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?

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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