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  =`0.00025 " m" = 2.5 = 2.5 xx 10^-4`

Area of cross-section,

A `= "A"pi^2`

`= 3.14xx(2.5xx10^-4)^2`

`= 0.96xx10^(-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  `"R"="l"/"A"`

R `= (1.7xx10^-8xx1000)/(19.6xx10^-8)`

So, R = 86.73 Ω

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