Related papers: On equivalent resistance of electrical circuits
This paper proposes a new analysis of graph using the concept of electric potential, and also proposes a graph simplification method based on this analysis. Suppose that each node in the weighted-graph has its respective potential value.…
The capacitance matrix relates potentials and charges on a system of conductors. We review and rigorously generalize its properties, block-diagonal structure and inequalities, deduced from the geometry of system of conductors and analytic…
Consider a unit-resistive plate in the shape of a regular polygon with 2n sides, in which even-numbered sides are wired to electrodes and odd-numbered sides are insulated. The response matrix, or Dirichlet-to-Neumann map, allows one to…
Finding the equivalent resistance of an infinite ladder circuit is a classical problem in physics. We expand this well-known challenge to new classes of network topologies, in which the unit cells are much more entangled together. The exact…
In solving the Schr\"odinger equation to simulate a nanoscale circuit, we note that the mean free path for electrons in some metals is as large as 48 nm. Thus, the wavefunction may propagate coherently through wires corresponding to the…
An analytic approach is presented to developing exact expressions for the two-point resistance between arbitrary nodes on certain non-regular resistor networks. This generalises previous approaches, which only deliver results for networks…
This tutorial article presents a "bottom-up" view of electrical resistance starting from something really small, like a molecule, and then discussing the issues that arises as we move to bigger conductors. Remarkably, no serious quantum…
For a connected graph $G$, its resistance distance matrix is denoted by $R(G)$. A graph is called resistance regular if all the row (or column) sums of $R(G)$ are equal. We provide a necessary and sufficient condition for a simple connected…
This paper presents a comprehensive approach to generating and utilizing accurate equivalent circuits for structures commonly found in the particle accelerator domain. After a discussion of equivalent circuits in general, a systematic…
A general equivalent circuit for two-port lossy non-symmetric reciprocal networks is proposed. The equivalent circuit is based on the eigenstate decomposition. It has three complex parameters that are obtained from the eigenvalues and…
We investigate the behavior of electric potentials on distance-regular graphs, and extend some results of a prior paper. Our main result, Theorem 4, shows(together with Corollary 3) that if distance is measured by the electric resistance…
In this paper we give a survey of methods used to calculate values of resistance distance (also known as effective resistance) in graphs. Resistance distance has played a prominent role not only in circuit theory and chemistry, but also in…
An explicit formula for the resistance between two nodes in a network with a non-symmetric Laplacian matrix L is obtained. This is of great advantage e.g. in electronic circuit fault analysis, where non-linear systems have to be solved…
Simplifications of a result from a prior paper concerning the electric resistance between points in a distance-regular graph are given. In particular, we prove that the maximal resistance between points is bounded by twice the resistance…
It is known that electrical networks with resistors are related to the Laplace operator and random walk on weighted graphs. In this paper we consider more general electrical networks with coils, capacitors, and resistors. We give two…
Based on a simple example, it is explained how the homological analysis may be applied for modeling of the electric circuits. The homological branch, mesh and nodal analyses are presented. Geometrical interpretations are given.
This brief examines the behavior of DC circuits comprised of resistively interconnected constant power devices, as may arise in DC microgrids containing micro-sources and constant power loads. We derive a sufficient condition for all…
Two dimensional electric potential maps based on voltage detection in conducting paper are common practice in many physics courses in college. Most frequently, students work on `capacitor-like' geometries with current flowing between two…
The electromagnetic analog of an elastic spring-mass network is constructed. These electromagnetic circuits offer the promise of manipulating electromagnetic fields in new ways, and linear electrical circuits correspond to a subclass of…
Electromagnetic circuits are the electromagnetic analog at fixed frequency of mass-spring networks in elastodynamics. By interchanging the roles of epsilon and mu in electromagnetic circuits one obtains magnetoelectric circuits. Here we…