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| aetherist:
--- Quote from: 2N3055 on August 14, 2023, 08:37:12 am --- --- Quote from: aetherist on August 14, 2023, 07:30:56 am --- --- Quote from: Simon on August 14, 2023, 06:14:55 am --- --- Quote from: aetherist on August 14, 2023, 04:08:13 am --- --- Quote from: TimFox on August 14, 2023, 03:33:06 am --- --- Quote from: aetherist on August 14, 2023, 12:40:38 am --- --- Quote from: TimFox on August 13, 2023, 11:46:45 pm ---Once again, if electricity “hugs the surface” of a wire, then why does the DC conductance (reciprocal of resistance) scale with the cross-sectional area, not the circumference? --- End quote --- Interesting -- are there good measurements? On the other hand -- why are lightning down conductors often flat strap? --- End quote --- One of a myriad of sources for resistance of copper wire: do the math. https://commons.wikimedia.org/wiki/File:Copper_cable_resistance.jpg --- End quote --- I did the math. That/there chart says that resistance decreases with radius R in a linear way. The circumference of round wire increases in a linear R way with radius. The area of a round wire increases in an RR way. Hence area has nothing to do with resistance. Circumference has everything to do with resistance. --- End quote --- I'll break the forum rules now and tell you that you are a fucking idiot! I don't know what math you are smoking but you are wrong. This is so basic that it is hard to explain to an idiot that will not listen! the area of a circle is r^2*pi the circumference is r*2*pi Now if you were not an idiot you would spot the obvious! but you are a fucking idiot!!! You should, if you were not a fucking idiot be able to see that the circumference will increase linearly with the radius while the area increases with the square. Maybe you would like to go down your local electrical store and buy different gauges of wire, then spend more money than you need to to learn basic physics and buy a milliohm meter, or buy so much of that wire in large gauges that it actually registers some ohms on a meter. Now measure them and tell us your results. WARNING: DO NOT post in this thread again until you come back with correct results. Failure to do so will result in instant banning! --- End quote --- Ok, i have the correct results. I got my results from the link provided by TimFox. A 1.0 mm Cu wire 1000 m long has a resistance of 35 ohm A 10.0 mm Cu wire 1000 m long has a resistance of 3.6 ohm. A 10.0 mm wire has a Xsectional area 100 times that of a 1.0 mm wire. Hence the resistance of a 10.0 mm wire should be 0.35 ohm based on Xsection area. And the resistance of a 10.0 mm wire should be 3.5 ohm based on circumference. So, my circumference theory has an "error" of 0.1 ohm. But your area theory has an error of 3.15 ohm. --- End quote --- That table is simply wrong. Here is one that is correct: https://www.engineeringtoolbox.com/copper-aluminum-conductor-resistance-d_1877.html Resistance scales with cross section area. That is not some stupid theory, that is proven fact. If you don't trust scientists, follow the money. Copper is sold by weight which is a cross section area x length x specific weight of copper. People would be VERY UNHAPPY with the price of cables if the current capacity was linear with diameter.... --- End quote --- Yes, that table says that resistance/area is constant -- for DC i suppose, solid circular. And for sure that is a problem for my elekton (photon) elekticity (hugging the surface of a wire). But i did not want to argue about elektons. I didnt even want to argue about electrons -- ie re the topic that electrons are round. I wanted to point out that there is no such thing as a hard little nutty electrons orbiting a nuclei -- i reckon that what we have is photons (elektrons) orbiting & hugging nuclei. And leave it at that. Bearing in mind that the nature of the atom & electrons has a long history of contrary ideas. |
| TimFox:
Sorry about the wrong values in the table I linked (one of many that pops up on Google). I was looking for one in straight metric units, without practical wire gauges, and did not re-calculate the values myself. Note that no one holds the "solar system" model of the atom to be appropriate any more, except graphic artists. Quantum mechanics is a difficult topic, but it is past the "hand waving" state. In atoms, spectroscopy is an advanced and accurate field of study: the early successes of quantum theory explained the spectra of light interaction with atoms. Further work in quantum electrodynamics included the incredibly accurate calculation of the Lamb Shift, which gives the "fine-structure constant" to within 1 ppm of the measured value. Since the Lamb Shift in hydrogen is a microwave frequency, it can be measured with high precision. Trigger warning: heavy mathematics. https://en.wikipedia.org/wiki/Lamb_shift If you want to contribute to a field where there are still unsolved questions, look at recent (g-2) measurements for the muon. |
| aetherist:
--- Quote from: TimFox on August 14, 2023, 02:04:50 pm ---Sorry about the wrong values in the table I linked (one of many that pops up on Google). Note that no one holds the "solar system" model of the atom to be appropriate any more, except graphic artists. Quantum mechanics is a difficult topic, but it is past the "hand waving" state. In atoms, spectroscopy is an advanced and accurate field of study: the early successes of quantum theory explained the spectra of light interaction with atoms. Further work in quantum electrodynamics included the incredibly accurate calculation of the Lamb Shift, which gives the "fine-structure constant" to within 1 ppm of the measured value. Since the Lamb Shift in hydrogen is a microwave frequency, it can be measured with high precision. Trigger warning: heavy mathematics. https://en.wikipedia.org/wiki/Lamb_shift If you want to contribute to a field where there are still unsolved questions, look at recent (g-2) measurements for the muon. --- End quote --- The atom is unsolved (but my elektrons help). Electricity is unsolved (but my elektons help). Quantum theory is a model -- & we need good models -- but models dont explain anything -- models give us numbers only. |
| T3sl4co1l:
--- Quote from: aetherist on August 14, 2023, 12:40:38 am --- --- Quote from: TimFox on August 13, 2023, 11:46:45 pm ---Once again, if electricity “hugs the surface” of a wire, then why does the DC conductance (reciprocal of resistance) scale with the cross-sectional area, not the circumference? --- End quote --- Interesting -- are there good measurements? On the other hand -- why are lightning down conductors often flat strap? --- End quote --- It does -- at AC. Wait, you again? God damnit. Well, Tim has his answer at least. You were never looking for answers so it doesn't matter. Tim |
| Nominal Animal:
--- Quote from: 2N3055 on August 14, 2023, 08:37:12 am ---That table is simply wrong. Here is one that is correct: https://www.engineeringtoolbox.com/copper-aluminum-conductor-resistance-d_1877.html --- End quote --- Agreed. And that table is easily reproduced using the simple steady-state DC conductor model, where resistance \$R\$ is a function of length \$\ell\$ and cross-sectional area \$A\$ at conductivity of \$\sigma = 58 \text{ S}/\mu\text{m} = 58 \times 10^6 \text{ S}/\text{m}\$ or equivalently resistivity \$\rho = 1/\sigma = 17 \text{ n}\Omega \cdot \text{m}\$ (for soft solid copper), $$R(\ell, A) = \frac{\ell}{\sigma A} = \frac{\ell \rho}{A}$$ or for a round single-strand wire of radius \$r\$, $$R(\ell, r) = \frac{\ell}{\sigma \pi r^2} = \frac{\ell \rho}{\pi r^2}$$ where the unit \$S\$ refers to siemens, \$[ \text{S} ] = [ \Omega^{-1} ]\$. One way to verify this in practice would be to measure the resistance of different shapes but constant amounts of liquid mercury. Its conductivity is only about a sixtieth of that of copper, but that just means you don't need stupid amounts of mercury or an unrealistically precise ohmmeter. You do need to control the temperature precisely, because that significantly affects the conductivity. For solids, one could use gallium, which melts at a very low temperature, but is a bit more conductive than mercury. Melt it to reshape it, then cool down to the precise measurement temperature (for example, at freezing point of water at a constant atmospheric pressure), to get each data point. An important point to remember is that even trace amounts of certain elements will significantly change the conductivity, so mixing the shapes instead of going from one extreme to the other is important to alleviate the drift in the results because of contamination. Of course, all that has already been done by many, many people, and the results are in agreement with the above model. |
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