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13 May, 21:27

A wire that has a resistance of 1Ω is to be built from an aluminum block of volume 1 cm3

. How long is the wire going to be?

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  1. 13 May, 21:54
    0
    L = 5,955 m

    Explanation:

    For this exercise we must use the relation

    R = ρ L / A

    where R is the resistance that indicates that it is 1 Ω, the resistivity is taken from the tables ρ = 2.82 10⁻⁸ Ω m, L is the length of the wire and A is the cross section.

    As it indicates to us in volume of aluminum to use we divide the two terms by the length

    R / L = ρ L / (A L)

    the volume of a body is its area times its length, therefore

    R / L = ρ L / V

    R = ρ L² / V

    we clear the length of the wire

    L = √ R V / ρ

    we reduce the volume to SI units

    v = 1 cm³ (1m / 10² cm) ³ = 1 10⁻⁶ m

    let's calculate

    L = √ (1 1 10⁻⁶ / 2.82 10⁻⁸)

    L = √ (0.3546 10²)

    L = 5,955 m
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