Abstract: We achieve the innovation in theory and method on the research of the electrical properties ( including

the branch current，voltage of any node，and equivalent resistance) of an arbitrary 2×n Fan resistor network

by the Recursion-Transform ( RT) method. In this paper，the matrix equation model and the boundary condition equation

model are established by using the branch current as the variable in terms of applying Kirchhoff’s law. We

study the general solution and special solution of the matrix equation by the matrix transform，thus the branch currents

　　of the 2×n Fan network are obtained，and derived the voltage formula of arbitrary node，at the same time，the

　　equivalent resistance formula between any two nodes is obtained as well. The special situation of the conclusion is

　　analyzed and discussed.

Key words: resistor network, recursion-transform method, matrix equation, electric properties