Path of current functional
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)? 
Re: Path of current functional
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. 
Re: Path of current functional
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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