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Find the diameter of copper wire 
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#1
May908, 05:47 AM

P: 81

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 


#2
May908, 05:57 AM

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PF Gold
P: 9,781




#3
May908, 05:59 AM

P: 81

What to do next 


#4
May908, 06:05 AM

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PF Gold
P: 9,781

Find the diameter of copper wire



#5
May908, 06:14 AM

P: 81




#6
May908, 06:18 AM

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PF Gold
P: 9,781

[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? 


#7
May908, 06:33 AM

P: 81

[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? 


#8
May908, 06:40 AM

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PF Gold
P: 9,781

Nice work! Thanks for LaTeX'ing it up for me



#9
May908, 07:14 AM

P: 81

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? 


#10
May908, 07:20 AM

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PF Gold
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#11
May908, 07:38 AM

P: 81

[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? 


#12
May908, 07:40 AM

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PF Gold
P: 9,781




#13
May908, 07:50 AM

P: 81

Thanks Hootenanny!! I got the final answer correct...



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