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Voltage Makes No Sense!

At least in circuits. Here we have a single-loop circuit:

And now, we have the following description:

I really tick on the first sentence of the last paragraph. What does resistance have to do with change in potential?? When I think potential, I always think

\[V=-\int{\vec { E} \cdot d\vec {s}}\]

I thus visualize an electric field extended from the positive end of the battery (+ terminal) to the negative end (- terminal) - and when I visualize a flowing current, I imagine this flow being mediated by the electric field - that is, as the charge "flows," there is a definite change in potential every step of the way. If \(V\) depends on \(s\), then how is the potential "unchanged"?? Unless, of course, I have the entire picture wrong and there is no electric field at all.

Help is GREATLY appreciated.

Note by John Muradeli
2 years ago

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Extra info:

This is how I visualize potential difference across the WIRE:

The image shows the calculation only between capacitors, but I apply this logic across the entire wire. Is this wrong?

Now just draw electric field lines along the wires and my understanding is complete. Is this wrong?

As for Voltage itself, here's how I visualize it:

Just imagine the sphere on the right is positively charged. Okay, so, the closer you bring the test charge to the sphere, more work is done against the electric field produced by the sphere, and the higher the electrical potential energy of the particle. The electrical potential energy per unit charge of the particle increases as well. Now what's the difference between the two descriptions there? To me, \(\frac{U}{q}\) - potential per charge - means that given a specific voltage, upon releasing the particle(s), each unit of charge will have gained the same amount of kinetic energy. So, if we have \(100V\), to me, this is \(100J/C\). Or, in other words, if we have a particle - let's call it Mendrin Charlesworth, and its charge is \(1/100C\), then it will acquire \(1J\) of kinetic energy upon release - so that when we have \(100\) Mendrin Charlesworths, we get the grand total of \(100J\) - for our \(1C\).

And thus, when say a positive charge carrier is closer to the positive terminal of the battery, it must only make sense that potential there is greater than if we were to consider a charge carrier a few millimeters up the wire. Is this reasoning correct at all???

\(\text{(Thank you!)}{}^{\infty}\) John Muradeli · 2 years ago

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@John Muradeli Okay, here's the key detail you're missing here. You're trying to compare a capacitor that has a direct electrical connection from plate to plate with a pair of charged spheres in free space, which is not a good electrical conductor. You are right, with the latter example, we can speak of an electric potential that varies from sphere to sphere, so "why not with the capacitor with a wire going from plate to plate?" Well, the INSTANT you make an electrical connection from plate to plate, you probably can speak of an electric potential in the wire that varies from plate to plate, but only for the briefest moment! Should there be a resistor in the wire somewhere, then, no, it will not be "for the briefest moment", because the resistor will limit how fast the capacitor may be discharged. Ditto for battery (even though because of internal resistance of typical batteries, the discharge isn't anywhere near as rapid as what would happen with a capacitor--which is why laboratory equipment that need instant power like to use capacitors, not batteries). As a [bad] analogy, think of a wire as a 1,000 lane wide freeway, and a resistor as a 1 lane construction detour road---how do you think the traffic is going to behave?

The point is, while there isn't a true fundamental difference between the two examples, differing only by the electrical resistance of "free space" and conducting wires, as a very good approximation, they can be treated differently. When doing physics, it's always a good mental habit to make such distinction simply because "it's a very good approximation to do so!" The same kind of thinking, for example, helps one deal with the qualitative differences between, say, classical mechanics and relativistic mechanics, or classical mechanics and quantum mechanics. Michael Mendrin · 2 years ago

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@Michael Mendrin UUUUUUUUmmmmmmmm.......... yeaah I think for now I will forget all this and just do what I hate doing the most when learning - ASSUME IT'S RIGHT. Trust me if I go on with this it won't end till probably a few days from now. Anyway, ironically I have covered this part of circuits in which I learned that the current and voltage during the charging process is VARIABLE - which undermines all of my previous assumptions. And yet still I really wish I knew the meaning of Voltage in a circuit, for it makes absolutely no sense to me with my foundational knowledge which relies on ball-physics - not wire-physics. Oh well no time for that. TIME FOR FORMULA GRINDING!

Thanks a lot for your input, nevertheless. John Muradeli · 2 years ago

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@John Muradeli Let me give you more advice about studying physics in college. If you're in a hurry and have no time to really grasp why different branches of physics don't make much sense or even contradict each other, don't bother trying to. Just learn it by rote, do whatever the textbooks say you should be doing, and then come back to it later if you want a deeper understanding "why it should be so". In my experience, that's how most undergraduates in physics get by--they don't ask too many questions. At least not at first.

I started college as a math major, which required physics as part of the curriculum. Like you, I was puzzled about all these seeming inconsistencies and contradictions, and it made no sense. So I switched my major to physics, because I found it so fascinating that it could even be like that. The curiosity got the best of me. Michael Mendrin · 2 years ago

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@Michael Mendrin Yup yup I can definitely see that happening to me. The farther away I go from mechanics, the less things make intuitive sense. Don't even get me started on optics and QUANTUM PHYSICS. All those Lagrangian and crazy differential expansions and relations blah blah is like WUUUUT!?? So you just go with it. And then, when you have ... ahem... TIME... you try to figure it out ;) Got it. John Muradeli · 2 years ago

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@John Muradeli I recall a while back I got into an argument with a physicist that worked for a laser manufacturer. He was saying that quantum mechanics was in "perfect agreement" with classical electromagnetism theory at least in predicting exact waveforms in 3D space (he was a LASER physicist, no less!), and I told him, no, they are almost exactly the same but nevertheless not quite. To make a long story short, we made a bet, and I worked up the "exact" 3D waveforms for a specific case both using QM and EM. The resulting equations looked almost EXACTLY alike, except that somewhere, buried deep in the equations, there was a plus sign for one and a negative sign for the other. Eventually, he had to admit he had lost the bet, to his shock.

The moral of the story is: Don't expect that all of the branches of physics are in perfect and exact agreement, as you would expect in mathematics. It's far from it. Does that mean physics is "false", and maybe just "stupid"? No, you just need to understand the nature of reality, and why physics is the way it is. It's very fascinating stuff. Michael Mendrin · 2 years ago

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@Michael Mendrin True - and I really feel that it is outright ignorant to say you're either a physicist or a mathematician. BRUH ALL I DO IN PHYSICS IS MATH!!! I've learned about vectors and fluxes and all other crazy sheep I've never learned in a math class! And what's better? You get to apply all that to real life!! That's why I see less value in studying non-application branches of mathematics - like Number Theory, Combinatorics, Integral-Solving ... I mean yeah they're fun and all, but ISN'T PHYSICS MORE FUN??!? You get understand how the freakin UNIVERSE works. Already at my level I can look at almost any object around me and think of the various laws and equations that govern it. What do people think when they look at the sunset? "Oh, what a view." What does John think when he looks at a sunset? "Atmospheric light parallel component refraction mediated redshift delayed about 8 minutes by the cosmic speed limit the source of which in the approximate 5 billion terrestrial orbits determined to use up its hydrogen fuel and collapse into a white dwarf upon which the consequential supernova shall devour the very matter positioned in the relative spatial arrangement of the solar system from which the neuron-mediated biochemical process of observation has been arranged in a probabilistic higher-entropy sequence of the universe."

BAM. John Muradeli · 2 years ago

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@John Muradeli On that note, I'll leave it up to you to find Richard Feynman's observation about the difference between physics and mathematics. Michael Mendrin · 2 years ago

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@Michael Mendrin

DING DING! MR. ELECTROMAGNETOPEDIA!!! I could use your genius in this.

Also, HAPPY BIRTHDAY!!! Sorry I missed it! Just noticed the \(+1\) in \(8^2+1\). I hope you have \(+25\) more of these, because Avatar D comes out and then IMMORTALITY!! MWHWAHHAHA John Muradeli · 2 years ago

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@John Muradeli I keep forgetting if there's going to be a massive explosion or implosion in the year 2040?

Meanwhile, I'll get back to your electrical question later today. Did you see my note about a ball looping the loop? Michael Mendrin · 2 years ago

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@Michael Mendrin Yes of course - and I knew the solution already. I just didn't know why you can't analyze it purely in terms of grav pot energies. But NEVERMIND THAT. That matters ZERO right now. I have 14 hours to read 100 pages - that's 9.0 minutes per page. FIVE CHAPTERS IN HALF A DAY!!! Before it took me 2.5 days to do a chapter!!! THIS IS MAD!!! I'm drinking coffee over night to not fall asleep. No time for sleep. IM GONNA DO IT!!!!!

Oh and what explosion/implosion? O_o Oh and sorry the actual figures is +30 years - avatar D's upper limit deadline is 2045. But bah with your mental vigor I'm sure you'll pull off +40. Just... make sure you jog daily and eat your veggies :D But it really doesn't matter since brain transplant will already be available in Avatar B - which is around 2025. Sooo... In +10 years, you sit around Avatar B, wait for Avatar C, move into avatar C, and screw Avatar D - because they gonna DESTROY YOUR BRAIN AND MAKE IT HOLOGRAPHIC. And due to the teleportation dilemma I've discussed earlier, that "you" isn't you. So yeah Avatar C is the way to go. John Muradeli · 2 years ago

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@John Muradeli 2045? You know, I just saw a video of Vladimir Putin "pumping iron". What iron? That man can't pump much iron. And he's 2 years younger than me! Wuss!

I think I'll be sticking around. Michael Mendrin · 2 years ago

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@Michael Mendrin Yeah well you may really want to shift that number to 2035 - not only because Avatar D is scary and Avatar C will do just fine instead, but because 2045 is also the year close to most Technological Singularity predictions... if you know what that means. Sooo you should get an avatar, earn hella money, and get a ticket to Mars - because the Earth will probably go KABOOM, if not Beep-Boop. Til then, let's help me get my engineering degree asap so I can start working on that wormhole! John Muradeli · 2 years ago

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