Week 5: Resistance 193
Advanced Problem 7.
Suppose you have an infinite network of identical resistorsR, arranged in a square 2d lattice. Find
the total resistance between two adjacent nodes as shown. Note well that there is a trick to this one
- your hint is to think aboutcurrentflowing into and out of this network through probes placed at
the junctions and superposition and symmetry. Once you get the square lattice, think about infinite
triangular lattices or infinite cubic lattices in 3d.