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Reciprocity of electrical networks is a special case of Lorentz reciprocity, but it can also be proven more directly from network theorems. This proof shows reciprocity for a two-node network in terms of its admittance matrix, and then shows reciprocity for a network with an arbitrary number of nodes by an induction argument.
A simple electric circuit made up of a voltage source and a resistor. Here, =, according to Ohm's law. An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, current sources, resistances, inductances ...
An n-terminal network can, at best, be reduced to n impedances (at worst ()). For a three terminal network, the three impedances can be expressed as a three node delta (Δ) network or four node star (Y) network. These two networks are equivalent and the transformations between them are given below.
Often, especially for electrical networks, one instead prefers to think of an externally applied voltage and the resulting currents. The Lorentz reciprocity theorem describes this case as well, assuming ohmic materials (i.e. currents that respond linearly to the applied field) with a 3×3 conductivity matrix σ that is required to be symmetric ...
In a network analysis of such a circuit from a topological point of view, the network nodes are the vertices of graph theory, and the network branches are the edges of graph theory. Standard graph theory can be extended to deal with active components and multi-terminal devices such as integrated circuits .
This page is a list of network theory topics. Network theorems. Max flow min cut theorem; ... Electrical network; Gene regulatory network; Global shipping network;
Two pairs of gauge transformed potentials (φ, A) and (φ′, A′) are called gauge equivalent, and the freedom to select any pair of potentials in its gauge equivalence class is called gauge freedom. Again by the Poincaré lemma (and under its assumptions), gauge freedom is the only source of indeterminacy, so the field formulation is ...
In an electrical network diagram, limited to linear systems, there are three passive elements: resistance, inductance, and capacitance; and two active elements: the voltage generator, and the current generator. [note 2] The mechanical analogs of these elements can be used to construct a mechanical network diagram. What the mechanical analogs of ...