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I would say that we should look up the real mechanism of current flow Here's the brief view Excess and deficient charges appear to the sides of the wire having connected to the battery ( the wire connected to the positive end will have a positive charge gradient ) Now the battery does continuous work to maintain these potential difference We know that drift velocity is constant in a given circuit so there must be more charge gradient (potential gradient to set up electric field) near the resistor so the electric field intensity is more near the resistor so more number of electrons will enter the cross-section of resistor per second causing charge coming out of resistor still same