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Suppose we have a circuit with and EMF source and a resistor. We know that when electron moves from one terminal of a voltage source to another it encounters resistance, which is basically collisions with stationary positive ions. During the collisions some of the electric potential energy and kinetic energy that electron has is passed in form of kinetic energy to the atoms of the material of the conductor. That means they lose some of their own kinetic energy, i.e. they're being slowed down. It seems reasonable to think that the electric current (charge per unit time) is changing, as the electrons slow down due to the collisions. Why then we still get a constant current? What is the flaw in what I've described?

Electrons must accelerate and gain a bigger velocity in medium with lower resistance. It seems reasonable for me to think that electrons are moving faster where the resistance is lower and slower where it is higher. So if we have zones with different resistances, electrons will move with different speed and thus the current will vary.

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You aret correct that the elctrons are slowing down but that is onlg part of the picture, what is happening is that after electrons gain a certain velocity they usually collide and lose it, then again they are accelerated by the electric field and the process again takes place. The forver chaning velocity of one electron when averaged for all electrons comes out to be constant and is known as drift velocity.and the current is directly proportional to this drift velocity. As a result even though a lot is happening to a particular electron not much is happening to thhe bulk of electrons and we get a constant current.

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    $\begingroup$ But what if electron is moving through a conductor with almost no resistance? Say, moving though the wires until it encounters some resistor (with not so negligible resistance). They must then accelerate and gain a bigger velocity when they're moving through medium with negligible resistance. It seems reasonable for me to think that electrons are moving faster where the resistance is lower and slower where it is higher. So if we have zones with different resistances, electrons will move with different speed and thus the current will vary. $\endgroup$
    – odg
    Commented Oct 24, 2013 at 17:09
  • $\begingroup$ Your assumption is wrong because at any time a given amount of charge has to pass through each and every portion of wire so that there is no accumulation of charge at any point of wire. When you increase the resistance for same length of wire yoh effectively decrease its cross sectional area, as same amount of charge has to pass through the now smaller area in same time so as to keep rate of flow constant it must flow at higher rate, you can even feel this high speed at high resistance portions of wire as they are heated more than the lower resistance portions. $\endgroup$
    – Rijul Gupta
    Commented Oct 24, 2013 at 18:19
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    $\begingroup$ I do understand that if we want a direct current no charge should accumulate. But the point in my question is why should it be constant? I'm trying to get a feeling of it, to understand the microscopic process itself. Why would charge move faster in a smaller cross sectional area? "Charge shall not accumulate" is not really an answer for my question. I'm curious about the cause itself of such a behavior of electrons. $\endgroup$
    – odg
    Commented Oct 25, 2013 at 12:31
  • $\begingroup$ Well charge shall not accumulate could be explained by saying that when electrons start passinv through smaller cross sectional area, they start leaving behind same amount of positive ions for a smaller area this results in an increased field which force the electrons to move faster through the region of lesser area. $\endgroup$
    – Rijul Gupta
    Commented Oct 25, 2013 at 13:05
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Just the big number of electron participating in the process. When you go from the microscopic consideration like you're discussing to the macroscopic property like current, you get a seemingly steady number by the wonders of what is called law of large numbers.

If you were able to measure perfectly and with very high precision, you would eventually see a random drift, which in the long run cancels itself out. You could check about brownian motion.

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