In view of the application importance of resistance network in modern science and technology, this paper presents the basic structure of a three terminals ladder shaped resistance network, for which, to study in- depth the equivalent resistance, carry out network analysis by applying virtual current method and construct a model of two elements three orders differential equation. Based on different marginal conditions, two general adaptive rules for the three-terminal ladder shaped inlet resistance, as well as two ultimate rules for the equiva- lent resistance of three-terminal infinite ladder shaped were given.
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