The free moving charged particles in the following substances are as follows
carbon electrode(made of graphite); Delocalized electrons.
molten mixture of aluminum oxide and cryolite;. Aluminium ions in Aluminium oxide.
Metal wire; Metal ions
Graphite, an allotrope of carbon has Delocalized (free-moving) electrons and these electrons serve to enable conductivity.
Although, cryolite is a bad conductor of electricity, when Molten Aluminium oxide and cryolite is used, the free moving Aluminium ions enable conductivity.
In metal wires, conductivity is solely the responsibility of metal ions.