Abstract: The equivalent transformation method for star circuit and polygon circuit and the equivalent condition construction method are applied to the 2×4 order cobweb circuit with different resistance，in which the circuit is termed into a simplest equivalent one. The equivalent resistances at A1 —A4 are calculated，and the Multisim 12 multi- meter is used to get a simulative test of the former circuit and equivalent resistances between A1 —A4 terminals. The results show that the theoretical calculation and the simulative test are consistent. The equivalence circuit problem of the 3×4 order cobweb resistance network is analyzed. The 4end cobweb resistance network with different resistance can be simplified as a 4end star circuit with 1 or 2 resistances between terminals，which is convenient for calculation. A new method is given for circuit equivalence. According to the method，the equivalent transformation method between star circuit and polygon circuit and equivalent condition construction method can be used to solve the problem of the equivalent simplification between general star circuit and polygon circuit.

Key words: cobweb model, equivalent conversion, star circuit, polygon circuit