Question

A copper cable is 1.2km long and has a cross-sectional Area of 5mm².Find it's resistance at 80°C if at 20°C the resistivity of copper is 0.02×10^-6 ohm m and it's temperature coefficient of resistance is 0.004/°C.

Answer 1

Resistance at 20°C $R_{20}=\frac{\rho{l}}{a} = \frac{0.02×10^{-6}×1.2×10^3M}{5×10{^-6}}=4.8ohms$

Resistance at 80°C $R_{80}=R_{20}[1+\alpha_{20}(80-60)] = 4.8[1+0.004(60)]= 5.95Ω$

$R_{80}= 5.95Ω$