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Homework Help: Electric Potential and Current

  1. Jun 24, 2010 #1
    1. The problem statement, all variables and given/known data

    A wire has a resistance of 0.010 ohms. What will the wire's resistance be if it is stretched to twice its original length without changing the volume?


    2. Relevant equations

    R = pL/A


    3. The attempt at a solution

    R = p(2L)/A
    pL/A = R/2
    =0.010/2
    =0.0050 ohms

    I think I this is wrong. Can anybody let me know? And, if so, can you please steer me in the right direction?
     
  2. jcsd
  3. Jun 24, 2010 #2

    Doc Al

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    Staff: Mentor

    It's wrong for two reasons:
    - You only considered the change in length. How does the area change?
    - You didn't calculate the change in resistance due to the doubled length correctly. Assuming everything else remains the same, what happens to the resistance if the length doubles?

    You must account for both the changing length and cross sectional area.
     
  4. Jun 24, 2010 #3

    berkeman

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    Staff: Mentor

    You started with the correct equation, but there are two things wrong with your work. First, if you stretch the wire and the volume stays constant, what else changes in addition to its length?

    Second, the resistance has to be going up, not down. Your algebra gets a bit off in your calculation. Remember, you are solving for R, not pL/A.
     
  5. Jun 24, 2010 #4
    So, if the length doubles, the area would have to be halved?

    R = p(2L)/(1/2)A?
     
  6. Jun 24, 2010 #5

    berkeman

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    Correct-a-mundo. So by inspection, what happens to the resistance?
     
  7. Jun 24, 2010 #6
    R = (0.010) x 4 = 0.040?
     
  8. Jun 24, 2010 #7

    berkeman

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    Staff: Mentor

    Correct. The resistance doubles because the length doubles, and it doubles again because the area is halved. Good job!
     
  9. Jun 24, 2010 #8
    Thanks for the for the help!!!!
     
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