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 β current
- parallel β serial (circuits)
- resistance β conductance
- impedance β admittance
- capacitance β inductance
- reactance β susceptance
- short circuit β open circuit
- Kirchhoff's current law β Kirchhoff's voltage law.
- ThΓ©venin's theorem β Norton's theorem
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 β differential form
- Capacitor and inductor β integral form
Voltage division β current division
Impedance and admittance
- Resistor and conductor
- Capacitor and inductor
See also
References
- Turner, Rufus P, Transistors Theory and Practice, Gernsback Library, Inc, New York, 1954, Chapter 6.
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