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Sometimes while solving problems Kirchoff's Voltage Law, there comes a resistor placed in such a position that in one of the loops the potential across that resistor is actually taken positive (which shows an increase). My question is how can this be possible, not that I doubt it but i need an explanation that explains it on the electron level. For example I understand that electrons normally loose energy due to work against the atoms inside a resistor. I need an explanation of how electrons gain potential (or energy) as they move across a resistor in the opposite direction of normal current flow. A microscopic (electron-scopic) scale explanation would be appreciated.

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The one thing you can take for sure is that whichever is the direction of the voltage drop, is the direction of the current. So if a resistor is placed so the voltage goes up, instead of down, it means the current is going to go the other way. It's a lot like elevation and the flow of water in a river. The electrons will be pushed in the direction of downward voltage drop.

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  • $\begingroup$ But its quite impossible for water to flow upstream. However in a closed loop you have to take current flow in a specific direction which results in the case described. I don't understand the manner in which this potential increase occurs since resistors primarily reduce voltage. $\endgroup$
    – ABDELTA
    Sep 23 '16 at 17:18
  • $\begingroup$ But if you guess wrongly about the direction of current flow, or you make a sign error in your calculations, then that will resolve your problem. As Ken G says, if you are sure that the potential drops in a certain direction for a resistor, then the conventional current is definitely in the same direction. $\endgroup$
    – Bill N
    Sep 23 '16 at 17:31
  • $\begingroup$ So you're saying that the increase in voltage is merely a theoretical supposition created to satisfy the problem? $\endgroup$
    – ABDELTA
    Sep 23 '16 at 18:20
  • $\begingroup$ Water can only flow uphill if it has a huge momentum already, it's generally not the way rivers work. Electrons do not have an inertia that could flow against a potential rise like that. Instead, imagine that electrons accelerate over a short distance and are stopped by a collision in the resistor, then do it again. When they move too freely, they have a way of cancelling out the field that would otherwise accelerate them. But in a resistor, the field is allowed to build up expressly because of the electron's limited ability to move, and that is why you get a potential drop. $\endgroup$
    – Ken G
    Sep 23 '16 at 22:07

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