[SOLVED] Find the diameter of copper wire 1. The problem statement, all variables and given/known data Find the diameter of copper wire which has the same resistance as an aluminum wire of equal length and diameter 1.2mm. The reactivities of copper and aluminum at room temperature are 1.7x10^-8Ωm and 2.6x10^-8Ωm respectively. Can someone please explain to me the way of solving this question? Thnx in advance
I'm sure you mean resistivity . Anyway, this is a simple application of resistivity, so what is the equation for resistivity?
You have two equations, [tex]R = \frac{\rho_c \ell}{A_c}[/tex] And [tex]R = \frac{\rho_a \ell}{A_a}[/tex] For the copper and aluminium wire respectively. Can you see what to do next?
[tex]\frac{P_c}{A_c} = \frac{P_a}{A_a}[/tex] [tex]P_c = 1.7 \times 10^{-8}\Omega{m}[/tex] [tex]P_a = 2.6 \times 10^{-8}\Omega{m}[/tex] [tex]A_a = \pi{r}^2[/tex] [tex]A_a = \pi \times \left(\frac{1.2 \times 10^{-3}}{2}\right)^2[/tex] [tex]A_a = 1.1 \times 10^{-6} m^2[/tex] [tex]\frac{P_c}{A_c} = \frac{P_a}{A_a}[/tex] [tex]\frac{1.7 \times 10^{-8}}{\pi{r}^2} = \frac{2.6 \times 10^{-8}}{1.1 \times 10^{-6}}[/tex] [tex]r = \sqrt{\frac{1.7 \times 10^{-8} \times 2.6 \times 10^{-8}}{2.6 \times 10^{-8}\pi}}[/tex] [tex]r = 7.36 \times 10^{-5}[/tex] Is my answer correct?
Nice work! Thanks for LaTeX'ing it up for me You're good up until this point. Your next line is wrong, A further word of caution: be careful with rounding errors, try not to round too early in your calculation, either leave all your calculations to the end, or store the intermediate answers in your calculator.
Welcome Hootenanny! and thanks for the help [tex]r = \sqrt{\frac{1.7 \times 10^{-8} \times 1.1 \times 10^{-6}}{2.6 \times 10^{-8}\pi}}[/tex] [tex]r = 4.78 \times 10^{-4}m[/tex] Is this right?
By rounding errors I think you meant the area of Aluminum [tex]P_a[/tex] right? [tex]A_a = \pi{r}^2[/tex] [tex]A_a = \pi \times \left(\frac{1.2 \times 10^{-3}}{2}\right)^2[/tex] [tex]A_a = 1.1309734 \times 10^{-6} m^2[/tex] [tex]r = \sqrt{\frac{1.7 \times 10^{-8} \times 1.1309734 \times 10^{-6}}{2.6 \times 10^{-8}\pi}}[/tex] [tex]r = 4.8 \times 10^{-6}[/tex] Is this right?:uhh: