The resistivity of iron is 1 x 10 -7 Ωm. The resistance of a iron wire of particular length and thickness is 1 ohm. If the length and the di

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The resistivity of iron is 1 x 10 -7 Ωm. The resistance of a iron wire of particular length and thickness is 1 ohm. If the length and the diameter of wire both are doubled, then the resistivity in Ωm will be

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Bơ 4 years 2021-08-25T10:20:55+00:00 1 Answers 175 views 0

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  1. dangkhoa
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    2021-08-25T10:22:31+00:00
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    Answer:

    2×10⁻⁷ Ωm

    Explanation:

    From the question,

    R = 4ρL/πd²……………….. Equation 1

    Where R = Resistance of the wire, ρ = resistivity of the wire, L = length of the wire, d = diameter of the wire.

    Therefore,

    ρ = Rπd²/4L…………. Equation 2

    Given: R = 1 ohm, ρ = 1×10⁻⁷Ωm

    1×10⁻⁷ = πd²/4L……………….. Equation 3

    If the length and the diameter are doubled, and the resistance remaining constant

    ρ’ = π(2d)²/4(2L)

    Where ρ’  = new resistivity

    ρ’ = 4πd²/8L

    ρ’ = 2πd²/4L = 2ρ

    ρ’ = 2(1×10⁻⁷)

    ρ’ = 2×10⁻⁷ Ωm

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