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| 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 (electricity and magnetism)|duality of electricity and magnetism]].
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| Here is a partial list of electrical dualities:
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| * [[voltage]] — [[Electric current|current]]
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| * [[Series and parallel circuits|parallel — serial]] (circuits)
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| * [[Electrical resistance|resistance]] — [[Electrical conductance|conductance]]
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| * [[Electrical impedance|impedance]] — [[admittance]]
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| * [[capacitance]] — [[inductance]]
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| * [[Reactance (electronics)|reactance]] — [[susceptance]]
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| * [[short circuit]] — [[open circuit]]
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| * [[Kirchhoff's current law]] — [[Kirchhoff's voltage law]].
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| * [[Thévenin's theorem]] — [[Norton's theorem]]
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| ==History==
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| The use of duality in [[circuit theory]] is due to Alexander Russell who published his ideas in 1904.<ref>Belevitch, V, "Summary of the history of circuit theory", ''Proceedings of the IRE'', '''vol 50''', Iss 5, pp.848-855, May 1962 {{doi|10.1109/JRPROC.1962.288301}}.</ref><ref>Alexander Russell, ''A Treatise on the Theory of Alternating Currents'', volume 1, chapter XXI, Cambridge: University Press 1904 {{OCLC|264936988}}.</ref> | |
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| == Examples ==
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| === Constitutive relations ===
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| * Resistor and conductor (Ohm's law)
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| :: <math>v=iR \iff i=vG \, </math>
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| * Capacitor and inductor – differential form
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| :: <math>i_C=C\frac{d}{dt}v_C \iff v_L=L\frac{d}{dt}i_L</math>
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| * Capacitor and inductor – integral form
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| :: <math>v_C(t) = V_0 + {1 \over C}\int_{0}^{t} i_C(\tau) \, d\tau \iff i_L(t) = I_0 + {1 \over L}\int_{0}^{t} v_L(\tau) \, d\tau </math>
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| === Voltage division — current division ===
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| :<math>v_{R_1}=v\frac{R_1}{R_1 + R_2} \iff i_{G_1}=i\frac{G_1}{G_1 + G_2}</math>
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| === Impedance and admittance ===
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| * Resistor and conductor
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| :: <math>Z_R = R \iff Y_G = G </math>
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| :: <math>Z_G = {1 \over G } \iff Y_R = { 1 \over R } </math>
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| * Capacitor and inductor
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| :: <math> Z_C = {1 \over Cs} \iff Y_L = {1 \over Ls} </math>
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| :: <math> Z_L = Ls \iff Y_c = Cs</math>
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| ==See also==
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| *[[Duality (electricity and magnetism)]]
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| *[[Duality (mechanical engineering)]]
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| *[[Dual impedance]]
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| ==References==
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| {{reflist}}
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| * Turner, Rufus P, ''Transistors Theory and Practice'', Gernsback Library, Inc, New York, 1954, Chapter 6.
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| [[Category:Electrical engineering]]
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| [[Category:Duality theories|Electrical circuits]]
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