In electrical engineering, electrical terms are associated into pairs called duals. A dual of a relationship is formed by interchanging

voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge t ...

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 – serial (circuits) *

resistance Resistance may refer to: Arts, entertainment, and media Comics * Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm: ** ''Resistance'' (comics), based on the video game of the same title ** ''T ...

– conductance * voltage division – current division * impedance –

admittance In electrical engineering, admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the reciprocal of impedance, analogous to how conductance & resistance are defined. The SI unit of admittan ...

capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized a ...

–

inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of t ...

* reactance –

susceptance In electrical engineering, susceptance (''B'') is the imaginary part of admittance, where the real part is conductance. The reciprocal of admittance is impedance, where the imaginary part is reactance and the real part is resistance. In SI un ...

short circuit A short circuit (sometimes abbreviated to short or s/c) is an electrical circuit that allows a current to travel along an unintended path with no or very low electrical impedance. This results in an excessive current flowing through the circuit ...

– open circuit * Kirchhoff's current law – Kirchhoff's voltage law. *

Thévenin's theorem As originally stated in terms of direct-current resistive circuits only, Thévenin's theorem states that ''"For any linear electrical network containing only voltage sources, current sources and resistances can be replaced at terminals A–B ...

– Norton's theorem

History

The use of duality in

circuit theory Circuit may refer to: Science and technology Electrical engineering * Electrical circuit, a complete electrical network with a closed-loop giving a return path for current ** Analog circuit, uses continuous signal levels ** Balanced circ ...

is due to Alexander Russell who published his ideas in 1904.Alexander Russell, ''A Treatise on the Theory of Alternating Currents'', volume 1, chapter XXI, 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

References

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