Answer to Question #171848 in Electricity and Magnetism for madeline

Question

find the ratio of the resistances of a copper wire to an aluminum wire if the length and diameter of the aluminum wire is twice the diameter of the copper

Answer 1

$R=\frac{\rho l}{S},$

$\frac{R_C}{R_A}=\frac{\rho_C}{\rho_A}\cdot \frac{l_C}{l_A}\cdot \frac{S_A}{S_C}=\frac{\rho_C}{\rho_A}\cdot \frac{l_C}{2l_C}\cdot \frac{4S_C}{S_C}=\frac{2\rho_C}{\rho_A}=\frac{2\cdot 0.017}{0.028}=1.21.$