A 11.7-Ω resistor is made from a coil of copper wire whose total mass is 13.5 g . The resistivity of copper is 1.68×10−8Ω⋅m, the density of

Question

A 11.7-Ω resistor is made from a coil of copper wire whose total mass is 13.5 g . The resistivity of copper is 1.68×10−8Ω⋅m, the density of copper is 8.9×103kg/m3.
a) What is the diameter of the wire?
b) What is the length of the wire?

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King 3 months 2021-08-13T20:39:54+00:00 1 Answers 2 views 0

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    2021-08-13T20:41:17+00:00

    Answer:

    a) d = 7.62 10⁻⁶ m, b)    l = 3.25 10⁴ m

    Explanation:

    Resistance is expressed by the formula

         R = ρ l / A                       (1)

    density is defined by

         density = m / V

    the volume of a wire is the cross section by the length

         V = A l

    we substitute

         density = m / A l

         A = m / density l

    we substitute in 1

         R = ρ l density l / m

         R =ρ density l² / m

         l = √ (R m /ρ density)

    let’s calculate the cable length

         l = √(11.7  13.5 10⁻³ / (1.68 10⁻⁸ 8.9 10³))

         l = √(10.56 10⁸)

         l = 3.25 10⁴ m

    now we can find the cable diameter with the density equation

          A = m / density l

          A = 13.5 10⁻³ / (8.9 10³ 3.25 10⁴)

          A = 4,557 10⁻¹¹ m²

    the area of ​​the circle is

          A = π r² = π d² / 4

          d = √ (4A /π)

          d = √ (4 4,557 10⁻¹¹/π)

          d = 7.62 10⁻⁶ m

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