Reversal of bounds in some dual-bound resistance calculations

Estimating the resistance of simple shapes provides an introduction to dual-bound variational methods. Imposition of equipotentials or current flow lines gives a physical understanding of the bounds. In developing a class of illustrative examples, some were found in which the bounds were reversed. This is due to approximation which in some cases is insufficiently precise; the range of validity has been explored. In two-dimensional current flow, new formulas for the bounds have been derived which do not reverse