Sorry, this doesn’t make sense. The resistor grid is the mathematical model.
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I’m talking about actual physical resistors that are soldered into place.
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next headline: 400 Scientists looked at politics and proclaimed unanimously - You can’t science this shit! and went back to their labs.
I hope some of them stick and become good politicians, we certainly need them.
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I understand that this is what you are imagining, but “there are things in nature” that are not just a finite set of resistors soldered in place, and the models for some of these are best dealt with by starting with a mathematical model of a resistor grid.
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Is this like Einstein building a paperclip straightener out of a paperclip so he could straighten a bent paperclip?
ETA: Also, the models are similar to a resistor grid model, but that’s where the similarities end.
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No. It’s modelling a continuous problem via discrete approximations. The point is not to understand the resistor grid itself, but, as @d_r said
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I just use finite element analysis for that, which sounds like what you’re talking about. There is software for that, although understanding the different formulations is important to using them properly. Cranking through an FEA by hand is not advisable.
Resistor cubes and resistor grids were just mental exercises to get us used to calculating equivalent resistance and for understanding Kirchhoff’s laws… These exercises were designed to understand the resistor grid itself. The closest I’ve come to seeing a resistor grid in the wild is a Wheatstone bridge/voltage divider/etc, or flash ADC/DAC, or complex loads that aren’t all resistors but whose components have complex impedance. Even these things aren’t approaching the types of resistance grids found in textbook exercises.
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What @Auld_Lang_Syne said. Moreover - and this is slightly paradoxical - once you use the limit of discrete approximations to understand continuous models, you can then turn around apply these continuous models as approximations of discrete systems. We do this all the time with differential equations, since it turns out that working with the DEs is simpler than working with the corresponding discrete difference equations.
In the 70s there was a (thankfully small) movement to replace Calculus in introductory physics with discrete concepts and numerical analysis. It was a mess, the discrete approach was simply not as powerful or simple as the traditional approach.
For sure understanding an infinite square array of resistors is easier than understanding a 100x100 grid of resistors. Ironically, the general solution is best expressed with Fourier Analysis-related integrals of complex-valued functions.
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