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Resistivity of a stretched wire VS unstretched state

  1. Mar 29, 2009 #1
    1. A wire of a 6.0[tex]\Omega[/tex] resistance is stretched to three times its original length. Assume the diameter and resistivity have stayed the same, what is its new resistance?



    2. R=[tex]\stackrel{\rho L}{A}[/tex]



    3. Since the only thing that's changed in the equation is L, having tripled, I was obviously thinking the resistance would now be 18[tex]\Omega[/tex], but the books answer is 54[tex]\Omega[/tex]. What am I doing wrong?
     
  2. jcsd
  3. Mar 29, 2009 #2

    Mapes

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    Hi SpecialMen, welcome to PF. When metals are plastically deformed, it's usually assumed that the volume remains constant, not the cross-sectional area. Know what I mean?
     
  4. Mar 29, 2009 #3
    Thanks, I appreciate the welcoming!
    And yes, I know exactly what you mean. This is what I told myself when I first read the question, thinking it was strange to neglect the change in diameter of the cable...I reread the question a couple times, and then realized that what the book really said was we were assuming the same resistivity and density, not diameter as I had originally read. Brain freeze, I've been doing these problems for the past 6 hours, literally! Still, thanks for yor input! Would have gotten me out of my hole had I not reread the question!
     
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