  We minimize the dissipation rate of an electrical network under a global
constraint on the sum of powers of the conductances. We construct the explicit
scaling relation between currents and conductances, and show equivalence to a a
previous model [J. R. Banavar {\it et al} Phys. Rev. Lett. {\bf 84}, 004745
(2000)] optimizing a power-law cost function in an abstract network. We show
the currents derive from a potential, and the scaling of the conductances
depends only locally on the currents. A numerical study reveals that the
transition in the topology of the optimal network corresponds to a
discontinuity in the slope of the power dissipation.
