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?

  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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