Same Ampere before and after a resistor

Question

I see that the current before and after a Resistor is the same. I want to prove this with the Drude-Lorentz model.
The situation is like this 
I put the Ammeter before the resistor and I measure k1 Ampere. I put the Ammeter after the resistor and I measure k2 Ampere.
I experience that k1=k2.
My model view is like this (with points I have drawn the grid of positive charges. Electron move in this grid):

How can I prove this intuitively? I have an electrical field E that move, with a drift velocity, my electrons left to right(...slowly, but this is not important). In my vision, I'll have an "accumulation" of electrons from R1 and R2. Electrons in this model can touch each other? If not I can't understand this event.

R.W. Bird · Answer

The current must be the same in all parts of a single DC circuit. If it were not, charge would be building up in some part of the circuit.  The electric field in a circuit does not drift. It is the free electrons that drift. The field is nearly constant and is proportional to the gradient of the charge density around the loop. (There must be more free electrons near the negative terminal of a battery or power supply.) With more free electrons, the drift velocity and E field should be slightly smaller.
You might see if you can detect a difference in the voltage gradient in a uniform conductor on the two sides of your power supply.

Same Ampere before and after a resistor

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