# Electric current

An electric current is the rate of flow of electric charge past a point[1]:2[2]:622 or region.[2]:614 An electric current is said to exist when there is a net flow of electric charge through a region.[3]:832 In electric circuits this charge is often carried by electrons moving through a wire. It can also be carried by ions in an electrolyte, or by both ions and electrons such as in an ionized gas (plasma).[4]

The SI unit of electric current is the ampere , which is the flow of electric charge across a surface at the rate of one coulomb per second. The ampere (symbol: A) is a SI base unit[5]:15 Electric current is measured using a device called an ammeter.[2]:788

Electric currents cause Joule heating, which creates light in incandescent light bulbs. They also create magnetic fields, which are used in motors, inductors and generators.

The moving charged particles in an electric current are called charge carriers. In metals, one or more electrons from each atom are loosely bound to the atom, and can move freely about within the metal. These conduction electrons are the charge carriers in metal conductors.

Electric current
A simple electric circuit, where current is represented by the letter i. The relationship between the voltage (V), resistance (R), and current (I) is V=IR; this is known as Ohm's law.
Common symbols
I
SI unitampere
Derivations from
other quantities
${\displaystyle I={V \over R}\,,I={Q \over t}}$
DimensionI

## Symbol

The conventional symbol for current is I, which originates from the French phrase intensité du courant, (current intensity).[6][7] Current intensity is often referred to simply as current.[8] The I symbol was used by André-Marie Ampère, after whom the unit of electric current is named, in formulating Ampère's force law (1820).[9] The notation travelled from France to Great Britain, where it became standard, although at least one journal did not change from using C to I until 1896.[10]

## Conventions

The electrons, the charge carriers in an electrical circuit, flow in the opposite direction of the conventional electric current.
The symbol for a battery in a circuit diagram.

In a conductive material, the moving charged particles that constitute the electric current are called charge carriers. In metals, which make up the wires and other conductors in most electrical circuits, the positively charged atomic nuclei of the atoms are held in a fixed position, and the negatively charged electrons are the charge carriers, free to move about in the metal. In other materials, notably the semiconductors, the charge carriers can be positive or negative, depending on the dopant used. Positive and negative charge carriers may even be present at the same time, as happens in an electrolyte in an electrochemical cell.

A flow of positive charges gives the same electric current, and has the same effect in a circuit, as an equal flow of negative charges in the opposite direction. Since current can be the flow of either positive or negative charges, or both, a convention is needed for the direction of current that is independent of the type of charge carriers. The direction of conventional current is arbitrarily defined as the same direction as positive charges flow.

Since electrons, the charge carriers in metal wires and most other parts of electric circuits, have a negative charge, as a consequence, they flow in the opposite direction of conventional current flow in an electrical circuit.

### Reference direction

Since the current in a wire or component can flow in either direction, when a variable I is defined to represent that current, the direction representing positive current must be specified, usually by an arrow on the circuit schematic diagram. This is called the reference direction of current I. If the current flows in the opposite direction, the variable I has a negative value.

When analyzing electrical circuits, the actual direction of current through a specific circuit element is usually unknown. Consequently, the reference directions of currents are often assigned arbitrarily. When the circuit is solved, a negative value for the variable means that the actual direction of current through that circuit element is opposite that of the chosen reference direction. In electronic circuits, the reference current directions are often chosen so that all currents are toward ground. This often corresponds to the actual current direction, because in many circuits the power supply voltage is positive with respect to ground.

## Ohm's law

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance,[11] one arrives at the usual mathematical equation that describes this relationship:[12]

${\displaystyle I={\frac {V}{R}}}$

where I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.[13]

## Alternating and direct current

In alternating current (AC) systems, the movement of electric charge periodically reverses direction. AC is the form of electric power most commonly delivered to businesses and residences. The usual waveform of an AC power circuit is a sine wave. Certain applications use different waveforms, such as triangular or square waves. Audio and radio signals carried on electrical wires are also examples of alternating current. An important goal in these applications is recovery of information encoded (or modulated) onto the AC signal.

In contrast, direct current (DC) is the unidirectional flow of electric charge, or a system in which the movement of electric charge is in one direction only. Direct current is produced by sources such as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through semiconductors, insulators, or even through a vacuum as in electron or ion beams. An old name for direct current was galvanic current.[14]

## Occurrences

Natural observable examples of electrical current include lightning, static electric discharge, and the solar wind, the source of the polar auroras.

Man-made occurrences of electric current include the flow of conduction electrons in metal wires such as the overhead power lines that deliver electrical energy across long distances and the smaller wires within electrical and electronic equipment. Eddy currents are electric currents that occur in conductors exposed to changing magnetic fields. Similarly, electric currents occur, particularly in the surface, of conductors exposed to electromagnetic waves. When oscillating electric currents flow at the correct voltages within radio antennas, radio waves are generated.

In electronics, other forms of electric current include the flow of electrons through resistors or through the vacuum in a vacuum tube, the flow of ions inside a battery or a neuron, and the flow of holes within metals and semiconductors.

## Current measurement

Current can be measured using an ammeter.

Electric current can be directly measured with a galvanometer, but this method involves breaking the electrical circuit, which is sometimes inconvenient.

Current can also be measured without breaking the circuit by detecting the magnetic field associated with the current. Devices, at the circuit level, use various techniques to measure current:

## Resistive heating

Joule heating, also known as ohmic heating and resistive heating, is the process of power dissipation[17]:36 by which the passage of an electric current through a conductor increases the internal energy of the conductor[3]:846, converting thermodynamic work into heat.[3]:846, fn. 5 The phenomenon was first studied by James Prescott Joule in 1841. Joule immersed a length of wire in a fixed mass of water and measured the temperature rise due to a known current through the wire for a 30 minute period. By varying the current and the length of the wire he deduced that the heat produced was proportional to the square of the current multiplied by the electrical resistance of the wire.

${\displaystyle P\propto I^{2}R}$

This relationship is known as Joule's Law.[17]:36 The SI unit of energy was subsequently named the joule and given the symbol J.[5]:20 The commonly known SI unit of power, the watt (symbol: W), is equivalent to one joule per second.[5]:20

## Electromagnetism

### Electromagnet

In an electromagnet a coil of wires behaves like a magnet when an electric current flows through it. When the current is switched off, the coil loses its magnetism immediately.

According to Ampère's circuital law, an electric current produces a magnetic field.

Electric current produces a magnetic field. The magnetic field can be visualized as a pattern of circular field lines surrounding the wire that persists as long as there is current.

### Electromagnetic induction

Magnetic fields can also be used to make electric currents. When a changing magnetic field is applied to a conductor, an electromotive force (EMF) is induced,[3]:1004 which starts an electric current, when there is a suitable path.

When an electric current flows in a suitably shaped conductor at radio frequencies, radio waves can be generated. These travel at the speed of light and can cause electric currents in distant conductors.

## Conduction mechanisms in various media

In metallic solids, electric charge flows by means of electrons, from lower to higher electrical potential. In other media, any stream of charged objects (ions, for example) may constitute an electric current. To provide a definition of current independent of the type of charge carriers, conventional current is defined as moving in the same direction as the positive charge flow. So, in metals where the charge carriers (electrons) are negative, conventional current is in the opposite direction as the electrons. In conductors where the charge carriers are positive, conventional current is in the same direction as the charge carriers.

In a vacuum, a beam of ions or electrons may be formed. In other conductive materials, the electric current is due to the flow of both positively and negatively charged particles at the same time. In still others, the current is entirely due to positive charge flow. For example, the electric currents in electrolytes are flows of positively and negatively charged ions. In a common lead-acid electrochemical cell, electric currents are composed of positive hydronium ions flowing in one direction, and negative sulfate ions flowing in the other. Electric currents in sparks or plasma are flows of electrons as well as positive and negative ions. In ice and in certain solid electrolytes, the electric current is entirely composed of flowing ions.

### Metals

In a metal, some of the outer electrons in each atom are not bound to the individual atom as they are in insulating materials, but are free to move within the metal lattice. These conduction electrons can serve as charge carriers, carrying a current. Metals are particularly conductive because there are a large number of these free electrons, typically one per atom in the lattice. With no external electric field applied, these electrons move about randomly due to thermal energy but, on average, there is zero net current within the metal. At room temperature, the average speed of these random motions is 106 metres per second.[18] Given a surface through which a metal wire passes, electrons move in both directions across the surface at an equal rate. As George Gamow wrote in his popular science book, One, Two, Three...Infinity (1947), "The metallic substances differ from all other materials by the fact that the outer shells of their atoms are bound rather loosely, and often let one of their electrons go free. Thus the interior of a metal is filled up with a large number of unattached electrons that travel aimlessly around like a crowd of displaced persons. When a metal wire is subjected to electric force applied on its opposite ends, these free electrons rush in the direction of the force, thus forming what we call an electric current."

When a metal wire is connected across the two terminals of a DC voltage source such as a battery, the source places an electric field across the conductor. The moment contact is made, the free electrons of the conductor are forced to drift toward the positive terminal under the influence of this field. The free electrons are therefore the charge carrier in a typical solid conductor.

For a steady flow of charge through a surface, the current I (in amperes) can be calculated with the following equation:

${\displaystyle I={Q \over t}\,,}$

where Q is the electric charge transferred through the surface over a time t. If Q and t are measured in coulombs and seconds respectively, I is in amperes.

More generally, electric current can be represented as the rate at which charge flows through a given surface as:

${\displaystyle I={\frac {\mathrm {d} Q}{\mathrm {d} t}}\,.}$

### Electrolytes

Electric currents in electrolytes are flows of electrically charged particles (ions). For example, if an electric field is placed across a solution of Na+ and Cl (and conditions are right) the sodium ions move towards the negative electrode (cathode), while the chloride ions move towards the positive electrode (anode). Reactions take place at both electrode surfaces, neutralizing each ion.

Water-ice and certain solid electrolytes called proton conductors contain positive hydrogen ions ("protons") that are mobile. In these materials, electric currents are composed of moving protons, as opposed to the moving electrons in metals.

In certain electrolyte mixtures, brightly coloured ions are the moving electric charges. The slow progress of the colour makes the current visible.[19]

### Gases and plasmas

In air and other ordinary gases below the breakdown field, the dominant source of electrical conduction is via relatively few mobile ions produced by radioactive gases, ultraviolet light, or cosmic rays. Since the electrical conductivity is low, gases are dielectrics or insulators. However, once the applied electric field approaches the breakdown value, free electrons become sufficiently accelerated by the electric field to create additional free electrons by colliding, and ionizing, neutral gas atoms or molecules in a process called avalanche breakdown. The breakdown process forms a plasma that contains enough mobile electrons and positive ions to make it an electrical conductor. In the process, it forms a light emitting conductive path, such as a spark, arc or lightning.

Plasma is the state of matter where some of the electrons in a gas are stripped or "ionized" from their molecules or atoms. A plasma can be formed by high temperature, or by application of a high electric or alternating magnetic field as noted above. Due to their lower mass, the electrons in a plasma accelerate more quickly in response to an electric field than the heavier positive ions, and hence carry the bulk of the current. The free ions recombine to create new chemical compounds (for example, breaking atmospheric oxygen into single oxygen [O2 → 2O], which then recombine creating ozone [O3]).[20]

### Vacuum

Since a "perfect vacuum" contains no charged particles, it normally behaves as a perfect insulator. However, metal electrode surfaces can cause a region of the vacuum to become conductive by injecting free electrons or ions through either field electron emission or thermionic emission. Thermionic emission occurs when the thermal energy exceeds the metal's work function, while field electron emission occurs when the electric field at the surface of the metal is high enough to cause tunneling, which results in the ejection of free electrons from the metal into the vacuum. Externally heated electrodes are often used to generate an electron cloud as in the filament or indirectly heated cathode of vacuum tubes. Cold electrodes can also spontaneously produce electron clouds via thermionic emission when small incandescent regions (called cathode spots or anode spots) are formed. These are incandescent regions of the electrode surface that are created by a localized high current. These regions may be initiated by field electron emission, but are then sustained by localized thermionic emission once a vacuum arc forms. These small electron-emitting regions can form quite rapidly, even explosively, on a metal surface subjected to a high electrical field. Vacuum tubes and sprytrons are some of the electronic switching and amplifying devices based on vacuum conductivity.

### Superconductivity

Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of magnetic fields occurring in certain materials when cooled below a characteristic critical temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum mechanical phenomenon. It is characterized by the Meissner effect, the complete ejection of magnetic field lines from the interior of the superconductor as it transitions into the superconducting state. The occurrence of the Meissner effect indicates that superconductivity cannot be understood simply as the idealization of perfect conductivity in classical physics.

### Semiconductor

In a semiconductor it is sometimes useful to think of the current as due to the flow of positive "holes" (the mobile positive charge carriers that are places where the semiconductor crystal is missing a valence electron). This is the case in a p-type semiconductor. A semiconductor has electrical conductivity intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 10−2 to 104 siemens per centimeter (S⋅cm−1).

In the classic crystalline semiconductors, electrons can have energies only within certain bands (i.e. ranges of levels of energy). Energetically, these bands are located between the energy of the ground state, the state in which electrons are tightly bound to the atomic nuclei of the material, and the free electron energy, the latter describing the energy required for an electron to escape entirely from the material. The energy bands each correspond to a large number of discrete quantum states of the electrons, and most of the states with low energy (closer to the nucleus) are occupied, up to a particular band called the valence band. Semiconductors and insulators are distinguished from metals because the valence band in any given metal is nearly filled with electrons under usual operating conditions, while very few (semiconductor) or virtually none (insulator) of them are available in the conduction band, the band immediately above the valence band.

The ease of exciting electrons in the semiconductor from the valence band to the conduction band depends on the band gap between the bands. The size of this energy band gap serves as an arbitrary dividing line (roughly 4 eV) between semiconductors and insulators.

With covalent bonds, an electron moves by hopping to a neighboring bond. The Pauli exclusion principle requires that the electron be lifted into the higher anti-bonding state of that bond. For delocalized states, for example in one dimension – that is in a nanowire, for every energy there is a state with electrons flowing in one direction and another state with the electrons flowing in the other. For a net current to flow, more states for one direction than for the other direction must be occupied. For this to occur, energy is required, as in the semiconductor the next higher states lie above the band gap. Often this is stated as: full bands do not contribute to the electrical conductivity. However, as a semiconductor's temperature rises above absolute zero, there is more energy in the semiconductor to spend on lattice vibration and on exciting electrons into the conduction band. The current-carrying electrons in the conduction band are known as free electrons, though they are often simply called electrons if that is clear in context.

## Current density and Ohm's law

Current density is the rate at which charge passes through a chosen unit area.[21]:31 It is defined as a vector whose magnitude is the current per unit cross-sectional area.[2]:749 As discussed in Reference direction, the direction is arbitrary. Conventionally, if the moving charges are positive, then the current density has the same sign as the velocity of the charges. For negative charges, the sign of the current density is opposite to the velocity of the charges.[2]:749 In SI units, current density (symbol: j) is expressed in the SI base units of amperes per square metre.[5]:22

In linear materials such as metals, and under low frequencies, the current density across the conductor surface is uniform. In such conditions, Ohm's law states that the current is directly proportional to the potential difference between two ends (across) of that metal (ideal) resistor (or other ohmic device):

${\displaystyle I={V \over R}\,,}$

where ${\displaystyle I}$ is the current, measured in amperes; ${\displaystyle V}$ is the potential difference, measured in volts; and ${\displaystyle R}$ is the resistance, measured in ohms. For alternating currents, especially at higher frequencies, skin effect causes the current to spread unevenly across the conductor cross-section, with higher density near the surface, thus increasing the apparent resistance.

## Drift speed

The mobile charged particles within a conductor move constantly in random directions, like the particles of a gas. (More accurately, a Fermi gas.) To create a net flow of charge, the particles must also move together with an average drift rate. Electrons are the charge carriers in most metals and they follow an erratic path, bouncing from atom to atom, but generally drifting in the opposite direction of the electric field. The speed they drift at can be calculated from the equation:

${\displaystyle I=nAvQ\,,}$

where

${\displaystyle I}$ is the electric current
${\displaystyle n}$ is number of charged particles per unit volume (or charge carrier density)
${\displaystyle A}$ is the cross-sectional area of the conductor
${\displaystyle v}$ is the drift velocity, and
${\displaystyle Q}$ is the charge on each particle.

Typically, electric charges in solids flow slowly. For example, in a copper wire of cross-section 0.5 mm2, carrying a current of 5 A, the drift velocity of the electrons is on the order of a millimetre per second. To take a different example, in the near-vacuum inside a cathode ray tube, the electrons travel in near-straight lines at about a tenth of the speed of light.

Any accelerating electric charge, and therefore any changing electric current, gives rise to an electromagnetic wave that propagates at very high speed outside the surface of the conductor. This speed is usually a significant fraction of the speed of light, as can be deduced from Maxwell's Equations, and is therefore many times faster than the drift velocity of the electrons. For example, in AC power lines, the waves of electromagnetic energy propagate through the space between the wires, moving from a source to a distant load, even though the electrons in the wires only move back and forth over a tiny distance.

The ratio of the speed of the electromagnetic wave to the speed of light in free space is called the velocity factor, and depends on the electromagnetic properties of the conductor and the insulating materials surrounding it, and on their shape and size.

The magnitudes (not the natures) of these three velocities can be illustrated by an analogy with the three similar velocities associated with gases. (See also hydraulic analogy.)

• The low drift velocity of charge carriers is analogous to air motion; in other words, winds.
• The high speed of electromagnetic waves is roughly analogous to the speed of sound in a gas (sound waves move through air much faster than large-scale motions such as convection)
• The random motion of charges is analogous to heat – the thermal velocity of randomly vibrating gas particles.

## References

1. ^ Horowitz, Paul; Hill, Winfield (2015). The art of electronics (3rd ed.). Cambridge University Press. ISBN 978-0-521-80926-9.
2. Walker, Jearl; Halliday, David; Resnick, Robert (2014). Fundamentals of physics (10th ed.). Hoboken, NJ: Wiley. ISBN 9781118230732. OCLC 950235056.
3. ^ a b c d Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Thomson Brooks/Cole. ISBN 0-534-40842-7.
4. ^ Anthony C. Fischer-Cripps (2004). The electronics companion. CRC Press. p. 13. ISBN 978-0-7503-1012-3.
5. ^ a b c d International Bureau of Weights and Measures (2018-02-05), SI Brochure: The International System of Units (SI) (PDF) (Draft) (9th ed.)
6. ^ T. L. Lowe, John Rounce, Calculations for A-level Physics, p. 2, Nelson Thornes, 2002 ISBN 0-7487-6748-7.
7. ^ Howard M. Berlin, Frank C. Getz, Principles of Electronic Instrumentation and Measurement, p. 37, Merrill Pub. Co., 1988 ISBN 0-675-20449-6.
8. ^ K. S. Suresh Kumar, Electric Circuit Analysis, Pearson Education India, 2013, ISBN 9332514100, section 1.2.3 "'Current intensity' is usually referred to as 'current' itself."
9. ^ A-M Ampère, Recueil d'Observations Électro-dynamiques, p. 56, Paris: Chez Crochard Libraire 1822 (in French).
10. ^ Electric Power, vol. 6, p. 411, 1894.
11. ^ Consoliver, Earl L.; Mitchell, Grover I. (1920). Automotive ignition systems. McGraw-Hill. p. 4.
12. ^ Robert A. Millikan and E. S. Bishop (1917). Elements of Electricity. American Technical Society. p. 54.
13. ^ Oliver Heaviside (1894). Electrical papers. 1. Macmillan and Co. p. 283. ISBN 978-0-8218-2840-3.
14. ^ Andrew J. Robinson; Lynn Snyder-Mackler (2007). Clinical Electrophysiology: Electrotherapy and Electrophysiologic Testing (3rd ed.). Lippincott Williams & Wilkins. p. 10. ISBN 978-0-7817-4484-3.
15. ^ What is a Current Sensor and How is it Used?. Focus.ti.com. Retrieved on 2011-12-22.
16. ^ Andreas P. Friedrich, Helmuth Lemme The Universal Current Sensor. Sensorsmag.com (2000-05-01). Retrieved on 2011-12-22.
17. ^ a b Jaffe, Robert L.; Taylor, Washington (2018). The physics of energy. Cambridge University Press.
18. ^ "The Mechanism Of Conduction In Metals", Think Quest.
19. ^ Rudolf Holze, Experimental Electrochemistry: A Laboratory Textbook, page 44, John Wiley & Sons, 2009 ISBN 3527310983.
20. ^ "Lab Note #106 Environmental Impact of Arc Suppression". Arc Suppression Technologies. April 2011. Retrieved March 15, 2012.
21. ^ Zangwill, Andrew (2013). Modern Electrodynamics. Cambridge University Press. ISBN 978-0-521-89697-9.
Alternating current

Alternating current (AC) is an electric current which periodically reverses direction, in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in which electric power is delivered to businesses and residences, and it is the form of electrical energy that consumers typically use when they plug kitchen appliances, televisions, fans and electric lamps into a wall socket. A common source of DC power is a battery cell in a flashlight. The abbreviations AC and DC are often used to mean simply alternating and direct, as when they modify current or voltage.The usual waveform of alternating current in most electric power circuits is a sine wave, whose positive half-period corresponds with positive direction of the current and vice versa. In certain applications, different waveforms are used, such as triangular or square waves. Audio and radio signals carried on electrical wires are also examples of alternating current. These types of alternating current carry information such as sound (audio) or images (video) sometimes carried by modulation of an AC carrier signal. These currents typically alternate at higher frequencies than those used in power transmission.

Ampere

The ampere (; symbol: A), often shortened to "amp", is the base unit of electric current in the International System of Units (SI). It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics.

The International System of Units defines the ampere in terms of other base units by measuring the electromagnetic force between electrical conductors carrying electric current. The earlier CGS measurement system had two different definitions of current, one essentially the same as the SI's and the other using electric charge as the base unit, with the unit of charge defined by measuring the force between two charged metal plates. The ampere was then defined as one coulomb of charge per second. In SI, the unit of charge, the coulomb, is defined as the charge carried by one ampere during one second.

New definitions, in terms of invariant constants of nature, specifically the elementary charge, will take effect on 20 May 2019.

Aqueous solution

An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be represented as Na+(aq) + Cl−(aq). The word aqueous (comes from aqua) means pertaining to, related to, similar to, or dissolved in, water. As water is an excellent solvent and is also naturally abundant, it is a ubiquitous solvent in chemistry. Aqueous solution is water with a pH of 7.0 where the hydrogen ions (H+) and hydroxide ions (OH-) are in Arrhenius balance (10-7).

A non-aqueous solution is a solution in which the solvent is a liquid, but is not water.Substances that are hydrophobic ('water-fearing') often do not dissolve well in water, whereas those that are hydrophilic ('water-friendly') do. An example of a hydrophilic substance is sodium chloride. Acids and bases are aqueous solutions, as part of their Arrhenius definitions.

The ability of a substance to dissolve in water is determined by whether the substance can match or exceed the strong attractive forces that water molecules generate between themselves. If the substance lacks the ability to dissolve in water the molecules form a precipitate.

Reactions in aqueous solutions are usually metathesis reactions. Metathesis reactions are another term for double-displacement; that is, when a cation displaces to form an ionic bond with the other anion. The cation bonded with the latter anion will dissociate and bond with the other anion.

Aqueous solutions that conduct electric current efficiently contain strong electrolytes, while ones that conduct poorly are considered to have weak electrolytes. Those strong electrolytes are substances that are completely ionized in water, whereas the weak electrolytes exhibit only a small degree of ionization in water.

Nonelectrolytes are substances that dissolve in water yet maintain their molecular integrity (do not dissociate into ions). Examples include sugar, urea, glycerol, and methylsulfonylmethane (MSM).

When writing the equations of aqueous reactions, it is essential to determine the precipitate. To determine the precipitate, one must consult a chart of solubility. Soluble compounds are aqueous, while insoluble compounds are the precipitate. There may not always be a precipitate.

When performing calculations regarding the reacting of one or more aqueous solutions, in general one must know the concentration, or molarity, of the aqueous solutions. Solution concentration is given in terms of the form of the solute prior to it dissolving.

Aqueous solutions may contain, especially in alcaline zone or subjected to radiolysis, hydrated atomic hydrogen an hydrated electron.

Biot–Savart law

In physics, specifically electromagnetism, the Biot–Savart Law ( or ) is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The Biot–Savart law is fundamental to magnetostatics, playing a role similar to that of Coulomb's law in electrostatics. When magnetostatics does not apply, the Biot–Savart law should be replaced by Jefimenko's equations. The law is valid in the magnetostatic approximation, and is consistent with both Ampère's circuital law and Gauss's law for magnetism. It is named after Jean-Baptiste Biot and Félix Savart, who discovered this relationship in 1820.

Current density

In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the charges at this point. In SI base units, the electric current density is measured in amperes per square metre.

Direct current

Direct current (DC) is the unidirectional flow of electric charge. A battery is a good example of a DC power supply. Direct current may flow in a conductor such as a wire, but can also flow through semiconductors, insulators, or even through a vacuum as in electron or ion beams. The electric current flows in a constant direction, distinguishing it from alternating current (AC). A term formerly used for this type of current was galvanic current.The abbreviations AC and DC are often used to mean simply alternating and direct, as when they modify current or voltage.Direct current may be obtained from an alternating current supply by use of a rectifier, which contains electronic elements (usually) or electromechanical elements (historically) that allow current to flow only in one direction. Direct current may be converted into alternating current with an inverter or a motor-generator set.

Direct current is used to charge batteries and as a power supply for electronic systems. Very large quantities of direct-current power are used in production of aluminum and other electrochemical processes. It is also used for some railways, especially in urban areas. High-voltage direct current is used to transmit large amounts of power from remote generation sites or to interconnect alternating current power grids.

Displacement current

In electromagnetism, displacement current density is the quantity ∂D/∂t appearing in Maxwell's equations that is defined in terms of the rate of change of D, the electric displacement field. Displacement current density has the same units as electric current density, and it is a source of the magnetic field just as actual current is. However it is not an electric current of moving charges, but a time-varying electric field. In physical materials (as opposed to vacuum), there is also a contribution from the slight motion of charges bound in atoms, called dielectric polarization.

The idea was conceived by James Clerk Maxwell in his 1861 paper On Physical Lines of Force, Part III in connection with the displacement of electric particles in a dielectric medium. Maxwell added displacement current to the electric current term in Ampère's Circuital Law. In his 1865 paper A Dynamical Theory of the Electromagnetic Field Maxwell used this amended version of Ampère's Circuital Law to derive the electromagnetic wave equation. This derivation is now generally accepted as a historical landmark in physics by virtue of uniting electricity, magnetism and optics into one single unified theory. The displacement current term is now seen as a crucial addition that completed Maxwell's equations and is necessary to explain many phenomena, most particularly the existence of electromagnetic waves.

Electrical energy

Electrical energy is energy derived from electric potential energy or kinetic energy. When used loosely, "electrical energy" refers to energy that has been converted from electric potential energy. This energy is supplied by the combination of electric current and electric potential that is delivered by an electrical circuit (e.g., provided by an electric power utility). At the point that this electric potential energy has been converted to another type of energy, it ceases to be electric potential energy.

Thus, all electrical energy is potential energy before it is delivered to the end-use. Once converted from potential energy, electrical energy can always be called another type of energy (heat, light, motion, etc.).

Electrical injury

Electrical injury is a physiological reaction caused by electric current passing through the (human) body. Electric shock occurs upon contact of a (human) body part with any source of electricity that causes a sufficient magnitude of current to pass through the victim's flesh, viscera or hair. Physical contact with energized wiring or devices is the most common cause of an electric shock. In cases of exposure to high voltages, such as on a power transmission tower, physical contact with energized wiring or objects may not be necessary to cause electric shock, as the voltage may be sufficient to "jump" the air gap between the electrical device and the victim.

The injury related to electric shock depends on the magnitude of the current. Very small currents may be imperceptible or produce a light tingling sensation. A shock caused by low current that would normally be harmless could startle an individual and cause injury due to suddenly jerking away from the source of electricity, resulting in one striking a stationary object, dropping an object being held or falling. Stronger currents may cause some degree of discomfort or pain, while more intense currents may induce involuntary muscle contractions, preventing the victim from breaking free of the source of electricity. Still larger currents usually result in tissue damage and may trigger fibrillation of the heart or cardiac arrest, any of which may ultimately be fatal. If death results from an electric shock the cause of death is generally referred to as electrocution.

Electrical resistance and conductance

The electrical resistance of an object is a measure of its opposition to the flow of electric current. The inverse quantity is electrical conductance, and is the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with the notion of mechanical friction. The SI unit of electrical resistance is the ohm (Ω), while electrical conductance is measured in siemens (S).

The resistance of an object depends in large part on the material it is made of—objects made of electrical insulators like rubber tend to have very high resistance and low conductivity, while objects made of electrical conductors like metals tend to have very low resistance and high conductivity. This material dependence is quantified by resistivity or conductivity. However, resistance and conductance are extensive rather than bulk properties, meaning that they also depend on the size and shape of an object. For example, a wire's resistance is higher if it is long and thin, and lower if it is short and thick. All objects show some resistance, except for superconductors, which have a resistance of zero.

The resistance (R) of an object is defined as the ratio of voltage across it (V) to current through it (I), while the conductance (G) is the inverse:

${\displaystyle R={V \over I},\qquad G={I \over V}={\frac {1}{R}}}$

For a wide variety of materials and conditions, V and I are directly proportional to each other, and therefore R and G are constants (although they will depend on the size and shape of the object, the material it is made of, and other factors like temperature or strain). This proportionality is called Ohm's law, and materials that satisfy it are called ohmic materials.

In other cases, such as a transformer, diode or battery, V and I are not directly proportional. The ratio V/I is sometimes still useful, and is referred to as a "chordal resistance" or "static resistance", since it corresponds to the inverse slope of a chord between the origin and an I–V curve. In other situations, the derivative ${\displaystyle {\frac {dV}{dI}}\,\!}$ may be most useful; this is called the "differential resistance".

Electrical resistivity and conductivity

Electrical resistivity (also called specific electrical resistance or volume resistivity) and its converse, electrical conductivity, is a fundamental property of a material that quantifies how strongly it resists or conducts the flow of electric current. A low resistivity indicates a material that readily allows the flow of electric current. Resistivity is commonly represented by the Greek letter ρ (rho). The SI unit of electrical resistivity is the ohm-metre (Ω⋅m). For example, if a 1 m × 1 m × 1 m solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is 1 Ω, then the resistivity of the material is 1 Ω⋅m.

Electrical conductivity or specific conductance is the reciprocal of electrical resistivity. It represents a material's ability to conduct electric current. It is commonly signified by the Greek letter σ (sigma), but κ (kappa) (especially in electrical engineering) and γ (gamma) are sometimes used. The SI unit of electrical conductivity is siemens per metre (S/m).

Electricity

Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. In early days, electricity was considered as being not related to magnetism. Later on, many experimental results and the development of Maxwell's equations indicated that both electricity and magnetism are from a single phenomenon: electromagnetism. Various common phenomena are related to electricity, including lightning, static electricity, electric heating, electric discharges and many others.

The presence of an electric charge, which can be either positive or negative, produces an electric field. The movement of electric charges is an electric current and produces a magnetic field.

When a charge is placed in a location with a non-zero electric field, a force will act on it. The magnitude of this force is given by Coulomb's law. Thus, if that charge were to move, the electric field would be doing work on the electric charge. Thus we can speak of electric potential at a certain point in space, which is equal to the work done by an external agent in carrying a unit of positive charge from an arbitrarily chosen reference point to that point without any acceleration and is typically measured in volts.

Electricity is at the heart of many modern technologies, being used for:

electric power where electric current is used to energise equipment;

electronics which deals with electrical circuits that involve active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies.Electrical phenomena have been studied since antiquity, though progress in theoretical understanding remained slow until the seventeenth and eighteenth centuries. Even then, practical applications for electricity were few, and it would not be until the late nineteenth century that electrical engineers were able to put it to industrial and residential use. The rapid expansion in electrical technology at this time transformed industry and society, becoming a driving force for the Second Industrial Revolution. Electricity's extraordinary versatility means it can be put to an almost limitless set of applications which include transport, heating, lighting, communications, and computation. Electrical power is now the backbone of modern industrial society.

Electrocution

Electrocution is death or serious injury caused by electric shock, electric current passing through the body. The word is derived from "electro" and "execution", but it is also used for accidental death. The word is also used to describe non-fatal injuries due to electricity.The term "electrocution" was coined in 1889 in the US just before the first use of the electric chair and originally referred only to electrical execution and not to accidental or suicidal electrical deaths. However, since no English word was available for non-judicial deaths due to electric shock, the word "electrocution" eventually took over as a description of all circumstances of electrical death from the new commercial electricity.

Electromagnetism

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force is carried by electromagnetic fields composed of electric fields and magnetic fields, is responsible for electromagnetic radiation such as light, and is one of the four fundamental interactions (commonly called forces) in nature. The other three fundamental interactions are the strong interaction, the weak interaction, and gravitation. At high energy the weak force and electromagnetic force are unified as a single electroweak force.

Electromagnetic phenomena are defined in terms of the electromagnetic force, sometimes called the Lorentz force, which includes both electricity and magnetism as different manifestations of the same phenomenon. The electromagnetic force plays a major role in determining the internal properties of most objects encountered in daily life. The electromagnetic attraction between atomic nuclei and their orbital electrons holds atoms together. Electromagnetic forces are responsible for the chemical bonds between atoms which create molecules, and intermolecular forces. The electromagnetic force governs all chemical processes, which arise from interactions between the electrons of neighboring atoms.

There are numerous mathematical descriptions of the electromagnetic field. In classical electrodynamics, electric fields are described as electric potential and electric current. In Faraday's law, magnetic fields are associated with electromagnetic induction and magnetism, and Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents.

The theoretical implications of electromagnetism, particularly the establishment of the speed of light based on properties of the "medium" of propagation (permeability and permittivity), led to the development of special relativity by Albert Einstein in 1905.

Galvanometer

A galvanometer is an electromechanical instrument used for detecting and indicating an electric current. A galvanometer works as an actuator, by producing a rotary deflection (of a "pointer"), in response to electric current flowing through a coil in a constant magnetic field. Early galvanometers were not calibrated, but their later developments were used as measuring instruments, called ammeters, to measure the current flowing through an electric circuit.

Galvanometers developed from the observation that the needle of a magnetic compass is deflected near a wire that has electric current flowing through it, first described by Hans Christian Ørsted in 1820. They were the first instruments used to detect and measure small amounts of electric currents. André-Marie Ampère, who gave mathematical expression to Ørsted's discovery and named the instrument after the Italian electricity researcher Luigi Galvani, who in 1791 discovered the principle of the frog galvanoscope – that electric current would make the legs of a dead frog jerk.

Sensitive galvanometers have been essential for the development of science and technology in many fields. For example, they enabled long range communication through submarine cables, such as the earliest Transatlantic telegraph cables, and were essential to discovering the electrical activity of the heart and brain, by their fine measurements of current.

Galvanometers also had widespread use as the visualising part in other kinds of analog meters, for example in light meters, VU meters, etc., where they were used to measure and display the output of other sensors. Today the main type of galvanometer mechanism, still in use, is the moving coil, D'Arsonval/Weston type.

Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around twenty thousand times per second (20 kHz) to around three hundred billion times per second (300 GHz). This is roughly between the upper limit of audio frequencies and the lower limit of infrared frequencies; these are the frequencies at which energy from an oscillating current can radiate off a conductor into space as radio waves. Different sources specify different upper and lower bounds for the frequency range.

Static electricity

Static electricity is an imbalance of electric charges within or on the surface of a material. The charge remains until it is able to move away by means of an electric current or electrical discharge. Static electricity is named in contrast with current electricity, which flows through wires or other conductors and transmits energy.A static electric charge can be created whenever two surfaces contact and separate, and at least one of the surfaces has a high resistance to electric current (and is therefore an electrical insulator). The effects of static electricity are familiar to most people because people can feel, hear, and even see the spark as the excess charge is neutralized when brought close to a large electrical conductor (for example, a path to ground), or a region with an excess charge of the opposite polarity (positive or negative). The familiar phenomenon of a static shock – more specifically, an electrostatic discharge – is caused by the neutralization of charge.

Voltage

Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points. The difference in electric potential between two points (i.e., voltage) in a static electric field is defined as the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named volt. In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule (of work) per 1 coulomb (of charge). The official SI definition for volt uses power and current, where 1 volt = 1 watt (of power) per 1 ampere (of current). This definition is equivalent to the more commonly used 'joules per coulomb'. Voltage or electric potential difference is denoted symbolically by ∆V, but more often simply as V, for instance in the context of Ohm's or Kirchhoff's circuit laws.

Electric potential differences between points can be caused by electric charge, by electric current through a magnetic field, by time-varying magnetic fields, or some combination of these three. A voltmeter can be used to measure the voltage (or potential difference) between two points in a system; often a common reference potential such as the ground of the system is used as one of the points. A voltage may represent either a source of energy (electromotive force) or lost, used, or stored energy (potential drop).

Voltaic pile

The voltaic pile was the first electrical battery that could continuously provide an electric current to a circuit. It was invented by Italian physicist Alessandro Volta, who published his experiments in 1799. The voltaic pile then enabled a rapid series of other discoveries including the electrical decomposition (electrolysis) of water into oxygen and hydrogen by William Nicholson and Anthony Carlisle (1800) and the discovery or isolation of the chemical elements sodium (1807), potassium (1807), calcium (1808), boron (1808), barium (1808), strontium (1808), and magnesium (1808) by Humphry Davy.The entire 19th-century electrical industry was powered by batteries related to Volta's (e.g. the Daniell cell and Grove cell) until the advent of the dynamo (the electrical generator) in the 1870s.

Volta's invention built on Luigi Galvani's 1780s discovery of how a circuit of two metals and a frog's leg can cause the frog's leg to respond. Volta demonstrated in 1794 that when two metals and brine-soaked cloth or cardboard are arranged in a circuit they produce an electric current. In 1800, Volta stacked several pairs of alternating copper (or silver) and zinc discs (electrodes) separated by cloth or cardboard soaked in brine (electrolyte) to increase the electrolyte conductivity. When the top and bottom contacts were connected by a wire, an electric current flowed through the voltaic pile and the connecting wire.

Base quantities