High-voltage power lines are a familiar sight throughout the country. The aluminum?

Question

High-voltage power lines are a familiar sight throughout the country. The aluminum (resistivity = 2.82 x 10^-8 Ohm *m) wire used for some of these lines has a cross-sectional area of 4.4 x 10^-4 m^2. What is the resistance of 12 kilometers of this wire?

Answer 1

resistivity is a measure of how well (or poorly) a substance conducts.

Suppose you have a cylinder of length L and cross sectional area A, made of a material of resistivity P. Its resistance R will be:

R = P x L / A

This makes sense because:

- for a given wire diameter, doubling the length doubles the resistance.

- for a given length, doubling the cross-sectional area is like putting two of the original wires in parallel, halving the resistance.

In this case you know P, L, and A, so you can compute R.

Answer 2

Resistivity of aluminium = 2.75x10^-8 ohm m Resistance, R of 10.9 kilometers of this twine with go-sectional section 3.7x10^-4 m^2 is given via R = (2.75x10^-8x 10.9x10^3)/3.7x10^-4 = 8.10x10^-one million = 0.810 ohm