Voltage source

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A schematic diagram of a real voltage source, V, driving a resistor, R, and creating a current I

Ideal voltage sources[edit]

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.[2] 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.

Voltage Source.svg Current Source.svg
Ideal Voltage Source Ideal Current Source
Controlled Voltage Source Controlled Current Source
Battery symbol.svg Cell.svg
Battery of cells Single cell
Symbols used for voltage sources

The internal resistance 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 resistance, 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.

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[edit]

Most sources of electrical energy (the mains, a battery) are modeled as voltage sources. An ideal voltage source provides no energy when it is loaded by an open circuit (i.e. an infinite impedance), but approaches infinite energy and current when the load resistance approaches zero (a short circuit). Such a theoretical device would have a zero ohm output impedance in series with the source. A real-world voltage source has a very low, but non-zero internal resistance & output impedance: often much less than 1 ohm.


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 impedance and vice versa. Voltage sources and current sources are sometimes said to be duals of each other and any non ideal source can be converted from one to the other by applying Norton's or Thévenin's theorems.

References and notes[edit]

  1. ^ An introduction to electronics
  2. ^ K. C. A. Smith, R. E. Alley , Electrical circuits: an introduction, Cambridge University Press, 1992 ISBN 0-521-37769-2, pp. 11-13

See also[edit]