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 × 10-4
Area of cross-section,
A = πr2
= 3.14 × (2.5 × 10-4)2
= 0.96 × 10-8 m2
Resistivity of the copper cable wire = 1.7 × 10−8 Ω m.
To find the resistance of the copper cable,
We know that
R \( = \frac I A\)
\(=\frac{1.7 \times 10^{-8} \times 1000}{19.6 \times 10^{-8}}\)
So, R = 86.73 Ω
Thus, the resistance of the copper wire, R = 86.73 Ω.