The two-point resistance of a resistor network: a new formulation and application to the cobweb network
نویسندگان
چکیده
We consider the problem of two-point resistance in a resistor network previously studied by one of us (Wu 2004 J. Phys. A: Math. Gen. 37 6653). By formulating the problem differently, we obtain a new expression for the two-point resistance between two arbitrary nodes which is simpler and can be easier to use in practice. We apply the new formulation to the cobweb resistor network to obtain the resistance between two nodes in the network. Particularly, our results prove a recently proposed conjecture on the resistance between the center node and a node on the network boundary. Our analysis also solves the spanning tree problem on the cobweb network.
منابع مشابه
Exact asymptotic expansion for the resistance between the center node and a node on the cobweb network boundary
The classic problem in electrical circuit theory, first studied by Kirchhoff in 1847, is the calculation of the resistance between two arbitrary nodes in a resistor network [1]. Besides its long-standing importance in electric circuit theory, the computation of resistances is also connected to a wide range of problems as diverse as random walks [2, 3], first-passage processes [4], lattice Green...
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