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What is the resistance of 1 000 m of 4-mm diameter copper wire? (rCu = 1.7 ´ 10-8 W × m)

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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.

User Richard Schwartz
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