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<jats:title>Abstract</jats:title> <jats:p>In this paper, we made a new breakthrough, which proposes a new Recursion–Transform (<jats:italic>RT</jats:italic>) 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 <jats:inline-formula> <jats:tex-math><?CDATA $m\times n$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>m</mml:mi> <mml:mo>×</mml:mo> <mml:mi>n</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_26_9_090503_ieqn3.gif" xlink:type="simple" /> </jats:inline-formula> cobweb and fan networks by the <jats:italic>RT</jats:italic> 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.</jats:p>