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Determining the current through a resistor

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Consider the circuit drawn on the attached picture. I have seen a calculation of what the current through each of the resistors is using Kirchoffs laws. Unfortunately I don't qualitatively understand how you are able to determine the current through them.
First of all, but this is probably nothing to worry about, how can you say a current is steady through a resistor when clearly the resistor is making the charges lose kinetic energy?
Secondly, I don't understand the underlying principle used to determine how much current should go through the one resistor and how much through the other. The proces that should determine that would be how fast they are going through each of them since the field will generally avoid piling up charge as much as possible. On the other hand kirchoffs laws are simply just statements of local conservation of energy and charge, how are they able to explain what the currents should be, when clearly none of them take into consideration how fast the charges pass through the resistors?
 

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