Duality (electrical circuits)

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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 of electricity and magnetism.

Here is a partial list of electrical dualities:

History

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

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

References

  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.
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