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The diameter of 0-gauge copper wire is 8.252 mm. Find the resistance of a 1.00-km length of such wire used for power transmission.

Sagot :

okpalawalter8

Answer:

The value is [tex]R = 0.321 \ \Omega[/tex]

Explanation:

From the question we are told that

   The diameter is  [tex]d = 8.252 \ mm = 0.008252 \ m[/tex]

    The length of the wire is  [tex]l = 1.0 \ km = 1000 \ m[/tex]

   Generally the cross sectional area of the copper wire is mathematically represented as

           [tex]A = \pi * \frac{d^2}{4}[/tex]

=>        [tex]A = 3.142 * \frac{ 0.008252^2}{4}[/tex]

=>         [tex]A = 5.349 *10^{ - 5} \ m^2[/tex]

Generally the resistance is mathematically represented as

      [tex]R = \frac{\rho * l }{A }[/tex]

Here [tex]\rho[/tex] is the resistivity of copper with the value  [tex]\rho = 1.72*10^{-8} \ \Omega \cdot m[/tex]

=>    [tex]R = \frac{1.72 *10^{-8} * 1000 }{5.349 *10^{ - 5} }[/tex]

=>    [tex]R = 0.321 \ \Omega[/tex]

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