Household wiring often uses 2.0 mm diameter copper wires. The wires can get rather long as they snake through the walls from the fuse box to the farthest corners of your house.

What is the potential difference across a 16 m long, 2.0 mm diameter copper wire carrying a 7.3 A current?

0.637 V

Explanation:

From Ohm's law,

V = IR Equation 1

Where V = Voltage, I = current, R = resistance.

Also

R = Lρ/A Equation 2

Where L = Length of the copper wire, ρ = resistivity of the copper wire, A = cross sectional area of the copper wire.

But,

A = πd²/4 Equation 2

Where d = diameter.

Substitute equation 2 into equation 1

R = 4Lρ/πd² Equation 3

Substitute equation 3 into equation 1

V = I(4Lρ/πd²) Equation 4

Given: I = 7.3 A, L = 16 m, d = 2 mm = 0.002 m, π = 3.14,

constant: ρ = 1.72 x 10⁻⁸ Ωm

Substitute into equation 4

V = 7.3(4×16×1.72x10⁻⁸)/(3.14×0.002²)

V = 8.04×10⁻⁶/(1.256×10⁻⁵)

V = 0.637 V

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