Hi Posplayr,
I'll submit that none of the available answers is actually correct, and my answer is "none of the above"
The correct answer is that the situation alternates rapidly and continuously between your #5, and my new drawing #7.
Drawing #5 would apply during those parts of the cycle when the regulator is not shunting.
Others have given the rationale for drawing #5, and I don't think I need to repeat any of that.
Regarding the inclusion of drawing #7
When the Regulator part of the R/R is regulating, it does so by briefly shunting all the power of the Stator internally.
(this occurs in the connections between the stator and R/R and those currents are not shown in any of drawings 1-7 above)
During that time, the stator and R/R are effectively not in the external circuit (battery and GS) at all, and all the loads on the bike draw their power directly from the battery.
This corresponds to drawing 7.
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Now I suspect you might argue that my description is either not one of the provided posibilities, or is getting too detailed and complicated, but I would counter with four thoughts.
1st, You used and capitalized the word "CORRECT" several times above when describing your desired answer.
Usually when choosing between several alternatives which are all more or less correct, the simplified case may be used to explain things to beginners, but the more detailed answer is the one considered more "correct"
For example: are the orbits of planets circles or ellipses? is it more correct to assume frictionless motion or motion with friction included?
Using these guidelines my answer is clearly more "correct" than the provided potential answers.
2nd, while all this may seem like a small nitpick compared to just averaging over time and saying the answer is only #5, it actually is pretty important depending on what you are analyzing.
During the shunting part of the cycle, ALL the power requirements of the bike are met by the battery, and the pulse of current the battery supplies is an order of magnitude larger (and in the opposite direction) than the average charging current.
Depending on what you are analyzing, that pulse will have significant implications.
3rd, you said you wanted this to be an educational contest ... I would say that learning additional details of how the R/R functions is educational. Even if someone would choose to use the simpler model in a given situation, they would now do so as an educated choice and understanding the possible implications of that choice, rather than just not realizing that there is additional complexity
And finally, while the rules of this contest steer one to specify a simple answer, REALITY is not so simple. In this case the actual physical operation of the circuit says the answer really is not one of the preformed choices provided us. If you actually want the "correct" answer ... It is more complex than the choices which were provided ... And if you actually want to analyse how a circuit behaves, you will need to use the REAL analysis, not the simplified one ... If you want to calculate the voltage dropped in some of the wiring, or the heat rise, you WILL have to use drawing seven as well in your answer ... Or your answer will be wrong ... And for predicting the actual behavior of the actual wiring on the bike, my answer will give more accurate numbers than the other options provided. Which as far as I am concerned makes it "CORRECT"
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In conclusion, it's fine to just use drawing 5 to provide a simplified explanation when desired; but if a detailed/correct analysis is required, then both drawing 5 and drawing 7 must be included.
I look forward to your reply.