Question

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.

Answer 1

Answer:

The value is $R = 0.321 \ \Omega$

Explanation:

From the question we are told that

   The diameter is  $d = 8.252 \ mm = 0.008252 \ m$

    The length of the wire is  $l = 1.0 \ km = 1000 \ m$

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

           $A = \pi * \frac{d^2}{4}$

=>        $A = 3.142 * \frac{ 0.008252^2}{4}$

=>         $A = 5.349 *10^{ - 5} \ m^2$

Generally the resistance is mathematically represented as

      $R = \frac{\rho * l }{A }$

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

=>    $R = \frac{1.72 *10^{-8} * 1000 }{5.349 *10^{ - 5} }$

=>    $R = 0.321 \ \Omega$