Path of current functional

  1. Current follows the path of least resistance or shortest path. I just want to prove this or rather reproduce it using calculus of variations. I just want to show it in a fancy way. I want help to form the FUNCTIONAL for it.
    Useful equations:
    I=dq/dt=nqvA
    R=rho*l/A
    Where v is drift velocity

    Any suggestion (may be using different equations and parameters)?
     
  2. jcsd
  3. K^2

    K^2 2,470
    Science Advisor

    The current does not actually take the path of least resistance. It takes all available paths. In general:

    [tex]J = \sigma E[/tex]

    Where J is current density, E is electric field, and σ is the electrical conductivity.
     
  4. It prefers path of least resistance. Or it maximum current follows the path of least resistance upon division at a point.
     
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