Question

There is an infinite wire grid with square cells (Fig. 3.38). The resistance of each wire between neighbouring ***** connections is equal to R0. Find the resistance R of the whole grid between points A and B.

Instruction. Make use of principles of symmetry and superposition.

Answer 1

Suppose that the voltage V is applied between the points A and B then

V = IR = I0 R0 ,

where R is resistance of whole the grid, l0 the current through the grid and I ,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 point A and similarly the amount of current flowing through the wires, meeting at B is also I/4. Thus a current I/2 flows through the conductor AS, i.e.

I0 = I/2

Hence, R = R0/2