Answer to Question #175125 in Electricity and Magnetism for Joshua Musyoki

Question

Find the diameter of a copper wire which has the same resistance as aluminium wire of equal 

length and diameter 1.20mm. The resistivities of copper and aluminium at room temperature are 

1.7 × 10^−8Ω𝑚 and 2.6 × 10^−8Ω𝑚 respectively.

Answer 1

The resistance is $R = \rho \cdot \dfrac{l}{S}.$

$\rho_c\cdot \dfrac{l}{\pi \dfrac{D_c^2}{4}} = \rho_a\cdot \dfrac{l}{\pi \dfrac{D_a^2}{4}}\,, \;\; \dfrac{\rho_c}{D_c^2} = \dfrac{\rho_a}{D_a^2}\,, \;\; \dfrac{1.7\cdot10^{-8}\,\mathrm{Ohm\cdot m}}{D_c^2} =\dfrac{2.6\cdot10^{-8}\,\mathrm{Ohm\cdot m}}{(1.2\cdot10^{-3}\text{m})^2}, \;\; D_c = 0.97\,\mathrm{mm}.$