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18 August, 18:09

A 10.3 g wire has a density of 10.7 g/cm3 and a resistivity of 6.9 * 10-8 Ω · m. The wire has a resistance of 59 Ω. How long is the wire?

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  1. 18 August, 19:34
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    Answer

    28.65 m

    Explanation

    First we need to find the cross sectional area of the wire and for that we need to find the radius of the wire, r

    density = mass / volume

    10.7 = 10.3 / volume

    volume = 10.3/10.7

    = 0.96cm³

    1,000,000 cubic centimeters = 1 cubic meter

    so

    0.96/1,000,000 = 9.6 x 10^-7m

    formula for volume

    volume of wire = πr² (L)

    9.6 x 10^-7 = πr² (L)

    r = √ (9.6 x 10^-7/π (L))

    cross sectional area of wire = πr²

    Formula for resistivity

    R = p * length / cross SA

    59 = 6.9 * 10^-8 (L) / πr²

    59 = 6.9 * 10^-8 (L) / π (9.6 x 10^-7/π (L)

    59 = 6.9 * 10^-8 (L) / 9.6 x 10^-7 / (L)

    59 / 6.9 * 10^-8 = L / 9.6 x 10^-7 / (L)

    L² = 59 (9.6 x 10^-7) / 6.9 * 10^-8

    L² = 820.87

    L = √ 820.87

    = 28.65m

    So, the wire is 28.65 m long
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