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PowerPedia:Voltage

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Voltage is the difference of electrical potential between two points of an electrical network, expressed in volts. It is a measure of the capacity of an electric field to cause an electric current in an electrical conductor.

Contents

Volts

The SI unit, Volt, is named after Alessandro Volta. As for all SI units whose names are derived from the proper name of a person, the first letter of its symbol is uppercase (V). But when an SI unit is spelled out, it should always be written in lowercase (volt), unless it begins a sentence or is the name "degree Celsius".

— Based on The International System of Units, section 5.2.

The volt (symbol: V) is the SI derived unit of electric potential difference or electromotive force. It is named in honor of the Italian physicist Alessandro Volta (1745–1827), who invented the voltaic pile, the first chemical battery.

Definition

The volt is defined as the potential difference across a conductor when a current of one ampere dissipates one watt of power. Hence, it is the base SI representation m2 · kg · s-3 · A-1, which can be equally represented as one joule of energy per coulomb of charge, J/C.

\mbox{V} = \mbox{W} \cdot \mbox{A}^{-1} = \mbox{J} \cdot \mbox{C}^{-1} = \mbox{m}^2 \cdot \mbox{kg} \cdot \mbox{s}^{-3} \cdot \mbox{A}^{-1}.

Since 1990 the volt is maintained internationally for practical measurement using the Josephson effect, where a conventional value is used for the Josephson constant, fixed by the 18th General Conference on Weights and Measures as

K{J-90} = 0.4835979 GHz/µV.

Common voltages

Nominal voltages of familiar sources:

Note: Where 'RMS' (root mean square) is stated above, the peak voltage is \sqrt{2} times higher than the RMS voltage.

History of the volt

In 1800, as the result of a professional disagreement over the galvanic response advocated by Luigi Galvani, Alessandro Volta developed the so-called Voltaic pile, a forerunner of the battery, which produced a steady electric current. Volta had determined that the most effective pair of dissimilar metals to produce electricity was zinc and silver. In the 1880s, the International Electrical Congress, now the International Electrotechnical Commission (IEC), approved the volt for electromotive force. The volt was defined as the potential difference across a conductor when a current of one ampere dissipates one watt of power.

Prior to the development of the Josephson junction voltage standard, the volt was maintained in national laboratories using specially constructed batteries called standard cells. The United States used a design called the Weston cell from 1905 to 1972.

Voltage explanation

Between two points in an electric field, such as exists in an electrical circuit, the difference in their electrical potentials is known as the electrical potential difference. This difference is proportional to the electrostatic force that tends to push electrons or other charge-carriers from one point to the other. Potential difference, electrical potential, and electromotive force are measured in volts, leading to the commonly used term voltage. Voltage is usually represented in equations by the symbols V, U or E. (E is often preferred in academic writing, because it avoids the confusion between V and the SI symbol for the volt, which is also V).

Electrical potential difference can be thought of as the ability to move electrical charge through a resistance. At a time in physics when the word force was used loosely, the potential difference was named the electromotive force or emf—a term which is still used in certain contexts.

Voltage is a property of an electric field, not individual electrons. An electron moving across a voltage difference experiences a net change in energy, often measured in electron-volts. This effect is analogous to a mass falling through a given height difference in a gravitational field.

When using the term 'potential difference' or voltage, one must be clear about the two points between which the voltage is specified or measured. There are two ways in which the term is used. This can lead to some confusion.

Voltage with respect to a common point

One way in which the term voltage is used is when specifying the voltage of a point in a circuit. When this is done, it is understood that the voltage is usually being specified or measured with respect to a stable and unchanging point in the circuit that is known as ground or common. We say that a point in a circuit has a particular voltage relative to ground when we take the time to say all the clarifying words. This voltage is really a voltage difference, one of the two points being the reference point, that is, ground. A voltage can be positive or negative. "High" or "low" voltage may refer to the magnitude (the absolute value relative to the reference point), thus a large negative voltage may be referred to as a high voltage. Other authors may refer to a voltage that is more negative, as being "lower".

Voltage between two stated points

Another usage 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 (loosely stated) or the voltage drop across the device (better, but not always stated for brevity) is really the first voltage taken (relative to ground) on one terminal of the device minus (hence a voltage difference) a second voltage taken (relative to ground) on the other terminal of the device. In practice, the voltage drop across a device can be measured directly and safely using a voltmeter (such as a battery-powered meter) that is isolated from ground, provided that the maximum voltage capability of the voltmeter is not exceeded.

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.

Two points in an electric circuit which are connected by an ideal conductor, without resistance and without the presence of a changing magnetic field, have a potential difference of zero. But other pairs of points may also have a potential difference of zero. If two such points are connected with a conductor, no current will flow through the connection.

High voltage

The term high voltage characterizes electrical circuits, in which the voltage used is the cause of particular safety concerns and insulation requirements. High voltage is used in electrical power distribution, in cathode-ray tubes, to generate X-rays and particle beams, to demonstrate arcing, for ignition, in photomultiplier tubes, and high power amplifier vacuum tubes.

The International Electrotechnical Commission and its national counterparts (IEE, IEEE, VDE, etc.) define high voltage circuits as those with at least 1000 V for alternating current and at least 1500 V for direct current, and distinguish it from low voltage (50–1000 V AC or 120–1500 V DC) and extra low voltage (<50 V AC or <120 V DC) circuits.

Other definitions exist as well. For example, in the United States 2005 National Electrical Code (NEC), high voltage is any voltage over 600 V (article 490.2). Laypersons may consider household mains circuits (100–250 V AC), which carry the highest and most dangerous voltages they normally encounter, to be high voltage. In digital electronics, a high voltage is the one that represents a logic 1 (1.1–5 V).

Safety and insurance industry

Whilst mains voltages are capable of delivering fatal shocks and may constitute high-voltage hazards, they cannot jump significant distances, so they are dangerous only if touched. Therefore standards bodies do not generally refer to them as high voltages.

Various safety and insurance organizations consider anything outside of the ELV range (i.e. greater than 50 V) to be dangerous and in need of regulation. Voltages above this range are capable of producing heart fibrillation if they produce electric currents in body tissues which happen to pass through the chest area. The electrocution danger is mostly determined by the low conductivity of dry human skin. If skin is wet (especially with electrolytes, including sea water) or if there are wounds, or if the voltage is applied to electrodes which penetrate through the skin, then even voltages far below 40 V can be lethally high. On the other hand, voltages above approximately 500 V have a natural defibrillating effect, so sometimes a higher voltage can be safer than a lower voltage, though by no means safe. A DC circuit may be especially dangerous because it will cause muscles to lock around the wire. It has also been noted that accidental contact with high voltage power lines has not always been fatal because sometimes the victim is thrown clear of the power line by the intensity of the arc that is created and has survived, although with extremely severe injuries.

Sparks in air

The dielectric breakdown strength of dry air, at Standard Temperature and Pressure (STP), between spherical electrodes is approximately 33 kV/cm. This value should be used as a rough guide since the actual breakdown voltage is highly dependent upon the electrode shape and size. High voltages, i.e. strong electric fields, often produce violet-colored corona discharges in air, as well as visible sparks. Voltages below about 500-700 volts cannot produce easily visible sparks or glows in air at atmospheric pressure, so by this rule these voltages are 'low.' However, under conditions of low atmospheric pressure (such as in high-altitude aircraft), or in an environment of noble gas such as argon, neon, etc., sparks will appear at much lower voltages. Five hundred to 700 volts is not a fixed minimum for producing spark breakdown, but it is a rule of thumb. For air at STP, the minimum sparkover voltage is around 380 volts.

While lower voltages will not generally jump a gap that is present before the voltage is applied, interrupting an existing current flow often produces a low voltage spark or arc. As the contacts are separated, a few small points of contact become the last to separate. The current becomes constricted to these small hot spots, causing them to become incandescent, so that they emit electrons (through thermionic emission). Even a small 9V battery can spark noticeably by this mechanism in a darkened room. The ionized air and metal vapour (from the contacts) form a plasma which temporarily bridges the widening gap. If the power supply and load allow sufficient current to flow, a self-sustaining arc may form. Once formed, an arc may be extended to a significant length before breaking the circuit. Attempting to open an inductive load facilitates the formation of an arc since the inductance provides a high voltage pulse whenever the current is interrupted. AC systems make sustained arcing somewhat less likely since the current returns to zero twice per cycle. The arc is extinguished every time the current goes through a zero crossing, and must reignite during the next half cycle in order to maintain the arc.

Science classroom devices

A high voltage is not necessarily dangerous. Physics demonstration devices such as Van de Graaff generators and Wimshurst machines can produce voltages approaching one million volts, yet at worst they deliver a brief sting. These devices have a limited amount of stored energy, so the current produced is low and usually for a short time. During the discharge, these machines apply high voltage to the body for only a millionth of a second or less. The discharge may involve extremely high power over very short periods, but in order to produce heart fibrillation, an electric power supply must produce a significant current in the heart muscle continuing for many milliseconds, and must deposit a total energy in the range of at least millijoules or higher. Alternatively, it must deliver enough energy to damage tissue through heating. Since the duration of the discharge is brief, it generates far less heat (spread over time) than a mobile phone.

Note that Tesla coils are a special case, and touching them is not recommended. Among other issues, they have a tendency to arc to their own bottom-end circuitry, which can introduce powerline frequency (50 Hz or 60 Hz, and capable in any case of depolarizing cells and stopping the heart) currents at lethally high voltages to the body.

Electrostatic attraction/repulsion

The terminals of DC high voltage machines can attract dust, lint, and bits of paper. On an everyday scale, voltages higher than a few thousand volts are required in order to create an electric field with a gradient large enough to produce nontrivial forces. On the other hand, the forces depend on the distance from the electrodes and the electrode shapes, and at the microscopic scale of MEMS, even a few tens of volts acts like a high voltage.

Power lines

Electrical transmission and distribution lines for electric power always use voltages significantly higher than 50 volts, so contact with or close approach to the line conductors presents a danger of electrocution. Contact with overhead wires is a frequent cause of injury or death. Metal ladders, farm equipment, boat masts, construction machinery, television antennas, and similar objects are frequently involved in fatal contact with overhead wires. Digging into a buried cable can also be dangerous to workers at the excavation site. Digging equipment (either hand tools or machine driven) that contacts a buried cable may energize piping or the ground in the area, resulting in electrocution of nearby workers. Unauthorized persons climbing on power pylons or electrical apparatus are also frequently the victims of electrocution. At very high transmission voltages even a close approach can be hazardous since the high voltage may spark across a significant air gap.

For high voltage and extra-high voltage transmission lines, specially trained personnel use so-called "live line" techniques to allow hands-on contact with energized equipment. In this case the worker is electrically connected to the high voltage line so that he is at the same electrical potential. Since training for such operations is lengthy, and still presents a danger to personnel, only very important transmission lines are the objects of live-line maintenance practices. Outside these specialized situations, one should not assume that being ungrounded allows one to safely touch energized objects; grounding, or arcing to ground, can occur in unexpected ways, and high-frequency currents can cause burns even to an ungrounded person (touching a transmitting antenna is dangerous for this reason, and likewise a high-frequency Tesla Coil can sustain a spark with only one endpoint).

Normally protective equipment on high-voltage transmission lines prevents formation of an unwanted arc, or insures it is de-energized within tens of milliseconds. Electrical apparatus designed to interrupt high-voltage circuits is designed to safely direct the resulting arc so that it dissipates without damage. High voltage circuit breakers often use a blast of high pressure air, a special dielectric gas (such as SF6 under pressure), or immersion in mineral oil to quench the arc when the high voltage circuit is broken.

Arc flash hazard

Depending on the short circuit current available at a switchgear line-up, a hazard is presented to maintenance and operating personnel due to the possibility of a high-intensity electric arc. Maximum temperature of an arc can exceed 10,000 kelvins, and the radiant heat, expanding hot air, and explosive vaporization of metal and insulation material can cause severe injury to unprotected workers. Such switchgear line-ups and high-energy arc sources are commonly present in electric power utility substations and generating stations, industrial plants and large commercial buildings. In the United States the National Fire Protection Association, has published a guideline standard NFPA 70E for evaluating and calculating arc flash hazard, and provides standards for the protective clothing required for electrical workers exposed to such hazards in the workplace.

Explosion hazard

Even voltages insufficient to break down air can be associated with enough energy to ignite atmospheres containing flammable gases or vapours, or suspended dust. For example, air containing hydrogen gas or natural gas or gasoline vapor can be ignited by sparks produced by electrical apparatus. Examples of industrial facilities with hazardous areas are petrochemical refineries, chemical plants, grain elevators, and some kinds of coal mines.

Measures taken to prevent such explosions include:

  • Intrinsic safety, which is apparatus designed to not accumulate enough stored energy to touch off an explosion
  • Increased safety, which applies to devices using measures such as oil-filled enclosures to prevent contact between sparking apparatus and an explosive atmosphere
  • Explosion-proof enclosures, which are designed so that an explosion within the enclosure cannot escape and touch off the surrounding atmosphere (this designation does not imply that the apparatus will survive an internal or external explosion).

In recent years standards for explosion hazard protection have become more uniform between European and North American practice. The "zone" system of classification is now used in modified form in U.S. National Electrical Code and in the Canadian electrical code. Intrinsic safety apparatus is now approved for use in North American applications, though the explosion-proof enclosures used in North America are still uncommon in Europe.

Toxic gases

Electrical discharges, including partial discharge and corona, can produce small quantities of toxic gases, which in a confined space can prove a serious health hazard. These gases include ozone and various oxides of nitrogen.

Lightning

The largest-scale sparks are those produced naturally by lightning. An average bolt of negative lightning carries a current of 30-to-50 kiloamperes, and transfers a charge of 5 coulombs, and disssipates 500 megajoules of energy (enough to light a 100 watt light bulb for 2 months). However, an average bolt of positive lightning (from the top of a thunderstorm) may carry a current of 300-to-500 kiloamperes, transfer a charge of up to 300 coulombs, have a potential difference up to 1 gigavolt (a billion volts), and may dissipate enough energy to light a 100 watt lightbulb for up to 95 years. A negative lightning stroke typically lasts for only tens of microseconds, but multiple strikes are common. A positive lightning stroke is typically a single event. However, the larger peak current may flow for hundreds of milliseconds, making it considerably hotter and more dangerous than negative lightning.

Hazards due to lightning obviously include a direct strike on persons or property. However, lightning can also create dangerous voltage gradients in the earth, and can charge extended metal objects such as telephone cables, fences, and pipelines to dangerous voltages that can be carried many miles from the site of the strike. These transferred potentials are dangerous to people, livestock, and electronic apparatus. Lightning strikes also start fires and explosions which result in fatalities, injuries, and property damage. For example, each year in North America, thousands of forest fires are started by lightning strikes.

Measures to control lightning can mitigate the hazard; these include lightning rods, shielding wires, and bonding of electrical and structural parts of buildings to form a continuous enclosure. Lightning discharges in the atmosphere of Jupiter are thought to be the source of that planet's powerful radio frequency emissions.

Hydraulic analogy

If one imagines water circulating in a network of pipes, driven by pumps in the absence of gravity, as an analogy of an electrical circuit, then the potential difference corresponds to the fluid pressure difference between two points. If there is a pressure difference between two points, then water flowing from the first point to the second will be able to do work, such as driving a turbine.

This hydraulic analogy is a useful method of teaching a range of electrical concepts. In a hydraulic 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 quantifying the ability to do work. In relation to electric current, the larger the gradient (voltage or hydraulic) the greater the current (assuming resistance is constant).

Mathematical definition

The electrical potential difference is defined as the amount of work needed to move a unit electric charge from the second point to the first, or equivalently, the amount of work that a unit charge flowing from the first point to the second can perform. The potential difference between two points a and b is the line integral of the electric field E:

V_a - V_b = \int _a ^b {E}\cdot d{l}

Useful formulas

DC circuits

V = \sqrt{PR}
V = \frac{P}{I}
V = IR \!\

Where V=voltage, I=current, R=resistance, P=power

AC circuits

V = \frac{P}{I\cos\theta}
V = \frac{\sqrt{PZ}}{\sqrt{\cos\theta}} \!\
V = \frac{IR}{\cos\theta}

Where V=voltage, I=current, R=resistance, P=true power, Z=impedance, θ=phasor angle between I and V

AC conversions

V_{avg} = .637\,V_{pk} \!\
V_{rms} = .707\,V_{pk} \!\
V_{rms} = .354\,V_{ppk}\!\
V_{avg} = .319\,V_{ppk} \!\
V_{avg} = 0.9\,V_{rms} \!\
V_{pk} = 0.5\,V_{ppk} \!\

Where Vpk=peak voltage, Vppk=peak-to-peak voltage, Vavg=average voltage over a half-cycle, Vrms=effective (root mean square) voltage

Total voltage

Voltage sources and drops in series:

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

Voltage sources and drops in parallel:

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

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.

Measuring instruments

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

Safety

Electrical safety is discussed in the articles on High voltage and Electric shock.

Related concepts

External articles and references

See also

- PowerPedia main index
- PESWiki home page

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