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I've been googling about this topic and have read from a number of different books but I still haven't found an exact answer to my question.

It is known that the current is equal when the resistors are in a series. But the resistors per definition reduce current flow. If there are 2 resistors R1 and R2 with different values, then the current flow in both of them will be different. The electrons will perhaps hit more atoms etc. If that is the case, then dQ/dt will in fact not be constant throughout the circuit and will be different when going through R1 and R2. Yes, the charges have nowhere else to go since there is only one path but still I am not convinced that "I" is the same through out the current circuit. I would speculate, that there would be some build up since the electric potential difference from the beginning of the circuit on the positive side to the very start of R1 will be higher than that of the electric potential from the beginning of R1 to the end of R1. Therefore there should be some time of build up of charge and the current will not be equal overall.

Can someone explain to me why this is false? I would really appreciate understanding why the current is the same throughout the entire circuit.