Puneet Varma (Editor)

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.

Contents

Here is a partial list of electrical dualities:

  • voltage – current
  • parallel – serial (circuits)
  • resistance – conductance
  • impedance – admittance
  • capacitance – inductance
  • reactance – susceptance
  • short circuit – open circuit
  • Kirchhoff's current law – Kirchhoff's voltage law.
  • 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.

    Constitutive relations

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

    • Voltage division — current division

    v R 1 = v R 1 R 1 + R 2 ⟺ i G 1 = i G 1 G 1 + G 2

    Impedance and admittance

  • Resistor and conductor
  • Capacitor and inductor

    • References

    Duality (electrical circuits) Wikipedia
    (Text) CC BY-SA