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Duality (electrical circuits)

Association of electrical terms into pairs based on interchanging voltage and current

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Source updated March 26, 2026

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:

01History

The use of duality in circuit theory is due to Alexander Russell who published his ideas in 1904.

02Examples

Constitutive relations

  • Resistor and conductor (Ohm's law) v=iR\iff i=vG\,
  • Capacitor and inductor , differential form i_{C}=C{\frac {d}{dt}}v_{C}\iff v_{L}=L{\frac {d}{dt}}i_{L}
  • Capacitor and inductor , integral form 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

Voltage division , current division

v_{R_{1}}=v{\frac {R_{1}}{R_{1}+R_{2}}}\iff i_{G_{1}}=i{\frac {G_{1}}{G_{1}+G_{2}}}

Impedance and admittance

  • Resistor and conductor Z_{R}=R\iff Y_{G}=G Z_{G}={1 \over G}\iff Y_{R}={1 \over R}
  • Capacitor and inductor Z_{C}={1 \over Cs}\iff Y_{L}={1 \over Ls} Z_{L}=Ls\iff Y_{c}=Cs
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Sources and credits

This article is adapted from the Wikipedia article “Duality (electrical circuits)”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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Related topics

Duality (electricity and magnetism)

In physics, the electromagnetic dual concept is based on the idea that, in the static case, electromagnetism has two separate facets: electric fields and magnetic fields. Expressions in one of these will have a directly analogous, or dual, expression in the other.

Duality (mechanical engineering)

In mechanical engineering, many terms are associated into pairs called duals. A dual of a relationship is formed by interchanging force and deformation (strain) in an expression.

Dual impedance

Dual impedance and dual network are terms used in electronic network analysis. The dual of an impedance Z {\displaystyle Z} is its reciprocal, or algebraic inverse Z ′ = 1 Z {\displaystyle Z'={\frac {1}{Z}}} .