Find the resistance of a wire after it is stretched

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SUMMARY

The resistance of a wire increases when it is stretched, specifically when its length is increased to 1.25 times its original length. The relationship governing this change is defined by the formula resistance = (resistivity × length) / area. As the wire is stretched, its cross-sectional area decreases, leading to an increase in resistance due to the conservation of volume principle. This principle asserts that the volume of the wire remains constant despite the change in dimensions.

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  • Understanding of electrical resistance and Ohm's Law
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  • Knowledge of geometric relationships in volume conservation
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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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