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The article says that resisivity in normal metals follows a quadratic curve, but the article also says that it follows an exponential curve. Does anyone know wh
by kens 1y ago
The article says that resisivity in normal metals follows a quadratic curve, but the article also says that it follows an exponential curve. Does anyone know which it right?
- fwip 1y agoIf I'm reading Wikipedia correctly, the formula is quadratic for some metals, and cubic or quintuplic(?) for others: https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity#Metals https://en.wikipedia.org/wiki/Electrical_resistivity_and_con...
- VygmraMGVl 1y agoTypically, the behavior of any given metal is a mix of mechanisms so the measured behavior is fit to a curve where you fit n. So for metals the exponent is typically a decimal between 2 and 5.
- fwip 1y agoThanks, I appreciate the explanation. :)
- Sniffnoy 1y agoYou would normally just say "5th degree" or "5th power".
- gjm11 1y agoBut the specific word they were looking for is "quintic". (And the corresponding word for 4th-degree, in case anyone is curious, is "quartic"; one sometimes sees "biquadratic", which unfortunately is also sometimes used to describe a particular subset of quartics.)
- Sniffnoy 1y agoOh right, silly me. Wow, my own vocabulary deserted me there, huh? Yeah I think generally "sextic" is the highest you see before people stop doing that, and that one's somewhat uncommon I'd say. ("Quintic" is actually fairly common, contrary to what I said earlier, oops.) The fact that seventh-degree would be "septic" might be one reason stop with the words at that point!
- gjm11 1y agoI'm pretty sure that more than half the times I've seen "quintic" are in one single context: talking about the fact that while you can solve polynomial equations of degree 1-4 by doing arithmetic and taking n'th roots, this stops being possible once you get as far as quintic equations. (The "insolubility of the quintic".)
- s1mplicissimus 1y agoafaiu quadratic is a subtype of exponential, so they are not mutually exlusive
- Sniffnoy 1y agoNo. Exponential growth or decay is much faster than quadratic growth or decay. You may be mixing up exponential functions, of the form x maps to ab^x, with power functions, of the form x maps to ax^b. These are very different! Annoyingly, people often use "exponential" colloquially to mean anything faster than linear, but in fact lots of things are faster than linear.
- sfink 1y agoOuch, not a good look for a technical article. From the other responses, it sounds like "none of the above". It's more like a "polynomial curve" that is only sometimes quadratic. Is "polynomial curve" a thing? "Power curve" / "power function"?