1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Resistance from Microscopic Ohm's law

  1. Feb 26, 2008 #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. Feb 27, 2008 #2
    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. Feb 27, 2008 #3
    Ah, wrong sigma. Got it, thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Resistance from Microscopic Ohm's law
  1. Microscopic Ohm's Law (Replies: 2)

Loading...