Voltage

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International safety symbol "Caution, risk of electric shock" (ISO 3864), colloquially known as High voltage.

Voltage is commonly used as a short name for electrical potential difference. Its corresponding SI unit is the volt (symbol: V, not italicized). Electric potential is a hypothetically measurable physical dimension, and is denoted by the algebraic variable V (italicized).^[1]

[edit] Definition

The voltage between two (electron) positions "A" and "B", inside a solid electrical conductor (or inside two electrically-connected, solid electrical conductors), is denoted by (V_A − V_B). This voltage is the electrical driving force that drives a conventional electric current in the direction A to B. Voltage can be directly measured by a voltmeter. Well-constructed, correctly used, real voltmeters approximate very well to ideal voltmeters. An analogy involving the flow of water is sometimes helpful in understanding the concept of voltage (see below).

Precise modern and historic definitions of voltage exist, but (due to the development of the electron theory of metal conduction in the period 1897 to 1933, and to developments in theoretical surface science from about 1910 to about 1950, particularly the theory of local work function) some older definitions are no longer regarded as strictly correct. This is because they neglect the existence of "chemical" effects and surface effects. A particular lesson from surface science is that, to get consistency and universality, formal definitions must relate to positions or (better) electron states inside conductors.

In conduction processes occurring in metals and most other solids, electric currents consist almost exclusively of the flow of electrons in the direction B to A. This movement of electrons is controlled by differences in a so-called "total local thermodynamic potential" often denoted by the symbol µ ("mu"). This parameter is often called the "local Fermi level" or sometimes the "(local) electrochemical potential of an electron" or the "total (local) chemical potential of an electron". The modern electron-based definition of voltage (V_A − V_B) is in terms of differences in µ:

$(V_{\mathrm{A}} - V_{\mathrm{B}}) = \; -({\mu}_{\mathrm{A}} - {\mu}_{\mathrm{B}})/e$

where e is the elementary positive charge. It is sometimes convenient to put µ_B=0 and V_B=0, and choose position "B" so that it can be a convenient reference zero for V. It is common to choose position "B" to be inside a good electrical conductor solidly connected (by a very-low-electrical-resistance path) to the local "Earth" or "Ground". In the analysis of electrical circuit diagrams, it is common to show the point in the circuit that is being taken as the reference position B, by attaching a "Ground" ("Earth") symbol to this point.

A common misapprehension is to assume that difference in voltage is always equal to difference in electric potential (i.e. electrostatic potential). This is often untrue, because differences in "chemical effects" (e.g., as between conductors made from different materials) also contribute to differences in µ, and hence to differences in voltage. Some textbooks (especially old physics textbooks) give historic definitions of voltage that are not strictly equivalent to the modern definition. However, the difference in value between a "voltage difference" and the related "electric potential difference" is always small (at most a few volts, often less), and in many contexts it is commonplace (and acceptable) to disregard the distinction. Nonetheless, in some contexts, such as the theory of contact potential differences, the distinction is vital.

[edit] Other terminology

The opening paragraph of this entry explains the difference between the names "voltage" and "electric potential difference". Historically this quantity has also been called "tension"^[2] and "pressure". Pressure is now obsolete but tension is still used, for example within the phrase "High Tension" (HT) which is commonly used in thermionic valve (vacuum tube) based electronics.

[edit] Hydraulic analogy

Main article: hydraulic analogy

A simple analogy for an electric circuit is water flowing in a closed circuit of pipework, driven by a mechanical pump. This can be called a water circuit. Voltage difference between two points corresponds to the water pressure difference between two points. If there is a water pressure difference between two points, then water flow (due to the pump) from the first point to the second will be able to do work, such as driving a turbine. In a similar way, work can be done by the electric current driven by the voltage difference due to an electric battery: for example, the current generated by an automobile battery can drive the starter motor in an automobile. If the pump isn't working, it produces no pressure difference, and the turbine will not rotate. Equally, if the automobile's battery is flat, then it will not turn the starter motor.

This water flow analogy is a useful way of understanding several electrical concepts. In such a system, the work done to move water is equal to the pressure multiplied by the volume of water moved. Similarly, in an electrical circuit, the work done to move electrons or other charge-carriers is equal to "electrical pressure" (an old term for voltage) multiplied by the quantity of electrical charge moved. Voltage is a convenient way of measuring the ability to do work. In relation to "flow", the larger the "pressure difference" between two points (voltage difference or water pressure difference) the greater the flow between them (either electric current or water flow).

[edit] Simple applications

Common usage (that "voltage" usually means "voltage difference") is now resumed. Obviously, when using the term "voltage" in the shorthand sense, one must be clear about the two points between which the voltage is specified or measured. When using a voltmeter to measure voltage difference, one electrical lead of the voltmeter must be connected to the first point, one to the second point.

[edit] Voltage between two stated points

A common use of the term "voltage" is in specifying how many volts are dropped across an electrical device (such as a resistor). In this case, the "voltage", or more accurately, the "voltage drop across the device", can usefully be understood as the difference between two measurements. The first measurement uses one electrical lead of the voltmeter on the first terminal of the device, with the other voltmeter lead connected to ground. The second measurement is similar, but with the first voltmeter lead on the second terminal of the device. The voltage drop is the difference between the two readings. In practice, the voltage drop across a device can be measured directly and safely using a voltmeter that is isolated from ground, provided that the maximum voltage capability of the voltmeter is not exceeded.

Two points in an electric circuit that are connected by an "ideal conductor," that is, a conductor without resistance and not within a changing magnetic field, have a voltage difference of zero. However, other pairs of points may also have a voltage difference of zero. If two such points are connected with a conductor, no current will flow through the connection.

[edit] Addition of voltages

Voltage is additive in the following sense: the voltage between A and C is the sum of the voltage between A and B and the voltage between B and C. The various voltages in a circuit can be computed using Kirchhoff's circuit laws.

When talking about alternating current (AC) there is a difference between instantaneous voltage and average voltage. Instantaneous voltages can be added as for direct current (DC), but average voltages can be meaningfully added only when they apply to signals that all have the same frequency and phase.

[edit] Useful formulas

[edit] DC (Direct current) circuits

$V = \; IR \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \mathrm{(Ohm's} \; \mathrm{Law)}$

$P = \; I V = I^2 R = V^2 /R$

$V = \sqrt{PR}$

where V = voltage difference (SI unit: volt), I = electric current (SI unit: ampere), R = resistance (SI unit: ohm), P = power (SI unit: watt).

[edit] AC (Alternating current) circuits

$V = \frac{P}{I\;\cos\phi}$

$V = \frac{\sqrt{P\;Z}}{\sqrt{\cos\phi}} \!\$

$V = \frac{I\;R}{\cos\phi}$

Where V=voltage, I=current, R=resistance, P=true power, Z=impedance, φ=phase difference between I and V.

[edit] AC conversions

$V_{avg} = 0.637\,V_{pk} = \frac{2}{\pi} V_{pk} = \frac{\omega}{\pi}\int_0^{\pi/\omega} V_{pk} \sin(\omega t - k x) {\rm{d}}x \!\$

$V_{rms} = 0.707\,V_{pk} = \frac{1}{\sqrt{2}} V_{pk} = V_{pk} \sqrt{\langle \sin^2(\omega t - k x) \rangle} \!\$

$V_{pk} = 0.5\,V_{ppk} \!\$

$V_{avg} = 0.319\,V_{ppk}\!\$

$V_{rms} = 0.354\,V_{ppk} = \frac{1}{2 \sqrt{2}} V_{ppk}\!\$

$V_{avg} = 0.900\,V_{rms} = \frac{2 \sqrt{2}}{\pi} V_{rms}\!\$

Where V_pk=peak voltage, V_ppk=peak-to-peak voltage, V_avg=average voltage over a half-cycle, V_rms=effective (root mean square) voltage, and we assumed a sinusoidal wave of the form $V p k sin(ω t - k x)$ , with a period $T = 2π / ω$ , and where the angle brackets (in the root-mean-square equation) denote a time average over an entire period.

[edit] Total voltage

Voltage sources and drops in series:

$V_T = V_1 + V_2 + V_3 + ... + V_n \!\$

Voltage sources and drops in parallel:

$V_T = V_1 = V_2 = V_3 = ... = V_n \!\$

Where $n \!\$ is the nth voltage source or drop

[edit] Voltage drops

Across a resistor (Resistor R):

$V_R = IR_R \!\$

Across a capacitor (Capacitor C):

$V_C = IX_C \!\$

Across an inductor (Inductor L):

$V_L = IX_L \!\$

Where V=voltage, I=current, R=resistance, X=reactance.

[edit] Measuring instruments

A multimeter set to measure voltage.

Instruments for measuring voltage differences include the voltmeter, the potentiometer, and the oscilloscope. The voltmeter works by measuring the current through a fixed resistor, which, according to Ohm's Law, is proportional to the voltage difference across the resistor. The potentiometer works by balancing the unknown voltage against a known voltage in a bridge circuit. The cathode-ray oscilloscope works by amplifying the voltage difference and using it to deflect an electron beam from a straight path, so that the deflection of the beam is proportional to the voltage difference.

[edit] Safety

Voltages as low as 50 volts can lead to a lethal electric shock under certain circumstances. Electrical safety is discussed in the articles on high voltage and electric shock.

[edit] See also

Alternating current (AC)
Direct current (DC)
Electric potential
Electrical measurements
Electrochemical potential
Fermi level
Mains electricity (an article about domestic power supply voltages)
Mains power systems (List of voltage by country)
Ohm's law
Phantom voltage
Voltage drop

[edit] References

^ Griffiths, D. (1999). Introduction to Electrodynamics. Upper Saddle River, NJ: Prentice-Hall.
^ CollinsLanguage.com

Electronics portal

[edit] External links

Look up voltage in Wiktionary, the free dictionary.

[0] Griffiths, D. (1999). Introduction to Electrodynamics. Upper Saddle River, NJ: Prentice-Hall.

[1] CollinsLanguage.com

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