Now I'm wondering if anyone has built a very large grid of resistors to try to approximate / curve fit this. Surely there's a youtube video in this ...
Infinite Grid of Resistors
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Re: Infinite Grid of Resistors
#72Re: Infinite Grid of Resistors
#73People think this is not relevant to real world problems but it actually is, albeit all the calculations aren't that relevant. Silicon substrate's resistance is basically an infinitely large grid of unut resistances at the distances relevant for a local point of an IC. Note that silicon substrate is often heavily doped (p-type) and all info you get from the fab is it's resistivity (often somewhere between 1 to 100 oh…
I'd argue the case you're describing is mathematically simpler precisely because it is continuous.
Re: Infinite Grid of Resistors
#74I'm a bit mathematician and a bit electrical engineer. The electrical engineer suggests it's not measurable unless you apply current and also asks "when" after the current is applied referring to the distributed inductive and capacitive element and the speed of field propagation. The mathematician goes to a bar and has a stiff drink after hearing that.
> The electrical engineer suggests it's not measurable unless you apply current and also asks "when" Just wait infinite time for all the transient responses to die down. The grid to enter steady state and to became true to the schematic.
An infinitely large grid never reaches equilibrium, like it says in the article.
Re: Infinite Grid of Resistors
#75My math isn't strong enough to follow the whole article, but my intuition as someone who works in electronics is that when a quantized system interacts with an infinity, the infinity is restricted based on the magnitude of the quantized factor. Electric charge is quantized. Less than one electron cannot pass through a node, therefore an infinite grid of resistors is effectively a finite grid of resistors whose size c…
That only matters if you're measuring in the time domain and seeing the noise due to individual carriers. Often you just care about averages over some time and space (e.g. the macroscopic flow of water behaves quite different from the speeds of the individual molecules).
Re: Infinite Grid of Resistors
#76This is a discrete case of "sheet resistance."[1] The resistance between any two points, nodes in this case, is the same. We covered this in the EE uni curriculum back in the day, but I don't remember the solution derivation anymore.
Re: Infinite Grid of Resistors
#77I'm a bit mathematician and a bit electrical engineer. The electrical engineer suggests it's not measurable unless you apply current and also asks "when" after the current is applied referring to the distributed inductive and capacitive element and the speed of field propagation. The mathematician goes to a bar and has a stiff drink after hearing that.
Eventually you need to pullin a physicist too who will point out that at an appropriate distance quantum effects will dominate - because eventually at a far enough distance the number of electrons moving per second (ie current flow) will be either 0 or 1 at some nodes
I don't think you'll ever get 0/1. You get a difference in voltage that influences all electrons to move slightly more in one direction than another in electric current. They'll just drift very very slightly as a group, not measurable when you get far enough. But they're always all affected, rather than individually.
Re: Infinite Grid of Resistors
#78Earlier quoted context omitted.
Eventually you need to pullin a physicist too who will point out that at an appropriate distance quantum effects will dominate - because eventually at a far enough distance the number of electrons moving per second (ie current flow) will be either 0 or 1 at some nodes
I've not studied QED directly, so by all means correct me if I'm wrong, but it seems to me that we'd get a double-slit like scenario where it's as if a partial electron went through either path. We might want to say that surely a whole electron took one path and not the other but we couldn't say which and if we tried to instrument to and find out we'd affect the resistance. But that's fine because knowing which path…
Resistance is inherently dissipative, so there is no coherent path the electron can take. No quantum effects here, the electron is always interacting with the resistor lattice.
Re: Infinite Grid of Resistors
#79People think this is not relevant to real world problems but it actually is, albeit all the calculations aren't that relevant. Silicon substrate's resistance is basically an infinitely large grid of unut resistances at the distances relevant for a local point of an IC. Note that silicon substrate is often heavily doped (p-type) and all info you get from the fab is it's resistivity (often somewhere between 1 to 100 oh…
I'd argue the case you're describing is mathematically simpler precisely because it is continuous.
You’re practically describing the invention of Calculus.
Re: Infinite Grid of Resistors
#80Earlier quoted context omitted.
Gee, I hope nobody ever puts you in charge of a train!
Well they can still be a conductor, even if they're not a resistor. Actually they'd be a pretty good conductor. A super-conductor, if you will.
So wait, if they resist the statement that they're a resistor, are they a resistor or not? I think they're a semiconductor. Maybe they work at a railway junction. :D