  We apply a recently developed formalism to study the evolution of a
current-carrying string network under the simple but generic assumption of a
linear equation of state. We demonstrate that the existence of a scaling
solution with non-trivial current depends on the expansion rate of the
universe, the initial root mean square current on the string, and the available
energy loss mechanisms. We find that the fast expansion rate after
radiation-matter equality will tend to rapidly dilute any pre-existing current
and the network will evolve towards the standard Nambu-Goto scaling solution
(provided there are no external current-generating mechanisms). During the
radiation era, current growth is possible provided the initial conditions for
the network generate a relatively large current and/or there is significant
early string damping. The network can then achieve scaling with a stable
non-trivial current, assuming large currents will be regulated by some leakage
mechanism. The potential existence of current-carrying string networks in the
radiation era, unlike the standard Nambu-Goto networks expected in the matter
era, could have interesting phenomenological consequences.
