Drift speed determines only the dtrength of the current and not the speed with which it travels through a conductor. (The speed of current is equal to the speed of propagation of electromagnetic wave which travels along the conductor. This speed is nearly equal to the speed of light in vacuum, i.e., `3 xx 10^8 m//s`. It is due to this reason that a bulb lights up immediately when it is switched on even if the source of electric supply is far away from it).
