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roxiney
Joined: 15 Sep 2010 Posts: 5 Location: north carolina

Posted: Thu Sep 30, 2010 9:13 pm Post subject: Radius and Resistance 


Two conductors are made of the same material and have the same length L. Conductor A is a hollow tube with inside diameter 1.29 mm and outside diameter 2.55 mm; conductor B is a solid wire with radius RB. What value of RB is required for the two conductors to have the same resistance measured between their ends? 

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hepcj Site Admin
Joined: 23 Jun 2007 Posts: 125

Posted: Thu Sep 30, 2010 9:58 pm Post subject: 


The resistivity is rho = R A/l
The wires have the same length.
You need to calculate the area of the anulus forms by the crosssection of the hollow wire. This is the circular area of the outer radius minus the circular area of the inner radius RB. (A = pi * RB^2)
Then to find the radius of the equivalent solid wire. RB = sqrt(A/pi) 

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roxiney
Joined: 15 Sep 2010 Posts: 5 Location: north carolina

Posted: Thu Sep 30, 2010 10:09 pm Post subject: 


How do you fins A if you are not given a length? 

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hepcj Site Admin
Joined: 23 Jun 2007 Posts: 125

Posted: Fri Oct 01, 2010 6:23 pm Post subject: 


The length is the same for both conductors and it is not used in the crosssectional area. The crosssectional area only depends on the radius.
A = pi * r^2 for a circular crosssection.
For a tube shape,
A = pi*(r_outer^2  r_inner^2). 

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