is current increases in a conductor when the velocity of electrons increases in conductor

 

Current = quantity of electrons flowing
Voltage = electrical pressure

 

And the velocity of the electrons (the net mean volocity) is quite the same for all cases. 8m/s independently of current and voltage. Of course the electromangetic force that drives the electrons is instantaneous. That is why a light bulb will light imediately, and not take 8 seconds to lit if it has a 8m cable.