141–150 of 216 posts
Like incompressible fluids, electricity is hard to reason about because we work in a limit that does not obey local causality. The entire system must be solved simultaneously, and there is not a well defined "input" or "output". This can be seen from the fact that when we analyze a circuit we also include the model the power source and the load. The combination of non-locality and complex boundary conditions makes it…
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My water analogy for a capacitor is a piston with pipes attached to both ends, with a spring system that pushes the piston towards the center position. Is that not a mathematically correct equivalent? (in an idealized system with no water resistance/inertia and disregarding that the piston is of fixed length - not that real capacitors have zero resistence, inductance or can store infinite charge)
From an energetic standpoint, a capacitor is something that takes a trickle over a long time, and releases a flood over a short time. So it would be a water tower with a small input and a large gated output.
So: does electricity have 'mass'? What I mean is, when current flows, is there a transfer of electrons (or something else) from the power source to whatever it is send to? And is there a difference between AC and DC?
The context of this question is that the core argument of a legal paper (of all things) I was reading at the time (on property rights of virtual goods) hinged on there being a transfer of mass, however small. I wasn't so sure.
(my SE question devolved into a semi-legal argument - I have a law degree, the context of the question is a lot more nuanced still than the above description, and is very much tied to some specific 80 year old Dutch case law - just saying that to point out that a legal argument on whether or not the question matters won't add much to the discussion.)
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I didn't agree with what you wrote and maybe I can explain why. Springs store inches. You measure displacement in inches. Spring constant is just the value that relates stored inches to available force. (You can swap roles of force and displacement if you wish, the point is the same. It sounds bad to say springs store force or displacement, to me.)
But inches are an abstract measurement of distance. Electrons are a thing. (Well, depending on who you ask... no one has ever seen one, and some people have claimed half-jokingly there's only one electron in the entire universe: https://en.wikipedia.org/wiki/One-electron_universe .)
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But inches are an abstract measurement of distance. Electrons are a thing. (Well, depending on who you ask... no one has ever seen one, and some people have claimed half-jokingly there's only one electron in the entire universe: https://en.wikipedia.org/wiki/One-electron_universe .)
What?? Okay then count by lengths of the spacing of carbon molecules in graphite, or Plank lengths, or whatever. I don't see why your objection is on inches or otherwise any unit I chose for dimension of length.
I think more than half the time I spent earning my EE degree has been spent unlearning the intuitive (but wrong) things that I was liberally taught. I was fortunate enough to have an exceptional Physics teacher in high school, who managed to avoid a lot of the bullshit that less fortunate students were fed; sadly, I compensated that with some of my own (misguided) self-study. This experience also taught me to activel…
Intuitive but wrong (and doggedly persistent) idea #1: "electric current is moving electrons". It is moving photons, exciting (largely) stationary electrons. I can't stress how crucial overcoming that misconception was when I was doing EE.
This sounded like he went mad to me...
I think more than half the time I spent earning my EE degree has been spent unlearning the intuitive (but wrong) things that I was liberally taught. I was fortunate enough to have an exceptional Physics teacher in high school, who managed to avoid a lot of the bullshit that less fortunate students were fed; sadly, I compensated that with some of my own (misguided) self-study. This experience also taught me to activel…
It took me a huge amount of time to get rid of all the BS learned in school. In some area I'm even still working on it (eg. analysis).
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Intuitive but wrong (and doggedly persistent) idea #1: "electric current is moving electrons". It is moving photons, exciting (largely) stationary electrons. I can't stress how crucial overcoming that misconception was when I was doing EE.
Is this why my EE prof once said, a metal cabel is like a fiber cabel, it trasfers EM energy but at a different wave length? This sounded like he went mad to me...
For example, finding answers to questions like "Why does absorption of EM waves in matter rise with lower wavelengths, but at the wavelengths of light matter starts to become more and more transparent again" isn't easy. But so are the involved phenomenons, after all.
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Not really sure I like that link. He seems to suggest that capacitors store "energy" instead of charge, which is just as ambiguous really. It's not like there is some sort of energy particle either. Of course what's really happening is that you are creating an electric potential between two plates. It's true that the net charge is the same, but you are moving electrons from one plate and forcing them (doing work) int…
My water analogy for a capacitor is a piston with pipes attached to both ends, with a spring system that pushes the piston towards the center position. Is that not a mathematically correct equivalent? (in an idealized system with no water resistance/inertia and disregarding that the piston is of fixed length - not that real capacitors have zero resistence, inductance or can store infinite charge)
Now if that was too easy try an inductor analogy. Something like a waterwheel hooked up to a very big flywheel so it works hard to keep the watercurrent flow constant.
The best thing about learning by analogies is eventually they get so hairy and crazy that reality is simpler in comparison...
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I am all for introducing things the correct way, but this example of yours just does not work for me. Fractions as equivalence classes? or as a solution to an equation. No. That might work for you. In fact I might even argue that it only works for you - the child idealization created by "current you". There are many things wrong with US education. But I do not think introducing fractions using concrete examples is on…
It's fine if this wouldn't work for you. Nothing works for everyone, and that's sort of the point. Kids are funneled through an extremely rigid sequence of topics focusing entirely on rote application of manipulative techniques. Anyone who doesn't conform to this sequence is just left to painfully deal with it on their own. I remember a bit later in school I discovered algebra on my own and became really interested i…
I realize this is going to go far beyond the thoughts of a toddler learning about fractions for the first time via the pizza analogy, but I think it demonstrates that even the seemingly obvious pizza analogy is more nuanced than it seems.
I've never bothered thinking about this before, but it seems obvious to me now. Using just a straight-edge and compass, it is not always possible to cut a pizza into N standard-shaped slices for all positive integers N. Doing so is equivalent to constructing a regular N-gon, and this is only possible when N takes on the special form
N = 2^k * p_1 * ... * p_M
for some nonnegative integer k and some sequence of distinct Fermat primes (that is, primes of the form 2^(2^j) + 1).
Thus, you cannot slice a pizza into 7 slices using a straight-edge and compass. So in the pizza analogy the number 1/7 corresponds to something that is not physically achievable with standard implements.