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

The value is
`R = 0.321 \ \Omega`

Step-by-step 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 * (d^2)/(4)`

=>
`A = 3.142 * ( 0.008252^2)/(4)`

=>
`A = 5.349 *10^( - 5) \ m^2`

Generally the resistance is mathematically represented as

`R = (\rho * l )/(A )`

Here
`\rho` is the resistivity of copper with the value
`\rho = 1.72*10^(-8) \ \Omega \cdot m`

=>
`R = (1.72 *10^(-8) * 1000 )/(5.349 *10^( - 5) )`

=>
`R = 0.321 \ \Omega`