Question

what is steady state current

Answer 1

An electric current that does not change with time

Answer 2

It's better to say the current after transients have died out.

A circuit with dc stimulus (eg a constant voltage as from a battery) will result in an unchanging current flowing through the circuit. This is steady state current.

A circuit with ac stimulus applied (eg plugged into the 120v 60Hz plugs in your home) will also result in a steady state current but it will be a sinusoidal current of the same frequency. But before that steady sinusoidal current emerges, brief transients will cause the current to deviate from the pure steady state sinusoidal current for a time.