Answer to Question #201618 in Electric Circuits for Nipesh Chaudhary

Question

The temperature cofficient of copper is 0.004°c^-1. Find the

resistance of a 5 m long copper wire of diameter 0.2mm at

100°c it the resistivity of copper at 0ºc is 1.7 x 10^-8 ohm meter.​

Answer 1

The resistivity at a certain temperature will be

$$\rho_T=\rho(1+\alpha(T-T_0)).$$

The resistance at 100°C:

$$R_T=\frac{\rho_TL}{A}=\frac{4\rho_TL}{\pi d^2}=\frac{4L\rho(1+\alpha(T-T_0))}{\pi d^2},\\\space\\ R_T=3.79\Omega.$$