Find the resistance of a wire after it is stretched

In summary, when a wire is lengthened to 1.25 times its original length by pulling it through a small hole, the resistance of the wire increases due to the decrease in area. This is because the volume of the wire, and therefore its density, remains constant. The equation for resistance, which takes into account the length, resistivity, and area, can be used to calculate the new resistance.
  • #1
collegeconfid
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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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  • #2


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.
 

FAQ: Find the resistance of a wire after it is stretched

What is the relationship between the resistance of a wire and its length?

The resistance of a wire is directly proportional to its length. This means that as the length of the wire increases, the resistance also increases.

How does stretching a wire affect its resistance?

Stretching a wire increases its length, which in turn increases its resistance. This is because the longer wire has more atoms and electrons, causing more collisions and hindering the flow of current.

Is the resistance of a wire after stretching permanent?

No, the resistance of a wire after it is stretched is not permanent. It can change if the wire is unstretched or stretched further. This is because the resistance is dependent on the length and cross-sectional area of the wire.

How can I calculate the resistance of a wire after it is stretched?

The resistance of a stretched wire can be calculated using the formula R = ρL/A, where R is the resistance, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.

Can the resistance of a wire be reduced by stretching it?

No, stretching a wire will not reduce its resistance. In fact, it will increase the resistance due to the increase in length. However, using a material with a lower resistivity or increasing the cross-sectional area of the wire can reduce its resistance.

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