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Finding New Resistance

  1. Apr 25, 2009 #1
    A wire has uniform cross sectional and resistance R. Then the wire is pulled so that the length increases by 10%. How to find the new resistance? Assumption: The wire thins uniformly.
     
  2. jcsd
  3. Apr 25, 2009 #2

    LowlyPion

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    What equation would you think to apply to figure this?
     
  4. Apr 25, 2009 #3
    R=rho*l / A
    I just don't get the part how the length of the wire affects the cross sectional area/radius.
     
  5. Apr 25, 2009 #4

    LowlyPion

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    Don't you figure that there is a conservation of mass?

    What happens to the volume of wire when you stretch it?

    Volume = L * A

    if the volume is constant, then if L = 1.1*L then A must equal A/1.1
     
  6. Apr 25, 2009 #5
    I got it. I thought the increase of L decrease the r to r/1.1.
    Can I ask another question about resistance?
    A square carbon film of thickness 5x10^-7m, rho 4x10^-5 ohm m is formed on an insulator rod of diameter 3mm.What is the length of the rod so that the carbon film on its curve surface has a resistance of 100 ohm.

    I tried:
    RA/rho = L
    100[3.142*(1.5mm+5x10^-7)^2]/4x10^-7 = L
    But the answer is 1.18cm which is different from mine. Where did it gone wrong
     
    Last edited: Apr 25, 2009
  7. Apr 25, 2009 #6

    LowlyPion

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    Consider that your cross sectional area is the cross section of a thin shelled tube.

    A = L * T = π * d * 5*10-7

    So:

    100Ω = 4*10-5 * L / (3.14*.003*5*10-7)
     
  8. Apr 25, 2009 #7
    I'm sorry but according to your equation, I don't get the answer which is 1.18cm. By the way, I also don't understand the statement "carbon film on its curve surface" means. Do you mind explaining it?
     
  9. Apr 25, 2009 #8

    LowlyPion

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    It's an insulating rod, so only the surface foil conducts.
    If you unwrap the foil off the rod its cross sectional area is width (π * d) and its thickness is 5*10-7

    Area then is W*T = (π * d) *( 5*10-7 ) = 3.14*.0003*5*10-7

    Substituting into

    R = 100 = p*L/A

    yields

    100*3.14*.0003*5*10-7 / 4*10-5 = L = 1.1775*10-2m
     
  10. Apr 25, 2009 #9
    I struggle with A = π r^2 and you cleared those. Thanks a lot.
     
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