That is like saying 3 x 3 is really 3 + 3 + 3. makes no difference as long as you know the underlying principle.
No, 3*3 also equals 3+3+3, 3+3+3, 3+3+3, 3+3+3, and 3+3+3. So it works for all 6 combinations, which means there's no limitations on its equivalence.
This is not the case in R1/R2.
Here:
Billy can run 16 MPH.
Little Sally can run 8 MPH.
8/16 = 1/2. Sally runs at one-half Billy's speed.
8 MPH - 16 MPH = -8 MPH. Sally runs 8 MPH slower than Billy.
Billy hurt his knee and can only run 10MPH. How fast can Little Sally run?
One half? 10/2 = 5 MPH?
Eight less? 10-8 = 2 MPH?
No, Little Sally isn't the one hurt. Little Sally can still run 8 MPH.
"One-half" and "eight less" are mathematical description, not prescription.
Similar situation with R1/R2. The laws of nature prescribe the relationships described by Ohm's Law. Because of those laws, the ratio between series resistances ends up being proportional to the voltage drops. But R1/R2 itself has no central meaning. The extracted ratio means nothing to the universe as such. Throw two resistors on the ground and the universe isn't going to magically generate voltage just because the combination can be described as 13/15.
Because the foundation is solid, the derived equation is solid. But the equation isn't foundational. And this is in fact WHY it is so useful for circuit design. To design, you have to be able to play with values. But I, E, and R are solidly locked together. To have conceptual freedom, you need to break that block. R1/R2 gives you a place from which to apply leverage.
TuxDave said:
For any decent EE, a voltage divider is one algebra step away from V=IR and to most of them making that "second order property" is a no-brainer.
That doesn't make it in any way efficient.
He's in a class that's obviously currently on electronics fundamentals. There's no design there, unless there's some really odd trend going on in the electric heater field that I'm not aware of. So, he'll be on Ohm's Law, and they'll be doing a lot of, "I give you two legs; find the third." One scat, many questions regarding it. So why are you trying to defend a method that gives you trash as an intermediate step? Why defend a method where every voltage divider calculation requires you to start from scratch? There's twelve of them in that circuit alone. (ignoring the big one)
One value: 4A, does away with all that. There's no need to keep adding up all the resistances, as current is a function of resistance. And there's a good chance that one of the questions will ask for current anyway.
It's a pretty basic test-taking skill to predict what questions will be asked and then to work the current problem in such a way as to push in the direction of their answers.
TuxDave said:
You don't see me trying to rederive the resistance based on cross section area, mobility of carriers and length.
You seem to have a really hard time differentiating troubleshooting from engineering.
When I say, "X doesn't make sense in a troubleshooting capacity, but I see how it would be useful in design," and you come back with, "DON'T TELL ME IT ISN'T USEFUL BECAUSE SEE I USE IT IN DESIGN ALL THE TIME HAHA PROVED YOU WRONG N00B" ... yeeeeah... do you see how that doesn't quite marry?
Anyway, if you want to know resistance, just put a known voltage across it and read the current.