TheInfoList

A voltage source is a two- terminal device which can maintain a fixed
voltage Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is the ...

. An ideal voltage source can maintain the fixed voltage independent of the
load resistanceThe input impedance of an electrical network is the measure of the opposition to current ( impedance), both static ( resistance) and dynamic ( reactance), into the load network that is ''external'' to the electrical source. The input admittance (1/i ...
or the output
current Currents or The Current may refer to: Science and technology * Current (fluid) A current in a fluid In physics, a fluid is a substance that continually Deformation (mechanics), deforms (flows) under an applied shear stress, or external force. ...
. However, a real-world voltage source cannot supply unlimited current. A voltage source is the
dual Dual or Duals may refer to: Paired/two things * Dual (mathematics), a notion of paired concepts that mirror one another ** Dual (category theory), a formalization of mathematical duality ** . . . see more cases in :Duality theories * Dual ...
of a
current source A current source is an electronic circuit that delivers or absorbs an electric current which is independent of the voltage across it. A current source is the duality (electrical circuits), dual of a voltage source. The term ''current sink'' is so ...

. Real-world sources of electrical energy, such as
batteries Battery may refer to: Energy source * Electric battery, an electrochemical device to provide electrical power ** Automotive battery, a device to provide power to certain functions of an automobile ** List of battery types * Energy storage, inclu ...
and generators, can be modeled for analysis purposes as a combination of an ideal voltage source and additional combinations of impedance elements.

# Ideal voltage sources

An ideal voltage source is a two-terminal device that maintains a fixed voltage drop across its terminals. It is often used as a mathematical abstraction that simplifies the analysis of real electric circuits. If the voltage across an ideal voltage source can be specified independently of any other variable in a circuit, it is called an independent voltage source. Conversely, if the voltage across an ideal voltage source is determined by some other voltage or current in a circuit, it is called a dependent or controlled voltage source. A mathematical model of an amplifier will include dependent voltage sources whose magnitude is governed by some fixed relation to an input signal, for example.K. C. A. Smith, R. E. Alley , ''Electrical circuits: an introduction'', Cambridge University Press, 1992 , pp. 11-13 In the analysis of faults on electrical power systems, the whole network of interconnected sources and transmission lines can be usefully replaced by an ideal (AC) voltage source and a single equivalent impedance. , - align="center" , style="padding: 1em 2em 0;", , style="padding: 1em 2em 0;", , - align="center" , Ideal Voltage Source , , - align="center" , style="padding: 1em 2em 0;", , style="padding: 1em 2em 0;", , - align="center" , Controlled Voltage Source , Controlled Current Source , - align="center" , style="padding: 1em 2em 0;", , style="padding: 1em 2em 0;", , - align="center" ,
Battery Battery may refer to: Energy source * Electric battery, an electrochemical device to provide electrical power ** Automotive battery, a device to provide power to certain functions of an automobile ** List of battery types * Energy storage, inclu ...
of cells , Single cell The
internal resistance A practical electrical power Electric power is the rate, per unit time, at which electrical energy Electrical energy is energy derived from electric potential energy or kinetic energy. When used loosely, ''electrical energy'' refers to ener ...

of an ideal voltage source is zero; it is able to supply or absorb any amount of current. The current through an ideal voltage source is completely determined by the external circuit. When connected to an open circuit, there is zero current and thus zero power. When connected to a
load resistanceThe input impedance of an electrical network is the measure of the opposition to current ( impedance), both static ( resistance) and dynamic ( reactance), into the load network that is ''external'' to the electrical source. The input admittance (1/i ...
, the current through the source approaches infinity as the load resistance approaches zero (a short circuit). Thus, an ideal voltage source can supply unlimited power. If two ideal independent voltage source are directly connected in
parallel Parallel may refer to: Computing * Parallel algorithm In computer science Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques for their a ...

, they must have exactly the same voltage; Otherwise, it creates a
fallacy A fallacy is the use of invalid or otherwise faulty reason Reason is the capacity of consciously applying logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously making sense of ...
in logic, similar to writing down the equation $1=2$. Voltage sources in parallel shares the burden of current: If an exact duplicate of voltage is connected in parallel to the original one, either one of them will provide half of the
electric current An electric current is a stream of charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, ...
that the original voltage source would provide. For the remainder of the circuit, nothing has changed: These two voltage sources together provide the same voltage, and the same current as the original one alone. No real voltage source is ideal; all have a non-zero effective internal resistance, and none can supply unlimited current. However, the internal resistance of a real voltage source is effectively modeled in linear circuit analysis by combining a non-zero resistance in series with an ideal voltage source (a Thévenin equivalent circuit).

# Comparison between voltage and current sources

Most sources of electrical energy (the mains, a
battery Battery may refer to: Energy source * Electric battery, an electrochemical device to provide electrical power ** Automotive battery, a device to provide power to certain functions of an automobile ** List of battery types * Energy storage, inclu ...
) are modeled as voltage sources. An ''ideal'' voltage source provides no energy when it is loaded by an
open circuitOpen circuit may refer to: *Open-circuit scuba A scuba set is any breathing apparatus that is carried entirely by an underwater diver and provides the diver with breathing gas A breathing gas is a mixture of gaseous chemical elements and comp ...
(i.e. an infinite impedance), but approaches infinite energy and current when the
load resistanceThe input impedance of an electrical network is the measure of the opposition to current ( impedance), both static ( resistance) and dynamic ( reactance), into the load network that is ''external'' to the electrical source. The input admittance (1/i ...
approaches zero (a
short circuit A short circuit (sometimes abbreviated to short or s/c) is an electrical circuit An electrical network is an interconnection of electronic component, electrical components (e.g., battery (electricity), batteries, resistors, inductors, capaci ...

). Such a theoretical device would have a zero
ohm The ohm (symbol: Ω) is the SI derived unit SI derived units are units of measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, ...
output impedance The output impedance of an electrical network An electrical network is an interconnection of electronic component, electrical components (e.g., battery (electricity), batteries, resistors, inductors, capacitors, switches, transistors) or a mo ...
in series with the source. A real-world voltage source has a very low, but non-zero
internal resistance A practical electrical power Electric power is the rate, per unit time, at which electrical energy Electrical energy is energy derived from electric potential energy or kinetic energy. When used loosely, ''electrical energy'' refers to ener ...

and
output impedance The output impedance of an electrical network An electrical network is an interconnection of electronic component, electrical components (e.g., battery (electricity), batteries, resistors, inductors, capacitors, switches, transistors) or a mo ...
, often much less than 1 ohm. Conversely, a
current source A current source is an electronic circuit that delivers or absorbs an electric current which is independent of the voltage across it. A current source is the duality (electrical circuits), dual of a voltage source. The term ''current sink'' is so ...

provides a constant current, as long as the load connected to the source terminals has sufficiently low impedance. An ideal current source would provide no energy to a short circuit and approach infinite energy and voltage as the
load resistanceThe input impedance of an electrical network is the measure of the opposition to current ( impedance), both static ( resistance) and dynamic ( reactance), into the load network that is ''external'' to the electrical source. The input admittance (1/i ...
approaches infinity (an open circuit). An ''ideal'' current source has an
infinite Infinite may refer to: Mathematics *Infinite set, a set that is not a finite set *Infinity, an abstract concept describing something without any limit Music *Infinite (band), a South Korean boy band *''Infinite'' (EP), debut EP of American musi ...

output impedance The output impedance of an electrical network An electrical network is an interconnection of electronic component, electrical components (e.g., battery (electricity), batteries, resistors, inductors, capacitors, switches, transistors) or a mo ...
in parallel with the source. A ''real-world'' current source has a very high, but finite
output impedance The output impedance of an electrical network An electrical network is an interconnection of electronic component, electrical components (e.g., battery (electricity), batteries, resistors, inductors, capacitors, switches, transistors) or a mo ...
. In the case of transistor current sources, impedance of a few
megohm The ohm (symbol: Omega, Ω) is the SI derived unit of electrical resistance, named after German physicist Georg Ohm. Various empirically derived standard units for electrical resistance were developed in connection with early telegraphy practic ...
s (at low frequencies) is typical. Since no ideal sources of either variety exist (all real-world examples have finite and non-zero source impedance), any current source can be considered as a voltage source with the ''same''
source impedanceThe output Electrical_impedance, impedance of an electrical network is the measure of the opposition to current flow (impedance), both static (Electrical resistance and conductance, resistance) and dynamic (Electrical reactance, reactance), into the ...
and vice versa. Voltage sources and current sources are sometimes said to be
dual Dual or Duals may refer to: Paired/two things * Dual (mathematics), a notion of paired concepts that mirror one another ** Dual (category theory), a formalization of mathematical duality ** . . . see more cases in :Duality theories * Dual ...
s of each other and any non ideal source can be converted from one to the other by applying
Norton's theorem In direct-current circuit theory, Norton's theorem (aka Mayer–Norton theorem) is a simplification that can be applied to networks made of linear time-invariant resistances, voltage sources, and current sources. At a pair of terminals of the n ...
or
Thévenin's theorem As originally stated in terms of direct-current resistive circuits only, Thévenin's theorem states that, ''"For any linear electrical network An electrical network is an interconnection of electrical components (e.g., batteries, resist ...
.