High-voltage power lines are a familiar sight throughout the country. The aluminum wire used for some of these lines has a cross-sectional area of 4.7 10-4 m2. What is the resistance of ten kilometers of this wire?
To find the resistance of the aluminum wire, we need to use the formula:
Resistance (R) = Resistivity (ρ) x Length (L) / Cross-sectional area (A)
The resistivity of aluminum is typically around 2.65 x 10^-8 Ω·m.
First, let's convert the length of the wire from kilometers to meters:
10 kilometers = 10,000 meters
Now, we can substitute the values into the formula:
R = (2.65 x 10^-8 Ω·m) x (10,000 m) / (4.7 x 10^-4 m^2)
Simplifying, we have:
R = (2.65 x 10^-8 Ω·m) x (10,000 m) / (4.7 x 10^-4 m^2)
= 2.65 x 10^-8 x 10^4 Ω / 4.7 x 10^-4 m
= (2.65 / 4.7) x (10^-8 x 10^4) Ω / m
= 0.5638 x 10^-4 Ω / m
= 5.638 x 10^-5 Ω / m
Therefore, the resistance of ten kilometers of this aluminum wire would be approximately 5.638 x 10^-5 Ω / m.