Doubling Resistance of 1 Mile Copper Wire - 68 ohms

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Doubling the length of a 1 mile copper wire with a resistance of 68 ohms results in a new resistance of 17 ohms when considering it as a single wire. This is due to the relationship between resistance, length, and cross-sectional area, where resistance is inversely proportional to the cross-sectional area and directly proportional to the length. When the wire is doubled in width, the cross-sectional area increases, reducing resistance. The calculations confirm that halving the length and doubling the width results in a quarter of the original resistance. Understanding these principles is essential for accurately determining resistance in electrical circuits.
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Homework Statement


A 1 mile long copper wire has a resistance of 68 ohms. What will be its new resistance when doubling it over and using it as "one" wire



Homework Equations

?
R=V/current



The Attempt at a Solution

unable to attempt, I know that when it is cut in half R=34 ohms
 
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dymand68 said:
I know that when it is cut in half R=34 ohms
OK. More generally, how does resistance depend on length and cross-sectional area?
 
inverse square rule?
 
the correct answer is 17 ohms...double width, 1/2 length =1/4 resistance?
 
dymand68 said:
the correct answer is 17 ohms...double width, 1/2 length =1/4 resistance?
That's right. As that site explains, the resistance is inversely proportional to the cross-sectional area (which gives one factor 1/2) and directly proportional to the length (which gives a second factor of 1/2).
 

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