Resistance from Microscopic Ohm's law

  1. 1. The problem statement, all variables and given/known data

    Your task is to calculate the resistance of a simple cylindrical resistor with wires connected to the ends, such as the carbon composition resistors that are used on electronic circuit boards. Imagine that the resistor is made by squirting material whose conductivity is [tex]\sigma[/tex] into a cylindrical mold with length L and cross-sectional area A. Assume that this material satisfies Ohm's law. (It should if the resistor is operated within its power dissipation limits.)

    What is the resistance R of this resistor?
    Express the resistance in terms of variables given in the introduction. Do not use V or I in your answer.

    [​IMG]

    2. Relevant equations

    J=[tex]\Sigma[/tex]E
    V=EL
    I=JA
    R = V/I

    3. The attempt at a solution

    I start out with Ohm's Law and get resistence R to be R = V/I and I know V = EL and I = JA so I get resistence R to be R = EL/JA. I also know J = [tex]\Sigma[/tex]E. So I get resistence R to be R = EL/[tex]\Sigma[/tex]EA

    Would the two E's cancel out?
     
  2. jcsd
  3. I will continue from your R = EL/JA expression.
    J = [tex]\sigma[/tex]E
    therefore,
    R = EL/[tex]\sigma[/tex]EA
    the E's cancel out and your answer should be R = L/[tex]\sigma[/tex]A

    Hope this helps.
     
  4. Ah, wrong sigma. Got it, thanks.
     
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