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An infinite number of identical resistors are connected in a square grid as shown. What is the effective resistance between two neighboring junctions (i.e. between A and B). R A R B R R R 1 If current +I0 is injected at point A and allowed to flow to infinity, each of the resistors connected directly to point A will, by symmetry, carry I0 /4 directed away from A. Similarly, if current −I0 is injected at point B, each resistor connected to B will carry current I0 /4 directed toward B. Superposing these two solutions yields a solution where current is injected at A and extracted at B. The net current flowing along the resistor connecting them is I0 /2 and so the voltage drop between A and B is V = I0 R/2. The effective resistance of the network is therefore V /I0 = R/2. 2