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The Algebra of an Infinite Grid of Resistors

The Algebra of an Infinite Grid of Resistors

9 comments

·June 15, 2025
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Koshkin

> we imagine injecting 1 amp of current into a single node

I have always had a problem with statements like this. Current is a (measurable) property of an edge, not a node (vertex). One can’t “inject” current into “a single node."

teraflop

By definition, an edge connects two nodes. So clearly, "inject current into a node" is just shorthand for "inject current along a (real or hypothetical) edge leading to a node". This is very common terminology in electronics.

Koshkin

Sure, but wouldn’t it be clearer if they talked about a specific edge? Because there can be several edges leading to a node. (Or, are they talking about, say, all of the “inbound” edges taken together?)

duped

Thats equivalent according to KCL - I think the equivalent model is "connect a current source I from ground to a node." Thats equivalent to saying "imagine the sum of all currents through edges was -I"

gus_massa

I imagine you are using an imaginary wire that is perpendicular to the grid and is not shown in the graphics. (Like a multimeter probe.)

ColinWright

See also: https://news.ycombinator.com/item?id=44279181

srean

Thanks for pointing towards this treasure trove of a website.

fh973

See also: https://xkcd.com/356/

glial

And the Google talk: https://youtu.be/zJOS0sV2a24?feature=shared&t=858