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Duality (electrical Circuits)
In electrical engineering, electrical terms are associated into pairs called duals. A dual of a relationship is formed by interchanging voltage and current in an expression. The dual expression thus produced is of the same form, and the reason that the dual is always a valid statement can be traced to the duality of electricity and magnetism. Here is a partial list of electrical dualities: * voltage – current * parallel – serial (circuits) * resistance – conductance * voltage division – current division * impedance – admittance * capacitance – inductance * reactance – susceptance * short circuit – open circuit * Kirchhoff's current law – Kirchhoff's voltage law. * Thévenin's theorem – Norton's theorem History The use of duality in circuit theory is due to Alexander Russell who published his ideas in 1904.Alexander Russell, ''A Treatise on the Theory of Alternating Currents'', volume 1, chapter XXI, Cambridge: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the latter half of the 19th century after commercialization of the electric telegraph, the telephone, and electrical power generation, distribution, and use. Electrical engineering is now divided into a wide range of different fields, including computer engineering, systems engineering, power engineering, telecommunications, radio-frequency engineering, signal processing, instrumentation, photovoltaic cells, electronics, and optics and photonics. Many of these disciplines overlap with other engineering branches, spanning a huge number of specializations including hardware engineering, power electronics, electromagnetics and waves, microwave engineering, nanotechnology, electrochemistry, renewable energies, mechatronics/control, and electrical m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Susceptance
In electrical engineering, susceptance (''B'') is the imaginary part of admittance, where the real part is conductance. The reciprocal of admittance is impedance, where the imaginary part is reactance and the real part is resistance. In SI units, susceptance is measured in siemens. Origin The term was coined by C.P. Steinmetz in a 1894 paper. In some sources Oliver Heaviside is given credit for coining the term, or with introducing the concept under the name ''permittance''. This claim is mistaken according to Steinmetz's biographer. The term ''susceptance'' does not appear anywhere in Heaviside's collected works, and Heaviside used the term ''permittance'' to mean capacitance, not ''susceptance''. Formula The general equation defining admittance is given by Y = G + j B \, where The admittance () is the reciprocal of the impedance (), if the impedance is not zero: Y = \frac = \frac = \left( \frac \right) \left( \frac \right) = \left( \frac \right) + j \left( \frac \right ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Dualities
Mathematics In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of ''A'' is ''B'', then the dual of ''B'' is ''A''. * Alexander duality * Alvis–Curtis duality * Artin–Verdier duality * Beta-dual space * Coherent duality * De Groot dual * Dual abelian variety * Dual basis in a field extension * Dual bundle * Dual curve * Dual (category theory) * Dual graph * Dual group * Dual object * Dual pair * Dual polygon * Dual polyhedron * Dual problem * Dual representation * Dual q-Hahn polynomials * Dual q-Krawtchouk polynomials * Dual space * Dual topology * Dual wavelet * Duality (optimization) * Duality (order theory) * Duality of stereotype spaces * Duality (projective geometry) * Duality theory for distributive lattices * Dualizing complex * Dualizing sheaf * Eckmann–Hilton dualit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Graph
In the mathematical discipline of graph theory, the dual graph of a plane graph is a graph that has a vertex for each face of . The dual graph has an edge for each pair of faces in that are separated from each other by an edge, and a self-loop when the same face appears on both sides of an edge. Thus, each edge of has a corresponding dual edge, whose endpoints are the dual vertices corresponding to the faces on either side of . The definition of the dual depends on the choice of embedding of the graph , so it is a property of plane graphs (graphs that are already embedded in the plane) rather than planar graphs (graphs that may be embedded but for which the embedding is not yet known). For planar graphs generally, there may be multiple dual graphs, depending on the choice of planar embedding of the graph. Historically, the first form of graph duality to be recognized was the association of the Platonic solids into pairs of dual polyhedra. Graph duality is a topological ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Impedance
Dual impedance and dual network are terms used in electronic network analysis. The dual of an impedance Z is its reciprocal, or algebraic inverse Z'=\frac. For this reason the dual impedance is also called the inverse impedance. Another way of stating this is that the dual of Z is the admittance Y'=Z. The dual of a network is the network whose impedances are the duals of the original impedances. In the case of a black-box network with multiple ports, the impedance looking into each port must be the dual of the impedance of the corresponding port of the dual network. This is consistent with the general notion duality of electric circuits, where the voltage and current are interchanged, etc., since Z=\frac yields Z'=\frac __TOC__ Scaled and normalised duals In physical units, the dual is taken with respect to some nominal or characteristic impedance. To do this, Z and Z' are scaled to the nominal impedance Z0 so that : \frac=\frac Z0 is usually taken to be a purely real ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duality (mechanical Engineering)
In mechanical engineering, many terms are associated into pairs called duals. A dual of a relationship is formed by interchanging force (stress) and deformation (strain) in an expression. Here is a partial list of mechanical dualities: * force — deformation * stress — strain * stiffness method — flexibility method Examples Constitutive relation * stress and strain (Hooke's law.) :: \sigma = E \varepsilon \iff \varepsilon = \frac{E} \sigma \, See also * Duality (electrical circuits) * Hydraulic analogy * List of dualities * Series and parallel springs References * Fung, Y. C., ''A First Course in CONTINUUM MECHANICS'', 2nd edition, Prentice-Hall, Inc. 1977 Mechanical engineering Mechanical engineering Mechanical engineering is the study of physical machines that may involve force and movement. It is an engineering branch that combines engineering physics and mathematics principles with materials science, to design, analyze, manufacture, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circuit Theory
Circuit may refer to: Science and technology Electrical engineering * Electrical circuit, a complete electrical network with a closed-loop giving a return path for current ** Analog circuit, uses continuous signal levels ** Balanced circuit, paths are impedance-matched ** Circuit analysis, the process of finding the voltages across, and the currents through, every component in an electrical circuit ** Circuit diagram, a graphical representation of an electrical circuit ** Digital circuit, uses discrete signal levels ** Electronic circuit, contains "active" (nonlinear) electronic components capable of performing amplification, computation, and data transfer *** Asynchronous circuit, or self-timed circuit, a sequential digital logic circuit that is not governed by a clock circuit or global clock signal *** Integrated circuit, a set of electronic circuits on a small "chip" of semiconductor material **** Mixed-signal integrated circuit, contains both analog and digital signals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norton's Theorem
In direct-current circuit theory, Norton's theorem, also called the Mayer–Norton theorem, is a simplification that can be applied to networks made of linear time-invariant resistances, voltage sources, and current sources. At a pair of terminals of the network, it can be replaced by a current source and a single resistor in parallel. For alternating current (AC) systems the theorem can be applied to reactive impedances as well as resistances. The Norton equivalent circuit is used to represent any network of linear sources and impedances at a given frequency. Norton's theorem and its dual, Thévenin's theorem, are widely used for circuit analysis simplification and to study circuit's initial-condition and steady-state response. Norton's theorem was independently derived in 1926 by Siemens & Halske researcher Hans Ferdinand Mayer (1895–1980) and Bell Labs engineer Edward Lawry Norton (1898–1983). To find the equivalent, the Norton current ''I''no is calculated as th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thévenin's Theorem
As originally stated in terms of direct-current resistive circuits only, Thévenin's theorem states that ''"For any linear electrical network containing only voltage sources, current sources and resistances can be replaced at terminals A–B by an equivalent combination of a voltage source Vth in a series connection with a resistance Rth."'' * The equivalent voltage ''V''th is the voltage obtained at terminals A–B of the network with terminals A–B open circuited. * The equivalent resistance ''R''th is the resistance that the circuit between terminals A and B would have if all ideal voltage sources in the circuit were replaced by a short circuit and all ideal current sources were replaced by an open circuit. * If terminals A and B are connected to one another, the current flowing from A to B will be ''V''th/''R''th. This means that ''R''th could alternatively be calculated as ''V''th divided by the short-circuit current between A and B when they are connected together. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kirchhoff's Voltage Law
Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of James Clerk Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws. These laws can be applied in time and frequency domains and form the basis for network analysis. Both of Kirchhoff's laws can be understood as corollaries of Maxwell's equations in the low-frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the circuits. Kirchhoff's current law This law, also called Kirchhoff's first law, or Kirchhoff's junction rule, states that, for any node (junction) in an electrical circuit, the sum of curre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kirchhoff's Current Law
Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of James Clerk Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws. These laws can be applied in time and frequency domains and form the basis for network analysis. Both of Kirchhoff's laws can be understood as corollaries of Maxwell's equations in the low-frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the circuits. Kirchhoff's current law This law, also called Kirchhoff's first law, or Kirchhoff's junction rule, states that, for any node (junction) in an electrical circuit, the sum of currents ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Open Circuit
Open circuit may refer to: *Open-circuit scuba, a type of SCUBA-diving equipment where the user breathes from the set and then exhales to the surroundings without recycling the exhaled air *Open-circuit test, a method used in electrical engineering to determine the impedance in the excitation branch of a real transformer *Open-circuit voltage, the difference of electrical potential between two terminals of a device when there is no external load connected *An electrical circuit is an "open circuit" if it lacks a complete path between the terminals of its power source See also *Closed-circuit (other) *Short circuit (other) A short circuit is an electrical circuit that allows a current to travel along an unintended path with no or a very low electrical impedance. Short Circuit may also refer to: Film * ''Short Circuit'' (1943 film), an Italian film * ''Short Circu ... * Open system (other) {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
