dual (electronics)

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.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) $v=iR \iff i=vG \,$
* Capacitor and inductor – differential form $i_C=C\fracv_C \iff v_L=L\fraci_L$
* Capacitor and inductor – integral form $v_C(t) = V_0 + \int_^ i_C(\tau) \, d\tau \iff i_L(t) = I_0 + \int_^ v_L(\tau) \, d\tau$

Voltage division — current division

$v_=v\frac \iff i_=i\frac$

Impedance and admittance

* Resistor and conductor $Z_R = R \iff Y_G = G$ $Z_G = \iff Y_R =$
* Capacitor and inductor $Z_C = \iff Y_L =$ $Z_L = Ls \iff Y_c = Cs$

See also

* Duality (electricity and magnetism)
* Duality (mechanical engineering)
* Dual impedance
* Dual graph
* Mechanical–electrical analogies
* List of dualities

References

{{reflist
* Turner, Rufus P, ''Transistors Theory and Practice'', Gernsback Library, Inc, New York, 1954, Chapter 6.

Electrical engineering
Electrical circuits