Does the speed of electrons depend on energy? I would like to know whether the speed of an electron depends on energy.
If yes then in a circuit when electrons flow out of a resistor the energy decreases by a considerable amount, leading to the charge per electron decrease and eventually to the decrease in current in a series circuit.
How is that possible?
 A: If you have current flowing one way through a resistor, then the electrons flow through the other way.  Since current flows from the high voltage end of a resistor to the low voltage end, then the electrons come in at the low voltage end and come out at the high voltage end.
When electrons (which are negatively charged) go from low voltage to high voltage, they gain energy from the electric field driving them.  However, in a resistor, they lose an equal and opposite amount of energy by repeatedly crashing into other parts of the resistor, thus heating up the resistor.  The power loss in a resistor is $IV$, which is exactly what the electrons would have gained in energy had they not lost it due to collisions within the resistor.
So two things happened, the electrons were given energy from the electric field, and they gave energy to the resistor by heating it up.  Easy come, easy go.  Equal numbers of electrons flowed in and out (from no charge buildup) and they leave with the same energy, hence same speed, so same current.
A: There may be a confusion between enery and power.  While the current, which is the number of charges per second, and the energy of the ,electron do'nt change at the output of the resistor, the power does.  Power is the amount of energy per unit time, and that does not affect the current which, again, is the amount of charge per unit time.
