High-voltage power lines are a familiar sight throughout the country. The aluminum (resistivity = 2.82 x 10-8 m) wire used for some of these lines has a cross-sectional area of 4.4 x 10-4 m2. What is the resistance of 12 kilometers of this wire?
Why did the power line go on a diet? Because it wanted to reduce its electrical resistance!
But let me calculate the resistance for you. We can use the formula for resistance: R = (ρ × L) / A, where ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area.
Given:
Resistivity (ρ) = 2.82 × 10^-8 m
Cross-sectional area (A) = 4.4 × 10^-4 m^2
Length (L) = 12,000 m (12 km)
Using the formula, we get:
R = (2.82 × 10^-8 × 12,000) / (4.4 × 10^-4)
Now let's do the math:
R = 3.384 × 10^-3 Ω
So, the resistance of the wire is approximately 3.384 milliseconds of waiting in line at the grocery store.
To find the resistance of the wire, we can use Ohm's Law, which states that resistance (R) is equal to the product of resistivity (ρ), length (L), and the inverse of cross-sectional area (A):
R = ρ * (L / A)
Given:
Resistivity (ρ) = 2.82 x 10^-8 m
Cross-sectional area (A) = 4.4 x 10^-4 m^2
Length (L) = 12 kilometers = 12,000 meters
Substituting the values into the formula:
R = (2.82 x 10^-8) * (12,000 / 4.4 x 10^-4)
Now, let's simplify this expression:
R = 2.82 x 10^-8 * 2.727 x 10^7
To multiply two numbers in scientific notation, you multiply the coefficients and add the exponents. Therefore:
R = 7.69694 x 10^-1
Round the value to an appropriate number of significant figures:
R = 0.7697 Ω
Therefore, the resistance of 12 kilometers of this wire is approximately 0.7697 ohms.