Relationship Between Resistivity and Conductor Dimensions

AI Thread Summary
The discussion centers on calculating the resistance of two cylindrical conductors with different dimensions and resistivities. The first conductor has resistance R, while the second has resistivity 2ρ, length 2l, and diameter 2D. Using the formula R = ρL/A, participants analyze how changes in resistivity and dimensions affect resistance. The confusion arises from the relationship between diameter and cross-sectional area, leading to the conclusion that the second conductor's resistance is actually R. The key takeaway is understanding how resistivity and geometric factors interplay in determining resistance.
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Homework Statement


A cylindrical conductor of length l, diameter D and resistivity ρ has resistance R. A different
cylindrical conductor of resistivity 2ρ, length 2l and diameter 2D has a resistance

A. 2R.
B. R.
C. R/2.
D. R/4



Homework Equations



I assume its R = pL/A


The Attempt at a Solution



I tried putting 2p2L/2A into the equation getting 4/2 = 2 then dividing both sides by 2 to give R/2 but apparently the answer should be B. R? Not sure how?
 
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The cross sectional area is proportional to the square of the diameter.
 

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