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"Veritasium" (YT) - "The Big Misconception About Electricity" ?
adx:
--- Quote from: SandyCox on March 24, 2022, 01:54:59 pm ---
--- Quote from: bsfeechannel on March 24, 2022, 01:29:46 am ---
--- Quote from: adx on March 23, 2022, 11:05:16 pm ---bsfeechannel: Seen your post come in. Yes j appears in a couple of places, as an annotation. I was thinking of cheap ass VNAs and Smith charts when I made my claim.
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Let me get this straight. Because j doesn't appear explicitly on the VNA display, does it mean it is not there? Isn't the display representing a two-dimensional vector space? Aren't VNAs, VECTOR Network Analyzers?
Your point seems moot.
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The concept of something being "physical" or "real" is in the eye of the beholder.
If you don't believe in complex numbers then just don't use them. You will still be able to do a large part of Electrical and Electronic Engineering by solving the underlying differential equations in the time domain and use a lot of trigonometric identities which will become extremely tedious.
If you chuck out the complex number then you also chuck out Phasor analysis and the whole frequency-domain perspective. You will also loose the Nyquist stability criterion which relies on Cauchy's argument principle. How would you do antenna theory without residues and branch cuts? What about root-locus analysis and design?
I find it strange that you have problems with the Complex numbers but apparently accept the axiom of choice.
And i = j. It is just a difference in notation. Its unclear why we use i for the current shouldn't it be a?
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Getting late so a quick reply.
Not liking complex numbers in electrical engineering is down to their physicality for me, so if that is in the eye of the beholder then I don't have any choice, because it is my eye not me who doesn't like it. I just don't think the concept of sqrt(-1) can have physical reality, where I do think (or feel) that the concept of negation can.
But ultimately it isn't that I don't like them, but they (I can only assume) catch many students out - given that some people do unquestioningly think the imaginaryness has some (or immense) physical reality.
I am perfectly happy with solving underlying differential equations in the time domain, and trig identities or evaluation, so long as I don't have to do it (a computer can). It's more direct, it's more physical.
I personally think chucking out the complex number is the best thing, or define j to be a unit vector which works with the same operations as i (or lie to students and tell them that, while still using complex numbers). Phasors are inherently 2D, there is no squaring and -1 involved. It, and frequency domain analysis (for real signals, Hermitian transform) still work like they always did - except the sins and cosses are explicit, and not some arcane 'exponentially' complicated notation (kind of like the weirdness of the C language that people get used to).
I'm going to have to pull an aetherist and say I don't know about root-locus analysis. I don't remember it being too horrible, so I might have forgotten it due to disuse, rather than blocking it out. I remember not liking it very much.
i for intensity? I never worked that out either. I was thinking c for current and call capacitors twangductors or something. It's the right thread for that sort of thing.
TimFox:
Here is a very simple circuit involving resistors and capacitors.
I was looking for a slightly more complicated circuit (RIAA equalization), but couldn't locate the file quickly.
It is very easy to solve for the ratio of (output voltage) / (input voltage) as a function of frequency, using elementary complex algebra (with XC = -j/wC).
Of course, one could derive the differential equation for the time-dependent output voltage with an input voltage equal to a (real-valued) sine function, and then solve it (perhaps with a LaPlace transformation).
Or, one could do an .AC analysis in SPICE (which is strictly algebraic and undoubtedly uses complex algebra internally).
I'll defer to HuronKing above about pedagogy. Fifty years ago, I had difficulty understanding or applying complex variables to electrical circuits, but after studying linear algebra and other useful mathematical subjects, I learned to appreciate the usefulness of "complex notation" for real problems. At the end of a practical calculation, one can express the voltage as a real-valued function of time.
I have several two-phase lock-in amplifiers, that display the "In-phase" and "Quadrature" components of an input signal with respect to a (coherent) reference signal. To confuse, these are called "I" and "Q", respectively, but are often referred to as "Real" and "Imaginary" components.
HuronKing:
--- Quote from: penfold on March 24, 2022, 01:42:31 am ---
--- Quote from: HuronKing on March 24, 2022, 12:47:53 am ---[...]
This is veering really close to the question of "is mathematics physical?" and that's a big question! :D
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Hang on, that's not a very big question, and the answer is relatively simple. Maths itself is not physical, or it is only as physical as any language in which you can express logic, it's conceptual. The links between that language and quantities defined within is also defined and there is an observable consistency between the results of additive processes in 'nature' and in the mathematical system etc... hence why one should always include units against any number with physical significance because that defines the process by which one takes the number on paper and stacks calibrated metre-rules end-on-end to reach a distance. It's all defined, we're safe.
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Okay, okay, now you hang on! :)
The question I've been answering, from adx, is this one,
--- Quote ---Is there any place in engineering, anywhere, where sqrt(-1) has any physical relevance at all? The only place I've ever seen it doing something useful (beyond being an arcane convenience for mathematicians) is in a Feynman lecture where it quasi-continuously described a wave function inside and out of an energy well or something (I can't find it now).
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If you're suggesting that sqrt(-1) has no physical relevance because MATHEMATICS has no physical relevance... then yea... okay let's go with that, sqrt(-1) has no physical relevance because it's part of mathematics which inherently has no physical relevance.... it's kind of a tautology and one I don't find that terribly helpful for 1) engineering students or 2) actual engineers trying to devise logical frameworks to relate phenomena to a method of describing and predicting them.
I read adx's question as, if we use sqrt(-1) in our engineering calculations, what does it mean? Does it have a physical meaning? Or is it just something used to torture students with 'claptrap' and is useless for all us manly-men practically practical-minded engineers? That's a valid question but totally independent of the philosophical question 'is mathematics physical' which I don't really care about (I mean I do, but not here). :)
Now in answering adx's question, in engineering, does sqrt(-1) have physical meaning? The answer is a resounding YES!!!
Just because people got confused by bad pedagogy in school (I'm included in that) or there are specific engineering lines of work or problem solving techniques that don't use sqrt(-1) is TOTALLY independent of my answers to his question.
Does sqrt(-1) have physical meaning in engineering? Yes. Steinmetz proved it (and I hope references to 'waffley' texts aren't in reference to Steinmetz's treatise). And Edith Clarke literally wrote the book on AC Power Analysis. She was hired as the first woman electrical engineer in the USA in an age of extreme sexism by General Electric to solve power problems stumping their engineers - some of these were problems no one else could figure out:
https://www.google.com/books/edition/Circuit_Analysis_of_A_C_Power_Systems/JB4hAAAAMAAJ?hl=en&gbpv=1&printsec=frontcover
I mean it... she literally solved problems no one else could figure out by using hyperbolic functions and complex impedances. She is a big reason our long-distance energy grid can even exist:
Steady-state stability in transmission systems calculation by means of equivalent circuits or circle diagrams
https://ieeexplore.ieee.org/document/6534694
You can read the paper here:
https://speakingwhilefemale.co/wp-content/uploads/2020/09/Clarke_Transmission.pdf
And I've already shared MY experience in RF engineering and antenna design that sqrt(-1) has tremendous physical meaning and application. If complex phasors and impedances and sqrt(-1) is all worthless claptrap for engineers - then don't use AnSys HFSS simulation software and stay away from RF, I guess? :-//
If the response to all this is 'nuh uh, I've never needed it..." well then... fine. Good for you. But don't be deluded into thinking that other engineers aren't using it and ascribing physical meaning to it all the time and changing the world. BTW I used complex impedances last night in my class explaining the origins of harmonics in motors and how to interpret a 3-phase phasor diagram like you'd see on a Keysight Power Analyzer:
I really don't think I need to provide more examples of the 'physical relevance' of sqrt(-1). Take it or leave it. The power engineers and RF engineers are quite happy with it.
One last thing about sqrt (-1), I REFUSE to let ourselves be biased against the attribution of physical meaning to sqrt(-1) because freaking Rene Descartes decided to be a smartass and call them 'imaginary numbers' as if they were 'less real' than other numbers in mathematics (which has been argued that NONE of the other numbers in math are real/physical either so the distinction is irrelevant).
So adx, I submit to you that your issue with the 'physicality' of sqrt(-1) is because of an idiotic naming convention.
This is a mess and as a teacher/working engineer/former student who also got confused, I hate it. Screw you Descartes and screw all the math teachers in the intervening centuries who perpetuated this tragedy of a ridiculous name. That bastard Descartes didn't even know how to take a derivative or do a surface integral (he did help us get there though). He shouldn't be allowed to confuse students for centuries because of his antiquated philosophical biases. :'(
At least when the Big Bang got a derogatory name it was kinda cool sounding... but it also has confused people about what cosmologists actually think about it. :-\
SandyCox:
Some people are of the opinion that only the natural numbers (excluding 0) have "physical meaning". (whatever "physical meaning" might be?)
Does 0 have physical meaning?
Do the negative numbers have physical meaning?
What about sqrt(2) which is an irrational number?
Extending the real numbers to an algebraic structure in which the square root of minus 1 exists is brilliant. Furthermore, all polynomials can be factored into monomials. How great is that?
The field of Complex numbers is not the same as the vector space of two-dimensional vectors over the real numbers. The multiplication is different. j isn't a unit since its square isn't equal to j. 1 is the unit of the Complex numbers.
In my opinion, trying to assign "physical meaning" to mathematical concepts only works for very simple problems. Just trust the Mathematics and look at what the theory tells you. Sometimes our intuition fails horribly. Trust the math.
PlainName:
--- Quote from: bsfeechannel on March 24, 2022, 12:45:20 am ---
--- Quote from: dunkemhigh on March 23, 2022, 11:32:27 pm ---Blimey, and they couldn't even number the ports sequentially. The mere thousands of dollars ones probably leave the labels off.
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They're not oscilloscope channels.
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Yeah, I thought the smiley was implied but on reflection I shouldn't have left that kind of thing to chance. Here's a belated one: 8)
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