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)?
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.
It prefers path of least resistance. Or it maximum current follows the path of least resistance upon division at a point.