A 3.7-mm-diameter wire carries a 20 A current when the electric field is 8.2×10−2 V/m . What is the wire’s resistivity? (in Ωm)

Question

A 3.7-mm-diameter wire carries a 20 A current when the electric field is 8.2×10−2 V/m .
What is the wire’s resistivity? (in Ωm)

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Thiên Ân 4 years 2021-07-24T04:13:40+00:00 1 Answers 140 views 0

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  1. ngochoa
    0
    2021-07-24T04:15:35+00:00
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    Answer:

       ρ = 4.4 10⁻⁸ Ω m

    Explanation:

    For this exercise let’s start by finding the value of the resistance using Ohm’s law

              V = I R

               R = V / I

       

    The voltage is related to the electric field

              V = E L

               

    let’s substitute

              R = E L / I

              R = 8.2 10⁻² / 20  

              R = 4.1 10⁻³ L

    now we can use the resistance relation

              R = ρ L / A

    the area of ​​a circular wire is

              A = π r² = π d² / 4

             ρ = R π d² / (4 L)

    let’s calculate

            ρ = (4.1 10⁻³ L) π 0.0037² / (4 L) = (4.1 10⁻³) π 0.0037² / (4)

            ρ = 4.4 10⁻⁸ Ω m

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