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Quick question on resistance&current in a sheet

  1. Sep 6, 2010 #1
    1. The problem statement, all variables and given/known data

    A sheet of copper 0.6m in total length and 0.2m wide is folded to create a uniform spacing of 1mm.
    the sheet is 1mm thick. a potential difference of 1mV is applied at the open end in such a way that the current is distrubuted unformly over the cross sectional area of the metal.
    I can neglect the effects of the fold (the vertical bit)

    http://yfrog.com/f/5mpicbvwp/
    (i also forgot to draw in the battery, connecting the two ends of the open side, it has a potential difference of 1mV)

    Find the resistance of the sheet,
    and the current.

    2. Relevant equations

    https://secure.wikimedia.org/wikipedia/en/wiki/Sheet_resistance

    In griffiths, I do not see this formula anywhere, however I'm going to use it anyway.

    properties of copper:
    electrical resistivity: 1.7*10^-8 ohms per metre
    density: 8.9*10^3 kg m^-3
    atomic weight = 64amu


    3. The attempt at a solution

    [tex] R = \rho \frac{L}{A} \Rightarrow A = 0.2m * 1mm [/tex]

    the length of the sheet is 0.6m

    plugging in the values

    [tex] R = (1.7*10^-8) * \frac{0.6}{0.2(1*10^-3)} = (5.1*10^-5) =51micro ohms [/tex]

    -

    finding the current through the sheet, i'm just going to use Ohm's law,
    [tex] \mathbf{J} = \sigma\mathbf{E} \Rightarrow \mathbf{V=IR} [/tex]

    plugging in the values, 1mV and 51 micro ohms, I get 19.6 Amps,
    however I don't know if I'm right, because that seems superlarge to me?
    where have I gone wrong???

    -> can I not use the formula on this page? https://secure.wikimedia.org/wikipedia/en/wiki/Sheet_resistance
     
  2. jcsd
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