Current and voltage I am current studying A level physics. I know that current is the same in all parts of a series circuit, however I cannot understand why. If adding resistance to the circuit causes the kinetic energy of the electron to drop ( potential difference) then the speed of the electron after that point should drop. This, in turn, would cause the current to decrease. 
Any help is much appreciated
 A: The (drift) speed of the charges in the circuit does not change.
You're right that a resistance would tend to slow down the charges. The only way it cannot is because there is an electric field within the resistor that is simultaneously pushing the charges forward.  The two forces cancel and the charges keep their speed/KE constant.
Think of a block sliding down some ramps.  Some ramps are steep, but have a lot of friction.  Some ramps are less steep with less friction.  But everything is set up so that the block never gains any speed as it slides down.  If you had several blocks, they would all be losing potential energy (converting it eventually into heat), but all moving at the same speed.  An analogous process is happening within the wire.
A: 
if adding resistance to the circuit causes the kinetic energy of the electron to drop ( potential difference) the speed of the electron after that point should drop

The kinetic energy of an electron in an ordinary circuit is roughly constant throughout the circuit and is essentially negligible. Energy in a circuit is not attached to electrons and carried by the electrons and deposited. Energy is carried by the fields, the electrons do not directly carry the energy but instead they establish the fields which transport the energy. 
A: You have probably already learned that when current flows flows through a resistor the temperature of the resistor rises and heat transfers to the environment. So where does that energy come from? It's the kinetic energy that charges continuously get from the electrical potential energy of the source but continuously loses due to collisions with the atoms and molecules of the resistor producing heat. Overall there is no net change in the kinetic energy so that the charge will have an an average constant drift velocity (current) throughout the circuit and the electrical work by the source equals the heat generated.
@BowlOfRed used the mechanical analogy of friction. Taking the analogy further, the block sliding at constant velocity on the ramp causes friction heating of the ramp, just like charge moving through a resistor results in electrical heating of the resistor. The electrical potential energy acquired by the charge winds up as heat.
Hope this helps.
A: Here is why the current in all parts of a series circuit has to be the same. Think of the series circuit as a garden hose carrying water. The hose has a few kinks in it that restrict the flow of water. We push one gallon of water into one end of the hose and note that one gallon flows out the other end because there are no holes or leaks in the hose anywhere, and the hose itself does not create or destroy water. 
Analogously, the electrical current that enters the series circuit must equal the current that leaves it, because there are no leaks in the circuit and the circuit itself does not create or destroy current.
What changes instead is that the pressure in the hose drops across each of the kinks in it, and the sum of those drops equals the original source pressure. In the circuit, the voltage drops across each resistor, and the sum of those drops equals the supply voltage. 
