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19 February, 20:59

If a mile of 24-gauge copper wire has a resistance of 0.14 kΩ and the resistivity of copper is 1.7 * 10-8 Ω ⋅ m, what is the diameter of the wire? (1 mile = 1.6 km)

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  1. 20 February, 00:31
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    D = 497.4x10⁻⁶m. The diameter of a mile of 24-gauge copper wire with resistance of 0.14 kΩ and resistivity of copper 1.7*10-8Ω⋅m is 497.4x10⁻⁶m.

    In order to solve this problem we have to use the equation that relates resistance and resistivity:

    R = ρL/A

    Where ρ is the resistivity of the matter, the length of the wire, and A the area of the cross section of the wire.

    If a mile of 24-gauge copper wire has a resistance of 0.14 kΩ and the resistivity of copper is 1.7*10⁻⁸ Ω⋅m. Determine the diameter of the wire.

    First, we have to clear A from the equation R = ρL/A:

    A = ρL/R

    Substituting the values

    A = [ (1.7*10⁻⁸Ω⋅m) (1.6x10³m) ] / (0.14x10³Ω)

    A = 1.9x10⁻⁷m²

    The area of a circle is given by A = πr² = π (D/2) ² = πD²/4, to calculate the diameter D we have to clear D from the equation:

    D = √4A/π

    Substituting the value of A:

    D = √4 (1.9x10⁻⁷m²) / π

    D = 497.4x10⁻⁶m
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