[[wiki-architecture]] · [[Urban Planning and City Architecture]] · [[ARCHITECTURE]] · [[000]] # 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 – series (circuits) resistance – conductance voltage division – current division impedance – admittance capacitance – inductance reactance – susceptance short circuit – open circuit Kirchhoff's current law (KCL) – Kirchhoff's voltage law (KVL) 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. == Examples == === Constitutive relations === Resistor and conductor (Ohm's law) v = i R ⟺ i = v G {\displaystyle v=iR\iff i=vG\,} Capacitor and inductor – differential form i C = C d d t v C ⟺ v L = L d d t i L {\displaystyle 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 C ∫ 0 t i C ( τ ) d τ ⟺ i L ( t ) = I 0 + 1 L ∫ 0 t v L ( τ ) d τ {\displaystyle 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 R 1 R 1 + R 2 ⟺ i G 1 = i G 1 G 1 + G 2 {\displaystyle 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 ⟺ Y G = G {\displaystyle Z_{R}=R\iff Y_{G}=G} Z G = 1 G ⟺ Y R = 1 R {\displaystyle Z_{G}={1 \over G}\iff Y_{R}={1 \over R}} Capacitor and inductor Z C = 1 C s ⟺ Y L = 1 L s {\displaystyle Z_{C}={1 \over Cs}\iff Y_{L}={1 \over Ls}} Z L = L s ⟺ Y c = C s {\displaystyle Z_{L}=Ls\iff Y_{c}=Cs} == See also == Duality (electricity and magnetism) Duality (mechanical engineering) Dual impedance Dual graph Mechanical–electrical analogies List of dualities == References == - [[Professional Practice/Codes & Standards/National Building Code of India/Part 08 - Building Services/Section 2 - Electrical Installations]] - [[Building Services/Electrical Systems]] - [[Building Services/Vertical Transportation]] - [[Professional Practice/Codes & Standards/National Building Code of India/Part 08 - Building Services/Section 5A - Lifts]] - [[Research, Analysis & Citations/Glossary]] - [[Research, Analysis & Citations/Conversion Tables]] - [[Urban and Planning/Housing]] - [[Professional Practice/Construction Management/Site Management]] - [[Building Construction/Construction & Materials/Building Material/Concrete and Cement]] - [[Environmental Design/Natural Ventilation]] Turner, Rufus P, Transistors Theory and Practice, Gernsback Library, Inc, New York, 1954, Chapter 6.