Find the resistance of a wire after it is stretched

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To find the resistance of a wire after it is stretched to 1.25 times its original length, the relationship between resistance, resistivity, length, and area must be applied. The conservation of volume principle indicates that the initial area multiplied by the original length equals the final area multiplied by the new length. As the wire is stretched, its cross-sectional area decreases, leading to an increase in resistance. The reduction in area by a factor of 1.25 results in higher resistance due to the relationship between area and resistance. Understanding these principles is crucial for accurately calculating the wire's resistance after stretching.
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Homework Statement


A wire is lengthened to 1.25 times its original length by pulling it through a small hole. Find the resistance of the wire after it is stretched.

Homework Equations



resistance=(resistivity)(length)/(area)

The Attempt at a Solution



Umm..the reasoning behind this is that the initial area times length should equal the final area times length. However, I am not sure why this "conservation of volume" applies. Is it because the current is constant so the volume must remain constant?

What does it mean pulling it through a small hole?
 
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Volume is conserved because you aren't changing the amount of metal or the density.

So yes the area is reduced by a factor of 1.25, less area means more resistance.
 

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