot m`) of the problem, the resistance is

`R= ((2.82 \cdot 10^(-8)\Omega m)(8200 m))/(4.1\cdot 10^(-4)m^2)=0.564 \Omega`