How Does Stretching a Wire Affect Its Resistance Ratio?

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In summary, the problem involves finding the resistance of a stretched wire with a given length, cross-sectional area, and resistivity. After setting up equations and using the fact that the volume is constant, it is determined that the ratio of the final resistance to the initial resistance is 2A1/A2, where A1 and A2 are the initial and final cross-sectional areas, respectively.
  • #1
Mdhiggenz
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Homework Statement



Hey guys a problem similar to this is going to be on my exam on Thursday, and I'm a bit stuck.

A wire of length L and cross-sectional area A, has resistance R.

What will be the resistance Rstretched of the wire if it is stretched to twice its original length? Assume that the density and resistivity of the material do not change when the wire is stretched.

However my professor wants us to do this problem as a ration, so he will ask us to find the ratio R2/R1.

So what I did was

L2=2L1

R1=P*L1/A1

R2=P*2L1/A2


R2/R1= 2L1P/A2 * A1/L1P

R2/R1= 2A1/A2

and now I am stuck.

Thanks for the help



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The Attempt at a Solution

 
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  • #2
Mdhiggenz said:

Homework Statement



Hey guys a problem similar to this is going to be on my exam on Thursday, and I'm a bit stuck.

A wire of length L and cross-sectional area A, has resistance R.

What will be the resistance Rstretched of the wire if it is stretched to twice its original length? Assume that the density and resistivity of the material do not change when the wire is stretched.

However my professor wants us to do this problem as a ration, so he will ask us to find the ratio R2/R1.

So what I did was

L2=2L1

R1=P*L1/A1

R2=P*2L1/A2


R2/R1= 2L1P/A2 * A1/L1P

R2/R1= 2A1/A2

and now I am stuck.

Thanks for the help
Is the volume of the wire after it's stretched the same as the volume of the unstretched wire?
 
  • #3
I think it would double as well since it is getting longer, but why would the volume have anything to do with the problem?
 
  • #4
Mdhiggenz said:
I think it would double as well since it is getting longer, but why would the volume have anything to do with the problem?
Yes, the volume is important. It let's you find the ratio of the final cross-sectional area to the initial cross-sectional area .

If the volume doubles, the the density will be reduced to half.
 
  • #5
Oh snap. So wouldn't the Area be reduced to half? and then I can make another relation

A1=1/2A2?
 
  • #6
Ok that works out since that got me the correct answer, but I don't understand how to put that into a ratio form.
 
  • #7
The volume is constant as no new copper is being added. If length doubles the area halves.

The resistance will be proportional to length and inversly proportional to area.

Write two equations eg

Rinitial = ?
Rstretched = ?

Then divide one by the other...

Rstretched/Rinitial = ?/?

Some terms on the right (such as the restivity of copper) will cancel.

Over to you to fill in the missing bits.
 
  • #8
Watters thanks for the response, and I was able to get the correct answer, just not sure how to put it in a ratio form.
 

Related to How Does Stretching a Wire Affect Its Resistance Ratio?

1. What is the meaning of R2/R1?

The ratio of R2/R1 is a mathematical comparison of two quantities, R2 and R1. It represents the relationship between the two values and can provide insight into the strength of that relationship.

2. How is R2/R1 calculated?

R2/R1 is calculated by dividing the value of R2 by the value of R1. This can be done using a calculator or by hand using basic division principles.

3. What does a high R2/R1 ratio indicate?

A high R2/R1 ratio generally indicates a strong positive correlation between the two values. This means that as R1 increases, R2 also tends to increase. However, it is important to consider other factors and not rely solely on the R2/R1 ratio for determining the strength of a relationship.

4. Can R2/R1 be negative?

Yes, R2/R1 can be negative if R2 and R1 have opposite signs. This would indicate a negative correlation between the two values, meaning that as R1 increases, R2 tends to decrease.

5. How is R2/R1 used in scientific research?

R2/R1 is commonly used in regression analysis to evaluate the strength of a relationship between two variables. It can also be used to compare different models and determine which one best fits the data. Additionally, R2/R1 can be used to make predictions about one variable based on the value of the other variable.

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