Question

Calculate the resistance of a copper wire 1.0 km long and 0.50 mm diameter if the resistivity of copper is 1.7 × 10⁻⁸ Ω m.

Answer 1

Length of the cable wire, l = 1 km = 1000 m

Diameter of the cable wire, d = 0.5 mm

Radius of the cable wire, r = 0.25 mm  =${\displaystyle 0.00025\text{m}=2.5=2.5\times {10}^{-4}}$

Area of cross-section,

A ${\displaystyle =\text{A}{\pi }^2}$

${\displaystyle =3.14\times {(2.5\times {10}^{-4})}^2}$

${\displaystyle =0.96\times {10}^{-8}{m}^2}$

Resistivity of the copper cable wire = 1.7 × 10⁻⁸ Ω m.

To find the resistance of the copper cable,

We know that  ${\displaystyle \text{R}=\frac{\text{l}}{\text{A}}}$

R ${\displaystyle =\frac{1.7\times {10}^{-8}\times 1000}{19.6\times {10}^{-8}}}$

So, R = 86.73 Ω

Thus, the resistance of the copper wire, R = 86.73 Ω