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That level of precision in a resistor would literally be thrown off if you breathed on it. If you actually needed that, then you need to build an extremely controlled environment around it. Even then, the heat from the electricity itself would throw it off. Maybe in a liquid nitrogen bath?
First, assume a spherical resistor in a vacuum, that can also dissipate heat with 100% efficiency.
Now that we’re in physics land, anything is possible.
Its funny the first thing I thought of was, at what temperature.
A big aspect of good design is being able to solve an issue as succinctly as possible, with as wide an operating range as possible. Lower tolerance requirements = better.
If you need that level of precision, you might want to reconsider your career in circuit design.
I'm a physicist. If you are an engineer that sounds like a "you" problem.
Too true, and my problem is about to be your problem and the cycle continues comrade.
Not using the correct resistors does cause a U problem every once in a while.
Or an I problem, depending on your perspective
OK, the solution is "how accurate will make the physicist and accountants both only kinda mad"
Sounds like a 6 ohm resistor solution.
They're 5.6 or 6.8 ohms usually
I'm not an engineer
This is also a "you" problem. Fix that at your earliest convenience.
i miss old school radioshack. i did not know what all those bins of tiny electronic hobby parts were for, but I desperately wanted to learn. I did eventually but you have to get all your stuff from some shady oligarch.
i did not know what all those bins of tiny electronic hobby parts were for, but I desperately wanted to learn.
From what I understand, prior to the personal computer boom of the 1980's, HAM radio was kind of a big deal with nerds. The parts were there for all manner of electronics tinkering, but a big mainstay was building and modifying radios. Yeah, you had people tinkering with computers in the 1970's too, but it was more niche (until it wasn't).
Yeah we’re living in the ruins of the old America already and have been for like 25 years.
It’s dirty they just use the same business names they did in the 20th century. While making smoke and mirrors versions of the old products.
Without using fancy components: Just simply adding a 6.2 and a 2400 Ohm resistor in parallel already gives you 6.18402 Ohm ⚡️
Real world resistors usually have a tolerance of ±5%, so you'll never get anything that precise.
That's why I keep a roll of 20 AWG nichrome on hand. Spool off 9.7195853528209 feet and it'll be bang on.
So 1 inch of your wire would weigh ~0.0987 grams, so to measure down to 8.6350242338508 inches of wire your scale would need to weigh down to ~0.00000000000007 grams. Which is the weight of about a dozen atoms or so.
Yeah which is why you use a Kibble balance. Are you sure you're cut out for this kind of work?
I've actually found 1% to be a lot more common nowadays.
Just put two π ohm resistors in series duh
Whats wrong with your 3!
Ugh, 3 factorial is most definitely not equal to π. It's something more like, idk, 9? Honestly I don't even know how I got here; I majored in Latin and barely past
Numbers like that are why I quit majoring in mechanical engineering. Physics took the beauty of math and made it ugly.
You knew something was wrong in calculus when you got a fucked up coefficient that wasn’t a nice number.
Numbers like that should have been why you kept going in mech E.
Once you get past the educational stage, every one of those calculations becomes "OK now round to the closest whole number that gives you the larger factor of safety and move on"
Using π = 4 is only a 27% safety margin, better go for π = 10 just to be safe.
Pi r square, square have 4 sides. No problem found.
Pi r not square. Pi r round. Cornbread r square
The trick is to round everything. Pi? Basically 3.
I've heard a story (so like 4th hand at this point) where an astrophysicist was talking about galaxy rotations or something. "And for this model, we can simplify pi to 10."
My thermodynamics professor made so approximations in his derivations that all of his equations had an “O” term to represent the inaccuracy. Every time he made another approximation he’d say “and, of course, the O sucks up the error”.
After calculus though, they just expect you to cope with fucked up coefficients. In Diff Eq, sometimes you do just get something like 3/111 cos (6/111 x). It gets harder to come up with examples that work out with nice integers.
Physics can also have some really beautiful math, look at Lissajous figures. Once you understand the connections between e, the imaginary plane, and sine/cosine, you get some profound understandings about how electric and magnetic fields work.
couldnt you technically fine tune a potentiometer to be this resistance if you were precise enough?
Mathematically yes. Practically, right now? No.
So you need a resistor of this value for your widget.
For that many places of precision you're looking at a potentiometer with a 10 nano-ohm precision.
I am not aware of any commercially available resistor that can do that but you could create one using microelectronic structures used for ICs and derive a 10 nano-ohm resistor by design and then chain enough of these elements into a resistor network or potentiometer to create the super precise resistance value you want.
Cool, congratulations.
Now how are you going to use this 10 nano-ohm resistor? What voltage will you be applying across it? What current do you expect it to handle? And therefore what are your power requirements? What are your tolerances, how much can the true value deviate from the designed ideal?
Because power generates heat through losses, and that will affect the resistance value so how tightly do you need to manage the power dissipation?
How will you connect to this resistor to other circuit components? Because a super precise resistor on it's own is nothing but an over-engineered heating element.
If you tried connecting other surface mount devices (SMDs) from the E24 or even E96 series to this super precise resistor then the several orders of magnitude wider tolerances of these other components alone will swallow any of the precision from your super accurate resistor.
So now your entire circuit has to be made to the same precision else all of your design work has been wasted.
Speaking of which, now your heat management solution now needs to be super precise as well and before you know it you've built the world's most accurate widget that probably took billions of dollars/euros/schmeckles and collaboration from the worlds leading engineers and scientists that probably cost more time and money than the Large Hadron Collider.
The only application I can think of off the top of my head that would require that precision is a R2R DAC.
Just sort through a bin until you find one.
Rheostat, my dudes
