Dave solves the famous Infinite Resistor Puzzle, the old fashioned way...
Пікірлер: 125
@Falney8 жыл бұрын
"I am not a math man" Says the man with a calculator fascination.
@JanicekTrnecka9 жыл бұрын
My favorite programming language ? Solder !
@iamdarkyoshi9 жыл бұрын
This needs to be a poster.
@johnclawed6 жыл бұрын
In the early 80's there was an article about an artist who did 3D sculptures made of components. They were real circuits. One of them detected someone passing by and made strange noises that varied with their position and speed.
@t33th4n8 жыл бұрын
Dave could not resist to do it :)
@MarkMcDaniel4 жыл бұрын
And, we haven't the capacitance to resist the clickbait.
@carmelpule69549 жыл бұрын
Congratulations for being so practical. This reminds me of the historic story when Edison was manufacturing light bulbs and for some reason he wanted to calculate the volume of the complex shape of a glass light bulb. Apparantly the mathematicians came up with some approximations but were not so sure about the accuracy of their result. Then Edison who was a very practical man came along and filled one glass bulb with water and he knew the volume of the water and also floated or immersed the glass bulb in water thus displacing the water according to Archemedes principle and again he found the outside volume of the bulb , hence he could find the volume of the glass used in the bulb. Mathematiics are very useful but being practical sometimes gets quicker results.
@imdeadserious61028 жыл бұрын
practical mathematics
@airgliderz8 жыл бұрын
Edison was on a camping trip in 1887 near Rawlings Wyoming, Battle Lake when he dropped the tip of his bamboo fishing pole in the cap finite noticing the glowing car nixed fishing pole tip.... I've driven by the spit many times it is marked with a historical marker. Story is a bit iffy but makes for a good tail.. That's why I go fishing, to be inspired to invent the next big thing, my story to my wife and I'm sticking to it...! 😊
@MarkMcDaniel4 жыл бұрын
The definition of applied mathematics.
@flutestarz13 жыл бұрын
Effective resistance across the single resistor is 2R/M. M is the number of resistors (R) connecting to each junction. For your square mesh M=4. If the 2D mesh was actually a 3D cube, then M=6
@k6eep5939 жыл бұрын
I made a 3D version using 1K resistors. The resistance across diagonal corners is 1K.
@EscapeMCP8 жыл бұрын
+K6EEP Diagonal on the face (i.e. min path=2), or across the cube (min path=3)??
@k6eep5938 жыл бұрын
+EscapeMCP This was a huge cube. 20 resistors across at least. So a facing side was a 20x20 array. The idea was to guess resistance from corner to the opposite corner across the cube. (min path=3 in your example) Some one had donated a thousands of preformed 1K resistors I kept growing it until my soldering hand got tired.
@absurdengineering4 жыл бұрын
The infinite resistor grids (in 2D, 3D, 4D, …) are awesome to demonstrate how physical structures give rise to sums of infinite series. Conversely, as a rule of thumb, if you have a series and can think of a resistor network where resistance between some two nodes is a sum of the series, then the series converges. This can actually be mathematically proven, no less.
@yuppiehi8 жыл бұрын
I'm going to build this at this year's Mini Maker Faire in Honolulu. I already bought 500 10K 1/4-watt metal film 1-percent resistors. It'll be interesting to see how many people will actually stop by and ask what the heck I'm doing. Have soldering iron, will travel...
@springgraphicstx7 жыл бұрын
I know this video is old, but I just recently found your channel. Amazing that the result is 2/pi. I like your practical approach. Would be interesting to see how the result changes if you gradually chop it down to smaller networks: 12x12, then 10x10, etc. Or if I get around to build one, maybe take measurements as it is being put together.
@absurdengineering4 жыл бұрын
David Scott Any finitely sized network has resistances that are a truncated sum of an infinite series. It’s possible to prove that by induction. The convergence rates depend, among other things, on how many dimensions does the resistor grid have. Try going from a 2D grid to a 3D grid with roughly same number of resistors. Then a 4D grid. Then try going from a hyper cube (square, cube, …) to hyper sphere shape (circle, sphere, …). You’ll get quite a tour of various forms of infinite series, and can then ponder questions such as “does the circular grid converge similarly like a square grid would”. While doing so you’ll rediscover some cool theorems in calculus. All from a “simple” resistor network. I urge anyone who’s so inclined to try it out. Sometimes having a physical object to think about makes the math easier to understand. That’s certainly the case for me. When I took a mechanical vibrations course, in my mind I modeled everything with electrical circuits :)
@EEVblog15 жыл бұрын
It made it onto the Hack-A-Day website, so a huge influx of new viewers and subscribers!
@codeprose15 жыл бұрын
Seeing you love measuring stuff, how about applying a voltage (say 10.000V) to the central resistor, and then measuring the voltage at various locations around the grid.
@grlg214 жыл бұрын
Hi Dave, This is fantastic (along with all your other videos). I like your comment about practicality and actually doing something as opposed to endless calculations. Cheers, Greg.
@holycatsbatman14 жыл бұрын
Beautiful, elegant, scientific. This is how an engineer solves math puzzles.
@cberge8 Жыл бұрын
It would be really interesting to see reading as the grib was being built to show the convergence of the solution as every new row/column is added
@ryanoconnor79579 жыл бұрын
This is definitely taking practicality to its limits.
@spodule600012 жыл бұрын
My own thought too. A geometric toroid. Intuitively i would think it would - then you could shrink that down to just a few resistors and solve it theoretically too.
@FisicacomRenatoBrito11 жыл бұрын
Dave I am a brazilian physics teacher. In Brazil most of people do not speak English. Would you mind if I use just a single of this video, around 3 minutes of it, translate your voice comments into portuguese to present it to my pupils ? I used my own voice in portuguese. Do you authorize me to use a peace of this video with this little changes ? In the end of the video, I gave all the credits to you, to your excelente Blog, I showed the URL of you blog here in KZbin.
@davidhoekje78427 жыл бұрын
As people have asked about three dimensional versions of this it occurs to me that if the lead lengths were constant, the resistance value between any two points might well be a constant percentage of the value of one resister. I initially expected the diagonal value to be 1/2 of the square root of 2 or .7, which it is nearly is. If lead lengths are all the same, then we can probably model this as a solid block of conductive material.
@hansolduron15 жыл бұрын
Nice work, plus more than 50 "you know"s in this video :)
@66127702 жыл бұрын
Array For Dave!!
@laidman200711 ай бұрын
This was a great demo.
@WillstDuNichtWissen8 жыл бұрын
Somehow I want to make a giant version of this with 0201 resistors and then put it under a glass table.
@mattlambert31189 жыл бұрын
I'm really glad I saw this.Brilliant. I also agree with crapcbm, a circle would be great. I'd do it if I had a big box o" resistors laying around. Cheers
@Desmaad13 жыл бұрын
Behold: the Jones Resistive Gridiron!
@chaosopher238 жыл бұрын
That Infinite Resistor Network you built is almost close enough to keep Rhode Island mosquitoes out. And... 420 of them to make up a problem that could keep a stoned engineer busy for hours!
@Adotbook12 жыл бұрын
Wouldn't it be easier to use an electrolyte solution for testing? Maybe salt water.
@neonharp8 жыл бұрын
That reminds me of going to school . The teacher drew up a 3 D cube of 100 ohm resistors , and said that anyone in the class who could solve it , would get an " A " grade . I didn't build the thing , I just did the math ! and got an " A " grade in the class ! anyway , Cheers , take care , and have a good day !...73 Ray aka KE8CWT & PG1920311
@filthylucreonyoutube2 жыл бұрын
And now it's time for Big Clive's Resistor Roulette...
@BTom168 жыл бұрын
I call this, "Dave's Tholian Web Episode."
@friedmule54035 жыл бұрын
It is irresistible :-)
@Afrotechmods15 жыл бұрын
AHahahha!
@Aadhyacedt9 жыл бұрын
Could you please describe how to derive equivalent resistance for diagonal case?
@TunioMir13 жыл бұрын
Great Video!!
@azyfloof12 жыл бұрын
I want to see this built with a million 0402 SMT packages :P Pick and Place workout much? :D
@davidhoekje78427 жыл бұрын
I'm always curious what causes people to give a thumbs down to a video like this. I suppose the end of the bell curve needs data, and perhaps it's best not looked at too closely.
@AnthonyShuker8 жыл бұрын
420 resistors? now we know how you came up with the idea
@davidhoekje78427 жыл бұрын
Yea, I was scratching my head about that one too. lol
@gman76utube11 жыл бұрын
Use LTspice to get answer quickly.
@TinLethax2 жыл бұрын
Hello from the future xD
@tomsgypsy15 жыл бұрын
Really good work mate. nice to see some fellow aussies getting themselves out there. love hearing measurements in millimeters and grams saves having to try and guess the values the yanks are talking about all the time. What company are you working at currently?
@jan.tichavsky15 жыл бұрын
I prefer less math and more practical things too :) I was thinking if anyone build it and how large and then you showed it, pretty nice :) The measurement is close enough, you don't need like 5 digits for most things anyway
@absurdengineering4 жыл бұрын
The math is very nifty though, and it’s not much more than good high school level math. It’s really cool how far simple math can go in modeling fairly complex physically realizable structures.
@hla27b14 жыл бұрын
365 resistors..... I'd rather do the math By the way I am reading your "PCB Design Tutorial" which is simply brilliant put it on the tube mate it will be useful to a lot of people on the tube
@thegrandmuftiofwakanda9 жыл бұрын
The pubs weren't open at the time right?
@Tutoelectro115 жыл бұрын
Haha, nice work!
@ArumesYT5 жыл бұрын
How sturdy is that grid? If you want to keep it for decoration, maybe you can also use it to hang other components onto to add a bit of variation.
@MrYamashici10 жыл бұрын
great vid, so funny xD
@bertblankenstein3738 Жыл бұрын
Question is asked, the person opens up a briefcase and pulls out the resistor network and a multimeter...
@RobertGallop15 жыл бұрын
Hehehehe, I like this one, nice puzzle and excellent answer to it :)
@FrozenHaxor12 жыл бұрын
Now send it to Photonicinduction and tell him to make some HV barbecue cooking with it! Just imagine cooking a steak on this! :D
@tutman9612 жыл бұрын
Infinite capacitor network next please!
@precycler5 жыл бұрын
How about if the outer most resistors on the perimeter were 5K to 'terminate' the grid since that's what the expected resistance would be.
@LaraSchilling14 жыл бұрын
My friend and I are going to totally make an infinite resistor grid out of 0Ω resistors for the lulz. It'll make a cool necklace and stump people :) (EEV isn't supposed to be -VEE backwards, is it? :P)
@jeremyo14578 жыл бұрын
ok dave, 420 resistors... we get it you vape bro :P
@imdeadserious61028 жыл бұрын
the mix of references in this burns...
@sk88-p7n14 жыл бұрын
Thanks much :)
@frankieboyo19698 жыл бұрын
What would it be in 3 dimensions? 4?
@bzduso5 жыл бұрын
@@pahom2 if "R" is the resistance on each edge, then the resistance between nearest neighbor vertices in a "D"-dimensional hypercube lattice is $R/D$.
@alm93736 жыл бұрын
I watched the #1000th EEVBlog Video, then the KZbin suggest me this video...coincidence?
@GRAHAMAUS13 жыл бұрын
@chandin69 pi crops up in all sorts of apparently unlikely situations. It's really quite remarkable. Read "The Life Of Pi", it's a fascinating read.
@rolfts57628 жыл бұрын
Haha :D ..thank you Dave! (..just watching this video now, and just 'had' to stop at plbckPos 3m20sec and coment it. Starting to watch again the rest.. )
@rolfts57628 жыл бұрын
+RolfT S --> And..Yes, frame it :) ..its electronics-art
@DirtbagD15 жыл бұрын
Good video. What about making it in to a cube?
@therugburnz8 жыл бұрын
Sorry bout the rant. I was on Facebook typing to my friends just a bit earlier and we were dissing guitarists. (I am one) We let it get a bit out of hand and I had to leak it instead of shunting it. Peace be with you my siblings in internet fun. the rugburnz 😰
@wolfgangerichwolfgang62759 жыл бұрын
Cool! 420 Resistors :-)
@pierQRzt1802 жыл бұрын
please revisit the topic after so many years of youtube!
@npopson14 жыл бұрын
He said "naught", as in zero.
@miaudottk90805 жыл бұрын
Forget math! Build bigger resistor array!
@DigGil311 жыл бұрын
I wonder if this is the kind of problem/solution one would find while measuring the resistance on 2 points in a flat conductor. I've thought the closest thing to an infinite grid in real world would be a grid along the surface of a sphere. What do you think?
@rich10514147 жыл бұрын
Would the ACTUAL formula for calculating the opposite node of a grid this be: n / (π * R * (n - 1)) Where n = Number of dimensions, and R = resistance of resistors?
@meiskam13 жыл бұрын
@GRAHAMAUS i remember reading "The Life Of Pi" about 5 years ago, and it was about some dude lost at sea .. nothing to do with math
@jasperheijer74525 жыл бұрын
what about a spherical infinite resistor dave?
@rolobotoman8 жыл бұрын
now i want the maths!
@pratherat11 жыл бұрын
Why not connect the ends of each row and column, such that electrically there would be no center. Each resistor would be attached to the same number of resistors in every direction, kind of like a scrolling game. Would this work?
@immortalsofar53148 жыл бұрын
For my next trick I present - Schrodinger's cat! Urgh!
@apprenticemart211 жыл бұрын
What would happen if you made a 3d shape like a cube?
@novafawks5 жыл бұрын
I'm new to EE so I'm confused. How does pi come in to play with 2 of them?
@absurdengineering4 жыл бұрын
Nova Fawks PI usually a comes into play in discrete systems when some quantity is effectively a sum of an infinite series (or a nested fraction). PI appears in sums or limits of quite a few series.
@NickyNiclas12 жыл бұрын
because shorted out caps will be so much fun? ;)
@Devalis10 жыл бұрын
could you build a cube out of six of those and get the infinite properties?
@orbik_fin10 жыл бұрын
I think the topological equivalent of the infinite grid would be a torus rather than a cube. Anyway, when you measure the resistance, that topology changes again so that there are also infinite zero-resistance "connections" between points at equal distances in the equivalent infinite grid.
@slinkytreekreeper9 жыл бұрын
An ifinite resistor torus with Rodin coil alignment would surely wet daves practical appetite and would look stunning
@unlost1178 жыл бұрын
+orbik Nicely said. If a grid of perfect zero tolerance resistors were overlayed on a toroid, would the measurement on any resistor or diagonal measurement (as dave did on 2D sheet he made) remain constant anywhere measured on the toroid? I expect it does. But can we apply a constant knowing how many resistors are in the grid and still get daves formula ?
@friedmule54036 жыл бұрын
unlost117 I think that depending on the size, it will show an not perfect value, but it will show the same error value no matter where you measure. :-)
@chaos.corner6 жыл бұрын
It doesn't work. If you think of a torus of only a small number of resistors (say 9 or perhaps less), it quickly becomes clear you can't make resistors apply multiple times in a way that makes it look like an infinite grid.
@TheOysterjam11 жыл бұрын
i dont think thats the same. you would simply measure the resistance between the two probes, without taking parallel paths into account. just a guess tho
@imaginacion200911 жыл бұрын
What about a cap's grid measures?? in a cubic form, I mean 6 sides
@chandin6914 жыл бұрын
how did a pi come into this? i just cant picture where the number came from
@absurdengineering4 жыл бұрын
Write out formulas for progressively larger networks, and you’ll see that the resistance is a sum of an infinite series. And the infinite series happens to be the one whose sum is some constant times the reciprocal of pi. Ou arises in many infinite series sums with nested fractions. Conversely, you could ask how to calculate pi using nothing but a 4-function calculator. This resistor network is a physical model for that :)
@DreitTheDarkDragon5 жыл бұрын
Would be interesting to make cylinder or globe :)
@mathman84944 жыл бұрын
Actually, you can build an icosahedron or any other platonic solid as an approximation of a globe. Such networks have an interesting duality property, see kzbin.info/www/bejne/hpespIqqjbyBjpY. This property was found by my student Martina Furrer and was later generalized in a joint paper with Norbert Hungerbühler and Simon Jantschgi: arxiv.org/pdf/1805.01380.pdf And one can of course also verify the duality theorem experimentally, as done in hsr.othello.ch/duality.pdf (in german, but see page 7).
@VoidHalo6 жыл бұрын
Good. Now let's analyze the whole circuit if you put 5v on one corner and ground the other. Every single junction for current and voltage drop.
@absurdengineering4 жыл бұрын
Nothing\ The analysis of any particular size of it is instructive, but it gets even more instructive when you see the patterns that are a series sum, and then you can get an analytic answer for an infinite grid without building one - and you can inductively prove that the answer you get indeed represents the result for an infinite grid.
@EddieRodJr8 жыл бұрын
Never imagined he was a pothead! lol
@riscy009 жыл бұрын
I wondered anyone done math, can they post solution and derivation?
@hansolduron13 жыл бұрын
you know, I counted more than 30 "you know"s half way to the video :)
@TheOysterjam11 жыл бұрын
that would only be a 40 cm by 40 cm square, neglecting connecting traces. thats a pretty big pcb, but lets do a 10x10 of those squares and get 100 million lol
@PauloConstantino1677 жыл бұрын
I'm your host, Dave fucking Jones.
@RandyLott13 жыл бұрын
What about a cube? :)
@sk88-p7n14 жыл бұрын
What did he exactly say after .5 an ohm? @1:15 did he say "not .5 *R "
@jtoddowen3 жыл бұрын
"naught" is another work for zero. wikipedia.org/wiki/0
@GoldSrc_8 жыл бұрын
Interesting. Also 51,000 view, noice.
@laernulienlaernulienlaernu89534 жыл бұрын
You can tell you're not s mathematician. If you were you'd have made a 3D representation of a 4 dimensional resistor network!
@TheAmmoniacal10 жыл бұрын
Wouldn't you expect the tolerance to increase over the total number of resistors? If the tolerance is 1% per resistor you are using, it would be 5% if using 5 resistors?
@datagawa10 жыл бұрын
Not if the tolerance is normally distributed. If its skewed or rounded, you would be correct.
@n03110 жыл бұрын
Not necessarily, actual tolerance calculations are more complicated, but just look it this way, if you have 1% 1ohm resistors, you expect them to be within 0.99 and 1.01ohm. If you use five of them in series, your expected result would be within 4.95 and 5.05ohm, which is still 5ohm 1% tolerance
@imdeadserious61028 жыл бұрын
+Daniel T sadly most companies have a tendency to lean to being high or low still writing spec
@helloriker9 жыл бұрын
Interesting... I wonder what would happen if instead of building it as a 2 dimensional grid if you made it a 3 dimensional cube. Could be interesting.
@davidhoekje78427 жыл бұрын
You'd want to get all Buckminster Fuller and build a geodesic form.
@m000nd5 ай бұрын
i created a series of videos on that topic: kzbin.info/aero/PLoGRr8ff1uXESrWh6z0BNTYpc4Y-hlBOm starting with EE basics. at the end also some numeric simulation with numpy.
@jaro698515 жыл бұрын
hah, beautiful
@ElectronicsPubVideos12 жыл бұрын
Do the math please :D
@Aleksandr_Shevchenko3 жыл бұрын
#420
@_general_error Жыл бұрын
But your expeimental method soes not give you the theory behind the mechanics of the problem... Though I like your arts skills!
@therugburnz8 жыл бұрын
fun fun fun. However, approach infinity at your peril ! infinity is not a number is it aka + fun - fun + fun - fun... is it. + ( fund fun+ fun ) or -(-fun +fun -fun). ! ! ! ! IDK 1fun+2fun+3fun+4fun... = -1/12 fun = LESS THAN NO FUN @ ALL. math is easy. engineering is hard! AKA @ the end of the day something needs to get built. AKA when the arrogant lead guitarist's $13000 hand soldered by children paid $7.89 per day tag board tube amp doesn't work it is YOUR FAULT. It is NOT at all the sales rep's that told him UNDERATED output transformers and 25watt super Distortionated double doped SELLestions are conservatively rated! "Make it work nerd!" is his polite response. OH SH!T I IS ON A RANT I'll stop sorry.