Duality (electrical circuits)

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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:

History[edit]

The use of duality in circuit theory is due to Alexander Russell who published his ideas in 1904.[1][2]

Examples[edit]

Constitutive relations[edit]

  • Resistor and conductor (Ohm's law)
  • Capacitor and inductor – differential form
  • Capacitor and inductor – integral form

Voltage division — current division[edit]

Impedance and admittance[edit]

  • Resistor and conductor
  • Capacitor and inductor

See also[edit]

References[edit]

  1. ^ 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.
  2. ^ Alexander Russell, A Treatise on the Theory of Alternating Currents, volume 1, chapter XXI, Cambridge: University Press 1904 OCLC 264936988.
  • Turner, Rufus P, Transistors Theory and Practice, Gernsback Library, Inc, New York, 1954, Chapter 6.