How Equilibrium is Reached and Voltage Shared in a Series Circuit with Two Resistors I've been reading up on basic electronics recently and to help me understand things better, I've been writing down my understanding of what I've read in layman's terms. One thing I've struggled with is understanding how equilibrium is reached in a series circuit with just two resistors in the fraction of a second after a battery is first connected and how voltage ends up being shared proportionately across each resistor. I understand how this works in a series circuit with just one resistor but adding a second changes things a bit and this is where confusion set in. I'm not really wanting to dive too deep into the maths, more an explanation of the mechanics of the situation. Would anyone be able to have a read over of my interpretation below and let me know if I've understood this correctly or if I'm way off. Thanks. 
"The first electron to be repelled from the anode travels through the first resistor as fast as it can, using all of its energy (voltage). It arrives at the second resistor but is unable to pass through it because it doesn’t have any energy to do so. As more and more electrons arrive, this causes a ‘queue’ of electrons to form at the base of the second resistor and with each new electron, the ‘queue’ gets bigger until it very quickly it spreads back along the wire connecting both resistors (R1 and R2).
Electrons then begin to 'build up' in R1 and because the density of atoms in this resistor is greater than in the wire, this causes a larger magnetic field to grow around it. The wire connecting R1 to the anode has not filled with electrons at this point and as each 'new' electron joins the 'queue' in R1, the growing combined magnetic field they create starts to push on the electrons at the base of R2 with greater magnitude until the point where this ‘push’ gives these electrons enough energy to slowly start moving through it. (This is very similar to how the build up of electrons on the anode pushes electrons out into and through the first wire in the first instance). At the same time as this is happening, because like charges repel, the 'new' electrons that leave the anode and travel along the wire connecting the battery to R1 also start to slow down.
Although the electrons in the 'queue' at the base R2 are moving again, the ‘push’ they initially receive is only comparatively small so the rate at which they start to move through R2 is less than the rate any ‘new’ electrons arrive at the back of the ‘queue’ in R1 . As a result, the number of electrons ‘queuing’ increases, which in turn creates an even bigger magnetic field in R1. This larger field provides a bigger ‘push’ to the electrons at the front of the ‘queue’ and these electrons are given more energy to move through R2. The electrons at the front therefore speed up slightly. 
This continues to happen and as electrons move through R2 more quickly, the build up starts to clear. Eventually the rate at which ‘new’ electrons arriving at the back of the ‘queue’ matches the rate the electrons are travelling through R2 at the front of the ‘queue’ and the flow of electrons becomes constant – equilibrium has been reached. 
This process is repeated with the addition of every new resistor/component until the current is such that ‘new’ electrons aren’t using ‘too much’ energy to get through a set resistance and the amount of energy they save by going through earlier components at a slower speed (in this example R1) equals the amount of energy they need to get through the remaining components in the circuit (in this case R2). (To get through a set resistance at a faster speed requires greater voltage). This means that once equilibrium is reached, the electrons are travelling at a constant speed and use the energy (voltage) they are provided with by the battery in the required amounts to get through each component until they reach the end of the circuit – they can make it all the way round in one go. This quite often leads to people wondering ‘how do the electrons know how much energy to save for each component in a circuit?’, however, electrons don’t know anything – the voltage drops are determined as a result of the process explained above which all happens inconceivably quickly once a battery is first connected to a circuit. 
It’s worth pointing out that the first group of electrons out of the battery and around the circuit actually use more energy than the voltage provided by the battery itself because unlike what happens after equilibrium has been reached, these electrons need a second 'push' to get them through R2. In the end, however, this second push becomes enough (gives the electrons enough energy) to get them through R2 at the same rate as any 'new' (slower moving) electrons are arriving at R1 so when equilibrium finally is reached, the amount of energy the 'new' electrons save by travelling at a slower speed, matches the amount of energy they need to get through R2 and all the way round the circuit with just the one initial push from the battery.
Once this current flow in a circuit with multiple components has reached equilibrium, the electrons travel more slowly than they potentially could (given the energy they have received as a result of the push/pulling force) because they have a ‘like’ charge in front of them keeping them 'at bay'. Because of this, whenever they experience a loss of energy (a resistance), they don't slow down because they are travelling more slowly than they could at that point and the force that is pushing/pulling them is providing them with more energy to move than what they are losing through the resistance – almost like this energy loss is immediately compensated for or delivered in ‘stages’ as and when needed. It still takes energy for them to travel through the circuit, they still experience voltage drops but this isn’t shown with a reduction in speed (current)."
 A: I will go through your analysis point by point attempting to use mechanical analogies where possible with the understanding that these analogues are rough and do not represent actual electrical behavior.

"The first electron to be repelled from the anode travels through the
  first resistor as fast as it can, using all of its energy (voltage).

Actually, individual electrons move very slowly through the circuit. The velocity of their collective movement is referred to as the drift velocity. Depending on the length of the circuit and how long it has been switched on, it is even possible that an electron leaving a battery at the negative terminal never reaches the positive terminal of the battery.
What does move very fast through the circuit, nearly the speed of light, is the electric field established in the circuit as soon as it is connected to the battery. All the electrons in the circuit immediately "feel" the force of the field. An electron leaves the battery at one terminal and another enters the battery at the other terminal essentially at the same time. 
A mechanical analogy you may be familiar with is "Newton's Cradle" (if not, look it up). A series of steel balls hang by strings and they are in contact with one another, side by side. One ball at one end is moved away and let go to contact the ball that it was touching before it was pulled away. As soon as the ball strikes the other ball, a single ball at the other end of the cradle bounces off. The momentum of the first ball appears to be instantaneously transmitted to the last ball. Think of the first and last ball as our electrons leaving and entering the battery terminals.

It arrives at the second resistor but is unable to pass through it
  because it doesn’t have any energy to do so. As more and more
  electrons arrive, this causes a ‘queue’ of electrons to form at the
  base of the second resistor and with each new electron, the ‘queue’
  gets bigger until it very quickly it spreads back along the wire
  connecting both resistors (R1 and R2).

As I said above, all of the electrons in the circuit essentially experience the force of the electric field simultaneously. So all of the electrons are simultaneously on the move. They are all moving through both resistors simultaneously with the same drift velocity. There is no "queue" of electrons. As you probably learned the current is the same throughout a series circuit. If it weren't electrons would build up somewhere, which doesn't happen.
Now as they move it is true they may can encounter different resistance to their movement in different size resistors. In order to keep all the electrons moving at the same constant drift velocity (current) the electric field has to do more work to push electrons through a resistor with higher resistance than through a lower resistance. That means the source of the electrical energy (e.g., a battery) uses up a greater fraction of its total electrical potential energy per unit charge (its voltage) doing work to move electrons through a larger resistor than a smaller one in a series circuit. The total electrical potential energy per unit charge supplied by the battery divides up among the resistors in proportion to each resistor's fraction of the total resistance. The sum of the voltage drops across the resistors equals the total voltage supplied to the circuit, per Kirchhoff's voltage law. 
If you understand the above, you should realize that all of your remaining analysis is not applicable. 
Hope this helps.
