Recursion-transform method and potential formulae of the m × n cobweb and fan networks* *Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20161278).

Abstract

In this paper, we made a new breakthrough, which proposes a new Recursion–Transform (RT) method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.