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.

Too true, and my problem is about to be your problem and the cycle continues comrade.

OK, the solution is "how accurate will make the physicist and accountants both only kinda mad"

Not using the correct resistors does cause a U problem every once in a while.

Sounds like a 6 ohm resistor solution.

I'm not an engineer

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.

Real world resistors usually have a tolerance of ±5%, so you'll never get anything that precise.

The trick is to round everything. Pi? Basically 3.

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"

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.

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.