The resistance of 1 000 m of 4-mm diameter copper wire is approximately 1.35 ohms.
To calculate the resistance of the copper wire, we can use the following formula:
R = ρ * L / A
where:
R is the resistance of the wire (Ω)
ρ is the resistivity of copper (1.7 × 10^-8 Ω⋅m)
L is the length of the wire (1000 m)
A is the cross-sectional area of the wire (m²)
First, we need to calculate the cross-sectional area of the wire.
The wire has a diameter of 4 mm, so the radius is 2 mm (4 mm / 2).
We can use the formula for the area of a circle to find the cross-sectional area:
A = π * r^2
where:
π is the mathematical constant pi (approximately 3.14159)
r is the radius of the wire (2 mm)
Plugging in the values, we get:
A = π * (2 mm)^2 ≈ 12.566 mm²
Now we can calculate the resistance of the wire:
R = 1.7 × 10^-8 Ω⋅m * 1000 m / 12.566 mm² ≈ 1.35 Ω
Therefore, the resistance of 1 000 m of 4-mm diameter copper wire is approximately 1.35 ohms.