my rusty A-level knowledge tells me the same thing, but its probably one of those fantastic "it doesnt quite work like that" moments

No, if you have a simple circuit where the electricity has the choice of passing through two different resistors, it will 'balance out' across the two. More current will flow through the lowest resistance, but some will flow through the higher resistance.

That's one of those annoying over-simplifications which messes with people's heads and should never be repeated, along with other crapola such as "nature abhors a vacuum", "Pi equals 22/7" or "Driving in a higher gear increases your traction".

As Ohm observed, the current flowing through many conductors is proportional to the voltage across it. The constant of proportionality is known as the resistance, and is measured in ohms. Thus, if you have two paths and one has twice the resistance, then 2/3 of the total currant flows through the path of least resistance and 1/3 through the higher. The effective resistance is 2/3 that of the better conductor alone.

Conductors that obey Ohm's law are knows as "Ohmic impedances" or "ideal resistors". Such things only exist in maths problems, along with infinite parallel planes and frictionless surfaces.

All you need for this problem is Ohm's law and Kirchhoff's junction rule:

The current flowing through each resistor is equal to the voltage across it divided by 1 Ohm.
The sum of currents flowing into each node is equal to the sum of currents flowing out of that node.

The total current through any resister is equal to the sum of the currents through all possible paths. Here there are an infinite number of paths, and it's not easy to find a recurring pattern or symmetry to significantly simplify the equations. Usually with these types of problems, a little lateral thinking reveals an elegant solution which you can do in your head. I just can't see it.

Annoyingly, if it was a uniformly conductive infinite sheet then I think it would be easier.

Me too, although I wouldn't be surprised if I'd missed something. I do like these sorts of things, though.

So, is it 3 then?

Bah! Silly forum not liking funny chars!

No.

The largest portion of the current will go down the paths of 3 ohms, a bit less will go down the paths of 4 ohms, a bit less still down the paths of 5 ohms, ..., the smallest amount of current will go down the paths of infinite ohms (I guess we could say this is defined as 0A, but again I'm not completely sure).

No. It's very much less. I think it's probably 1 ohm.

There is a path of 3 ohms, but it's in parallel with many other paths. Current flows through every path. Consider this massively simplified version:



The resistance between A and D is 1.5 Ohms because there are two paths of 3 ohms each. As more paths are added, the resistance drops. The paths further away reduce it by a lesser amount, but there are more such paths...

You can get an A Level with thinking like that these days??? (8-p)

46/(3*pi) - 4 or 0.881 Ohms

From:

Dammmit I was just typing that out myself, you beat me to it.

Google is your friend.

Mathematicians know how to work it out. Engineers know how to look it up.

Which is why engineers are faster.

Nill point because you didn't show your workings

And of course you've all been run over on a pedestrian crossing!

Now I've had breakfast when can I have lunch?

Let me fix that for you.

Mark