# Why does current arrange itself in such a way as to minimize power loss in resistors connected in parallel?

In problem 2 in Problem Set 6, it is said:

"Electricity prefers to flow in the way that minimizes energy loss to resistance."

Using Lagrange multipliers I was able to show that assuming the above statement, in parallel, $$I_kR_k=V$$, a constant, for each resistor attached in parallel. Physically, this makes sense since if we assume Ohm's law is obeyed, this result is just an immediate corollary of putting resistors in parallel: the terminals of all the resistors coincide so the potential differences across all the resistors, which are path-independent, are the same.

So my question is, is there a deeper physical reason why current distributes itself so that it minimizes power loss?