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Resistivity of a Rod

  1. Jul 8, 2012 #1
    1. The problem statement, all variables and given/known data
    A uniform metallic rod, with a cross-sectional area of 1.83 cm2
    and a length of 7.08 m, contains 6.24E28 conduction electrons per cubic meter of material, which have a mean collision time of 20.2 femtoseconds.

    (a) Determine the resistivity of the rod.

    When the rod experiences a potential diff erence of 2.52 mV from end to end, determine
    (b) the drift velocity of the electrons and
    (c) the current density in the rod.

    2. Relevant equations

    R = ρl/A
    J = ΔV/(ρl)
    vd = I/(neA) (n being the number of mobile charge carriers per unit volume, e is electron charge)

    3. The attempt at a solution

    So I know exactly how to do b and c, those are a piece of cake. Unfortunately, to actually answer those parts I need the answer from part a which I have no idea how to do.

    I started by saying ρ=AR/l, but then I realized I don't have R directly given to me. All of the methods I thought of to get R involved needing information I wouldn't get till later steps (using Ohm's law and finding R from Iavg = nqvdA and known value of V, don't have vd; using ρ=E/J, J being current density which I also don't have yet.

    I can't find anything in my book. I would guess that materials with higher resistivities have more frequent collisions (so higher mean collision times); more collisions, more resisting going on. As for conduction electron intuition, I'm not really sure. Any help?? I know the answer ranges from 1.5E-08 to 3.00E-08, so I even got desperate and tried multiplying values together to see if I could get anything within that order of magnitude.
     
  2. jcsd
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