Platinum and copper wires of equal length are found to have the same resistance. What is the ratio of their radii?

+3 votes

Platinum and copper wires of equal length are found to have the same resistance. What is the ratio of their radii?

(r_(text( Pt)))/(r_(text( Cu))) =

asked Feb 3, 2012 in Physics by Joey33 ~Expert~ (1,216 points)
    

1 Answer

+2 votes

The two have the same lenth and resistance so they can be related by:

(pPt * l) / (pi*(rPt)^2)  =   (pCu * l) / (pi*(rCu)^2)

rearrange equation so you have the ratio given in the question:

rPt / rCu  =  squareroot(pPt / pCu)
 
Here is a list of the resistivity of various materials:


Plug in the value for pPt and pCu into the equation and you get:

rPt / rCu  =  squareroot(11*10^-8 / 1.7*10^-8) = 2.54

rPt / rCu = 2.54

answered Feb 3, 2012 by Roar3215 ~Expert~ (1,318 points)
edited Feb 4, 2012 by Roar3215

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