In
electrical engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
, electrical terms are associated into pairs called duals. A dual of a relationship is formed by interchanging
voltage
Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...
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
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 multiplicative inverse, reciprocal of Electrical impedance, impedance, analogous to how Electrical resistanc ...
*
capacitance
Capacitance is the ability of an object 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 are two closely related ...
–
inductance
Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the ...
*
reactance –
susceptance
In electrical engineering, susceptance () 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 ( ...
*
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 Open circuit may refer to:
* Open circuit breathing apparatus, any type of breathing apparatus where the exhaled gas is discharged to the surroundings without recycling any of it
** Open-circuit scuba, a type of Scuba-diving equipment where the user ...
*
Kirchhoff's current law
Kirchhoff's circuit laws are two Equality (mathematics), equalities that deal with the Electric current, current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in ...
(KCL) –
Kirchhoff's voltage law
Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchh ...
(KVL)
*
Thévenin's theorem
As originally stated in terms of direct-current resistance (electricity), resistive circuits only, Thévenin's theorem states that ''"Any linear circuit, linear electrical network containing only voltage source, voltage sources, current source, c ...
–
Norton's theorem
In Direct current, direct-current circuit theory, Norton's theorem, also called the Mayer–Norton theorem, is a simplification that can be applied to Electrical network, networks made of Linear time-invariant system, linear time-invariant Resi ...
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 circu ...
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)
* 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
*
Duality (electricity and magnetism)
*
Duality (mechanical engineering) In mechanical engineering, many terms are associated into pairs called duals. A dual of a relationship is formed by interchanging force (stress) and deformation (strain) in an expression.
Here is a partial list of mechanical dualities:
* force & ...
*
Dual impedance
Dual Electrical impedance, impedance and dual network are terms used in Network analysis (electronics), electronic network analysis. The dual of an impedance Z is its reciprocal, or algebraic inverse Z'=\frac. For this reason, the dual impedance i ...
*
Dual graph
In the mathematics, mathematical discipline of graph theory, the dual graph of a planar graph is a graph that has a vertex (graph theory), vertex for each face (graph theory), face of . The dual graph has an edge (graph theory), edge for each p ...
*
Mechanical–electrical analogies
Mechanical–electrical analogies are the representation of mechanical systems as electrical networks. At first, such analogies were used in reverse to help explain electrical phenomena in familiar mechanical terms. James Clerk Maxwell introd ...
*
List of dualities
Mathematics
In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operat ...
References
{{reflist
* Turner, Rufus P, ''Transistors Theory and Practice'', Gernsback Library, Inc, New York, 1954, Chapter 6.
Electrical engineering
Electrical circuits
An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage so ...