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

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