There is an infinite wire grid with square cells (Fig). The resistance of each wire between neighbouring joint connections is equal to `R_(0)` . Find the resistance `R` of the whole grid between points `A` and `B`.
Instruction. Make use of principles of symmetry and superposition.

Explanation

Suppose that the voltage `V` is applied between the points `A` and `B` then
`V = IR = I_(0) R_(0)`
where `R` is resistance of whole the grid `I`, the current through the grid and `I_(0)` the current through the segment `AB`. Now from symmetry , `I//4` is the part of the current, flowing through all the four wire segments, meeting at the poin `A` and similarly the amount of current flowing through the wires, meeting at `B` is also `I//4`. Thus a current `1//2` flows through the conductor `AB`, ie.
`I_(0) = (1)/(2)`
Hence, `R = (R_(0))/(2)`