Effective resistances of two dimensional resistor networks

Abstract

We investigate the behavior of two dimensional resistor networks, with finite sizes and different kinds (rectangular, hexagonal, and triangular) of lattice geometry. We construct the network by having a network-element repeat itself $L_x$ times in $x$-direction and $L_y$ times in the $y$-direction. We study the relationship between the effective resistance ($R_{\mathrm{eff}}$) of the network on dimensions $L_x$ and $L_y$. The behavior is simple and intuitive for a network with rectangular geometry, however, it becomes non-trivial for other geometries which are solved numerically. We find that $R_{\mathrm{eff}}$ depends on the ratio $L_x/L_y$ in all the three studied networks. We also check the consistency of our numerical results experimentally for small network sizes.

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References in corpus (11)

• The electronic properties of graphene
• Theory of resistor networks: The two-point resistance
• Application of the lattice Green's function for calculating the resistance of an infinite networks of resistors
• Resistivity of Mixed-Phase Manganites
• Armchair graphene nanoribbons: Electronic structure and electric field modulation
• Microwave imaging of mesoscopic percolating network in a manganite thin film
• The two-point resistance of a resistor network: A new formulation and application to the cobweb network
• Recursion-transform method on computing the complex resistor network with three arbitrary boundaries
• Current Flow in Random Resistor Networks: The Role of Percolation in Weak and Strong Disorder
• On equivalent resistance of electrical circuits
• Crossover behavior of conductivity in a discontinuous percolation model

Cited by in corpus (1)

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