A power transmission line is made of copper that is 1.8 cm in diameter. If the resistivity of copper is 1.725 10-8 Ω · m, find the resistance of 7 mi of the line.
To find the resistance of the power transmission line, we can use the formula:
R = ρ * (L / A)
where:
R is the resistance
ρ is the resistivity of copper
L is the length of the wire
A is the cross-sectional area of the wire
First, we need to convert the diameter of the copper wire into its radius. The radius (r) can be calculated by dividing the diameter (d) by 2:
r = d / 2
Given that the diameter is 1.8 cm, we have:
r = 1.8 cm / 2 = 0.9 cm
Next, we need to convert the radius from centimeters to meters:
r = 0.9 cm * (1 m / 100 cm) = 0.009 m
To calculate the cross-sectional area of the wire (A), we can use the formula for the area of a circle:
A = π * r^2
where π is a mathematical constant approximately equal to 3.14159.
Given the radius (r), we have:
A = π * (0.009 m)^2
Next, we need to convert the length of the wire into meters. Given 1 mile is approximately 1.60934 kilometers, and 1 kilometer is 1000 meters, we have:
7 mi = 7 * 1.60934 km = 11.26638 km = 11.26638 * 1000 m = 11266.38 m
Now, we have all the values needed to calculate the resistance:
R = (1.725 * 10^(-8) Ω · m) * (11266.38 m / (π * (0.009 m)^2))
Performing the calculations, we can find the resistance of the power transmission line.