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Infinite Grid of Resistors

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Re: Infinite Grid of Resistors

#91

Post by jfengel »

kqr wrote: post #62
jfengel wrote: post #24

Earlier quoted context omitted.

It becomes a black hole, but it doesn't necessarily collapse, at least not at first. A supermassive black hole has very low density and a very gentle gravitational gradient. All of the mass does end up in the singularity, in finite time (at least for any finite subset of the black hole), but it doesn't automatically become super dense just because it's a black hole. It can remain quite ordinary for a very long time.

Wait, can you take this a little slower? I was not aware black holes could have sensible density.

In the formula for a Schwarzchild black hole, the mass is proportional to the radius. Since volume goes up with the cube of the radius, the density drops quickly.

The kind of black hole that forms from a collapsing star is super dense. But a supermassive black hole forms differently, as a denser region of gas and stars during galaxy formation. The density can be lower than that of water. You could be inside it without even realizing anything is odd.

There is no known way to form black holes bigger than that. We had been discussing a pure thought exercise. Though it is possible that the universe as a whole has enough density to be a black hole. (Signs point to no, but it's an open question.)

Re: Infinite Grid of Resistors

#93

Post by bilsbie »

mort96 wrote: post #89
bilsbie wrote: post #88

Offshoot question. Why don’t we make resistors by making wire so thin that only a certain current can fit through? Wouldn’t that be more efficient than converting current to heat?

You're describing thin film resistors, and they exist. They also just convert current to heat though. Some amount of current moving through a material with some amount of resistance always produces a fixed amount of current in accordance with Ohm's law. You can't really get away from that.

Thanks. So Is there a physical reason resistors have to make heat? Is it theoretically possible to find a material that limits current but produces very little heat?

I guess the explanations always confuse me. Let’s say a short circuit with no resistors has a certain amount of power. Then we add a resistor and the power in the circuit goes down. The resistor isn’t turning the difference in power into heat, right.

Re: Infinite Grid of Resistors

#94

Post by Koshkin »

neepi wrote: post #3

I'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.

> apply current

Going on something of a tangent: in engineering, it seems unusual to talk about “applying current,” it’s usually voltage (say, across a resistor) or some sort of an “electromotive force.”

Re: Infinite Grid of Resistors

#95

Post by analog31 »

bilsbie wrote: post #93
mort96 wrote: post #89

Earlier quoted context omitted.

You're describing thin film resistors, and they exist. They also just convert current to heat though. Some amount of current moving through a material with some amount of resistance always produces a fixed amount of current in accordance with Ohm's law. You can't really get away from that.

Thanks. So Is there a physical reason resistors have to make heat? Is it theoretically possible to find a material that limits current but produces very little heat? I guess the explanations always confuse me. Let’s say a short circuit with no resistors has a certain amount of power. Then we add a resistor and the power in the circuit goes down. The resistor isn’t turning the difference in power into heat, right.

It's useful to look at the units of measure. Voltage is energy per unit charge. As the charge carriers go across the resistors, their energy changes, and that energy has to go somewhere. It's not always lost as heat in all devices. In an LED, some of the energy is "lost" as light. But still, the sum total of heat and light power generated by an LED is equal to the product of the current and the forward voltage.

Another useful heuristic is that heat is generated from what's left after all of of the other ways of converting energy are used up, such as light, chemical potential, and so forth. It's energy's last resort. The usefulness of a resistor lies in its simple voltage-current relationship, which is equivalent to saying that the only thing it generates is heat.

Re: Infinite Grid of Resistors

#96

Post by ChoGGi »

bgnn wrote: post #70

People 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…

My vague understanding of photolithography is that it's hard, though I didn't realise it's bad enough to evoke an egyptian goddess.

I'll see myself out.

Re: Infinite Grid of Resistors

#97

Post by gugagore »

eternauta3k wrote: post #73
bgnn wrote: post #70

People 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.

Right, why is it a 4-connected grid instead of 8-connected, or any other topology, like a hex grid.

Re: Infinite Grid of Resistors

#98

Post by gugagore »

Koshkin wrote: post #94
neepi wrote: post #3

I'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.

> apply current Going on something of a tangent: in engineering, it seems unusual to talk about “applying current,” it’s usually voltage (say, across a resistor) or some sort of an “electromotive force.”

In idealizations, there are both voltage sources and current do m sources.

Re: Infinite Grid of Resistors

#99

Post by Koshkin »

nofunsir wrote: post #82
neepi wrote: post #3

I'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.

Does Schrodinger's cat study Fourier transforms?

But you already know that it does and it doesn’t at the same time.

Re: Infinite Grid of Resistors

#100

Post by grues-dinner »

bilsbie wrote: post #88

Offshoot question. Why don’t we make resistors by making wire so thin that only a certain current can fit through? Wouldn’t that be more efficient than converting current to heat?

Resistance is V/I. You literally cannot have current flowing in a resistor without a voltage across it (either the voltage causes the current to flow, or the resistor in the path of a flowing current has a voltage appear across it).

A voltage drop with a flowing current is power (P=VI).

There is literally nothing you can do to avoid resistors dissipating that power as heat, it's just what they are. If they didn't do it, they wouldn't be resistors.

What you can do is use larger resistances which need less current to see the same voltage (e.g. change a pull up from 10k to 100k or higher, but that's more sensitive to noise), or smaller resistances that drop less power from a given current (e.g. a miiliohm-range current shunt, and then you need a more sensitive input circuit) or find another way to do what you want (e.g. a switched-mode power supply is far more efficient than a voltage divider at stepping down voltage). This is usually much more complex and often requires fiddly active control, but is worth it in power-constrained applications, and with modern integrated technology, there's often a chip that does what you need "magically" for not much money.

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