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Radius and Resistance

 
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roxiney



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

PostPosted: Thu Sep 30, 2010 9:13 pm    Post subject: Radius and Resistance Reply with quote

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
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Joined: 23 Jun 2007
Posts: 125

PostPosted: Thu Sep 30, 2010 9:58 pm    Post subject: Reply with quote

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 cross-section 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

PostPosted: Thu Sep 30, 2010 10:09 pm    Post subject: Reply with quote

How do you fins A if you are not given a length?
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hepcj
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Joined: 23 Jun 2007
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PostPosted: Fri Oct 01, 2010 6:23 pm    Post subject: Reply with quote

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