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Ressistance when current-density is not constant

  1. Sep 28, 2010 #1
    I am trying to figure out how it would effect the ressistance R of a wire with length L and variyng cross-sectional area A(x) if the current density was a fuction of the radius of the wire. That is J = J(r).

    I'm having trouble with this when it seems like ressistance is the result of a derivation of ohm's law assuming constant E-field such that [tex]E = \frac{J}{\sigma} = \frac{V}{l}[/tex], but if E is not constant how can one then relate the ressitance to the current-density J?

    A qualitative answer is good enough.
  2. jcsd
  3. Sep 29, 2010 #2
    Resistance is by definition ΔV/i(and this is not Ohm's Law).Even though the electric field is not constant it is a law accurate for differential elements. So if you calculate E(x) function and integrate for the corresponding potential drop you can calculate resistance.
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