Question

An electric cable contains a single copper wire of radius 9mm. It's resistance is 5 ohms. This cable is replaced by 6 insulated copper wires, each of radius 3mm. The resultant resultance of cable will be?

Answer 1

Find the length-resistivity ratio of the 9mm-cable:

$$R=\frac{\rho L}{A_9},\\\space\\ \rho L=RA_9.$$

The resistance of the new cable:

$$R_e=\frac{\rho L}{nA_3},\\\space\\ R_e=\frac{RA_9}{nA_3}=\frac{R\pi r_9^2}{n\pi r_3^2}=\frac{R r_9^2}{n r_3^2},\\\space\\ R_e=\frac{5·0.009^2}{6·0.003^2}=7.5\Omega.$$