# Conceptual question on electron flow between two types of resistors

#### pedda

Hey,

I have a question on resistivity. When I first studied circuits as an undergrad, I just accepted the principle of voltage division and related things they taught us. I now major in condensed matter physics and now having seen the formalism for conductivity in the Drude model and the framework of non-equilibrium thermodynamics, I somehow have trouble reconiling my knowledge from before with these formalisms and I hope that you can help me.

What I have trouble with:
When deriving Ohm's law in the Drude model, one assumes that there is a certain mean free path leading to a drift velocity that is constant throughout the entire conductor. This makes sense and I also get why, if we put a source and a sink at the ends of one conductor, the electric field is constant, drops uniformally over the entire length and the electron flow is limited by the scattering.

Now here's where things start to become confusing for me: When adding a second resistor in series, with let's say a lower drift velocity, why is the current not determined by this conductor only but by the sum of the two? When thinking of water flowing in a pipe whose diameter is reduced twice, I would assume that the total flow is limited by the part with the smallest diameter?

I would be very happy to hear your thoughts!

Bye, Peter

EDIT I guess if someone could point me towards a paper where they use the Onsager relations for a system made up of two resistors would already help me a lot!

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#### pedda

Hey,

I think I just realized the conceptual error in my question: Since the drift velocity is of course dependent on the voltage drop occurring across the resistor, the lower mobility of charges in the part with higher resistance is compensated for by the higher voltage drop leading to the same current density just as it should be. Is this correct?

Thanks, Peter

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