D = 497.4x10⁻⁶m. The diameter of a mile of 24-gauge copper wire with resistance of 0.14 kΩ and resistivity of copper 1.7×10−8Ω⋅m is 497.4x10⁻⁶m.
In order to solve this problem we have to use the equation that relates resistance and resistivity:
R = ρL/A
Where ρ is the resistivity of the matter, the length of the wire, and A the area of the cross section of the wire.
If a mile of 24-gauge copper wire has a resistance of 0.14 kΩ and the resistivity of copper is 1.7×10⁻⁸ Ω⋅m. Determine the diameter of the wire.
First, we have to clear A from the equation R = ρL/A:
A = ρL/R
Substituting the values
A = [(1.7×10⁻⁸Ω⋅m)(1.6x10³m)]/(0.14x10³Ω)
A = 1.9x10⁻⁷m²
The area of a circle is given by A = πr² = π(D/2)² = πD²/4, to calculate the diameter D we have to clear D from the equation:
D = √4A/π
Substituting the value of A:
D = √4(1.9x10⁻⁷m²)/π
D = 497.4x10⁻⁶m
The diameter of a mile of 24-gauge copper wire with resistance of 0.14 kΩ and resistivity of copper 1.7×10−8Ω⋅m is D = 497.4x10⁻⁶m.
Resistivity, electrical resistance of a conductor of unit cross-sectional area and unit length. A characteristic property of each material, resistivity is useful in comparing various materials on the basis of their ability to conduct electric currents. High resistivity designates poor conductors.
In order to solve this problem we have to use the equation that relates resistance and resistivity:
[tex]R = \dfrac{\rho L}{A}[/tex]
Where ρ is the resistivity of the matter, the length of the wire, and A the area of the cross section of the wire.
If a mile of 24-gauge copper wire has a resistance of 0.14 kΩ and the resistivity of copper is 1.7×10⁻⁸ Ω⋅m. Determine the diameter of the wire.
First, we have to clear A from the equation R = ρL/A:
[tex]A = \dfrac{\rho L}{R}[/tex]
Substituting the values
[tex]A = \dfrac{[(1.7\times10^{-8} )(1.6\times10^3)]}{(0.14\times10^3)}[/tex]
A = 1.9x10⁻⁷m²
The area of a circle is given by A = πr² = π(D/2)² = πD²/4, to calculate the diameter D we have to clear D from the equation:
[tex]D = \sqrt{\dfrac{4A}{\pi}[/tex]
Substituting the value of A:
[tex]D = \sqrt{\dfrac{4(1.9\times10^{-7})}{\pi}[/tex]
D = 497.4x10⁻⁶m
Hence the diameter of a mile of 24-gauge copper wire with resistance of 0.14 kΩ and resistivity of copper 1.7×10−8Ω⋅m is D = 497.4x10⁻⁶m.
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