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.Belevitch, V, "Summary of the history of circuit theory", Proceedings of the IRE, vol 50, Iss 5, pp. 848–855, May 1962 .Alexander Russell, A Treatise on the Theory of Alternating Currents, volume 1, chapter XVII, Cambridge: University Press 1904 .
Examples Constitutive relations
Resistor and conductor (Ohm's law) Capacitor and inductor – differential form Capacitor and inductor – integral form
Voltage division — current division
Impedance and admittance
Resistor and conductor Capacitor and inductor
See also Duality (electricity and magnetism) Duality (mechanical engineering) Dual impedance Dual graph Mechanical–electrical analogies List of dualities
References
Turner, Rufus P, Transistors Theory and Practice, Gernsback Library, Inc, New York, 1954, Chapter 6.