Infinite Resistor Grid Puzzle

[reetupareek]

CAN yoy help me find eq. resistance across a side of a hexagon of an infinite mesh of hexagons

[turbflat]

For the one ohm infinite grid, R across diagonal is 2/pi.

Solution involves fairly difficult math. But it is very reminiscent of Buffon's needle, isn't it?

[jaimelannister]

The 0.25A current which flows in is taken to be different than the 0.25A current flowing out. Why is that so?
Why isn't the 0.25A entering taken as the 0.25 A, leaving.
While one may argue on the basis of the principle of superposition, how come the net current is then not taken to be 2A, superimposing the 1A entering and the 1A leaving?

[manchurianable]

how wud we solve if we need to take the equivalent res across A and C

[Aadhyacedt]

Excellent Solution. Between A&C the equivalent resistance is 2/3, is this correct?

[colinrebello]

Imagine there was a single current source say "i" where one end(current enters) was connected to one node say A and the other (current exits) was connected to node B which is adjacent to A. Because B is closest to A one would expect most of the current to flow direct from A to B ie the path of least resistance. So current entering Node A would divide into 4 unequal parts and NOT 4 equal parts. Similarly current exiting B is not 1/4 i though each branch but actually 4 unequal currents. The flaw is assuming the current divides equally into 4 parts. It cannot because we have a single current source connected from A to B which is equivalent to your having 2 current sources placed in exactly the same way and because A is closest B Route-wise the 4 divisions of current cannot be equal

[saicharan]

Please Clear me this doubt Academia...here you have told that the current through the resistor across A, B terminals is one half of the total here the total current is 2A But not 1A when both Conditions were superimposed.... hence, the current through resistance between A, B is not half of 2A(total current)....please give me reply fast...

[knvcsg]

But, really I didn't know about this superposition principle.