Infinite Grid of Resistors
The diagram shows an infinite grid of resistors. Find the equivalent resistance between A and B

Question

Infinite Grid of Resistors
The diagram shows an infinite grid of resistors. Find the equivalent resistance between A and B

lastdaywork · Answer

Each "line segment" has a resistance R
|dw:1391750846362:dw|

lastdaywork · Answer

I know this is a popular puzzle; but I could never understand its solution.

The following is my attempt -
If we divide the circuit into four symmetric quadrants (like the Cartesian system)
- Quadrant I : current flows towards left or downwards
- Quadrant II : current flows towards left or upwards
- Quadrant III : current flows towards left or downwards
- Quadrant IV : current flows towards left of upwards
|dw:1391751637579:dw|

We can remove all the resistance lying in these quadrants as they are part of an open circuit. (The current which leaves the battery from one terminal never enters the other one; and vice-versa)

Hence, the circuit simplifies into the following (which can then be easily solved) -
|dw:1391751904517:dw|