Electromotive force

From Wikipedia, the free encyclopedia

Electromotive force, abbreviated emf (denoted ${\displaystyle {\mathcal {E}}}$ and measured in volts), is the electrical intensity or "pressure" developed by a source of electrical energy such as a battery or generator. A device that converts other forms of energy into electrical energy (a "transducer") provides an emf as its output. (The word "force" in this case is not used to mean mechanical force, as may be measured in pounds or newtons.)

In electromagnetic induction, emf can be defined around a closed loop of conductor as the electromagnetic work that would be done on an electric charge (an electron in this instance) if it travels once around the loop. For a time-varying magnetic flux linking a loop, the electric potential scalar field is not defined due to a circulating electric vector field, but an emf nevertheless does work that can be measured as a virtual electric potential around the loop. (While electrical charges travel around the loop, their energy is typically converted into thermal energy due to the resistance of the conductor comprising the loop.)

In the case of a two-terminal device (such as an electrochemical cell) which is modeled as a Thévenin's equivalent circuit, the equivalent emf can be measured as the open-circuit potential difference or "voltage" between the two terminals. This potential difference can drive an electric current if an external circuit is attached to the terminals.

Overview

Devices that can provide emf include electrochemical cells, thermoelectric devices, solar cells, photodiodes, electrical generators, transformers and even Van de Graaff generators. In nature, emf is generated whenever magnetic field fluctuations occur through a surface. The shifting of the Earth's magnetic field during a geomagnetic storm induces currents in the electrical grid as the lines of the magnetic field are shifted about and cut across the conductors.

In the case of a battery, the charge separation that gives rise to a voltage difference between the terminals is accomplished by chemical reactions at the electrodes that convert chemical potential energy into electromagnetic potential energy. A voltaic cell can be thought of as having a "charge pump" of atomic dimensions at each electrode, that is:

A source of emf can be thought of as a kind of charge pump that acts to move positive charge from a point of low potential through its interior to a point of high potential. … By chemical, mechanical or other means, the source of emf performs work dW on that charge to move it to the high potential terminal. The emf ℰ of the source is defined as the work dW done per charge dq: ℰ = dW/dq.

In the case of an electrical generator, a time-varying magnetic field inside the generator creates an electric field via electromagnetic induction, which in turn creates a voltage difference between the generator terminals. Charge separation takes place within the generator, with electrons flowing away from one terminal and toward the other, until, in the open-circuit case, sufficient electric field builds up to make further charge separation impossible. Again, the emf is countered by the electrical voltage due to charge separation. If a load is attached, this voltage can drive a current. The general principle governing the emf in such electrical machines is Faraday's law of induction.

History

Around 1830, Michael Faraday established that the reactions at each of the two electrode–electrolyte interfaces provide the "seat of emf" for the voltaic cell, that is, these reactions drive the current and are not an endless source of energy as was initially thought. In the open-circuit case, charge separation continues until the electrical field from the separated charges is sufficient to arrest the reactions. Years earlier, Alessandro Volta, who had measured a contact potential difference at the metal–metal (electrode–electrode) interface of his cells, had held the incorrect opinion that contact alone (without taking into account a chemical reaction) was the origin of the emf.

Notation and units of measurement

Electromotive force is often denoted by ${\displaystyle {\mathcal {E}}}$ or ℰ (script capital E, Unicode U+2130).

In a device without internal resistance, if an electric charge Q passes through that device, and gains an energy W, the net emf for that device is the energy gained per unit charge, or W/Q. Like other measures of energy per charge, emf uses the SI unit volt, which is equivalent to a joule per coulomb.

Electromotive force in electrostatic units is the statvolt (in the centimeter gram second system of units equal in amount to an erg per electrostatic unit of charge).

Formal definitions

Inside a source of emf that is open-circuited, the conservative electrostatic field created by separation of charge exactly cancels the forces producing the emf. Thus, the emf has the same value but opposite sign as the integral of the electric field aligned with an internal path between two terminals A and B of a source of emf in open-circuit condition (the path is taken from the negative terminal to the positive terminal to yield a positive emf, indicating work done on the electrons moving in the circuit). Mathematically:

${\displaystyle {\mathcal {E}}=-\int _{A}^{B}{\boldsymbol {E}}_{\mathrm {cs} }\cdot \mathrm {d} {\boldsymbol {\ell }}\ ,}$

where E_cs is the conservative electrostatic field created by the charge separation associated with the emf, dℓ is an element of the path from terminal A to terminal B, and ‘·’ denotes the vector dot product. This equation applies only to locations A and B that are terminals, and does not apply to paths between points A and B with portions outside the source of emf. This equation involves the electrostatic electric field due to charge separation E_cs and does not involve (for example) any non-conservative component of electric field due to Faraday's law of induction.

In the case of a closed path in the presence of a varying magnetic field, the integral of the electric field around a closed loop may be nonzero; one common application of the concept of emf, known as "induced emf" is the voltage induced in such a loop. The "induced emf" around a stationary closed path C is:

${\displaystyle {\mathcal {E}}=\oint _{C}{\boldsymbol {E}}\cdot \mathrm {d} {\boldsymbol {\ell }}\ ,}$

where now E is the entire electric field, conservative and non-conservative, and the integral is around an arbitrary but stationary closed curve C through which there is a varying magnetic field. The electrostatic field does not contribute to the net emf around a circuit because the electrostatic portion of the electric field is conservative (that is, the work done against the field around a closed path is zero).

This definition can be extended to arbitrary sources of emf and moving paths C:

${\displaystyle {\mathcal {E}}=\oint _{C}\left[{\boldsymbol {E}}+{\boldsymbol {v}}\times {\boldsymbol {B}}\right]\cdot \mathrm {d} {\boldsymbol {\ell }}\ }$ ${\displaystyle +{\frac {1}{q}}\oint _{C}\mathrm {Effective\ chemical\ forces\ \cdot } \ \mathrm {d} {\boldsymbol {\ell }}\ }$
${\displaystyle +{\frac {1}{q}}\oint _{C}\mathrm {Effective\ thermal\ forces\ \cdot } \ \mathrm {d} {\boldsymbol {\ell }}\ ,}$

which is a conceptual equation mainly, because the determination of the "effective forces" is difficult.

In thermodynamics

When multiplied by an amount of charge dQ the emf ℰ yields a thermodynamic work term ℰdQ that is used in the formalism for the change in Gibbs energy when charge is passed in a battery:

${\displaystyle dG=-SdT+VdP+{\mathcal {E}}dQ\ ,}$

where G is the Gibb's free energy, S is the entropy, V is the system volume, P is its pressure and T is its absolute temperature.

The combination ( ℰ, Q ) is an example of a conjugate pair of variables. At constant pressure the above relationship produces a Maxwell relation that links the change in open cell voltage with temperature T (a measurable quantity) to the change in entropy S when charge is passed isothermally and isobarically. The latter is closely related to the reaction entropy of the electrochemical reaction that lends the battery its power. This Maxwell relation is:

${\displaystyle \left({\frac {\partial {\mathcal {E}}}{\partial T}}\right)_{Q}=-\left({\frac {\partial S}{\partial Q}}\right)_{T}}$

If a mole of ions goes into solution (for example, in a Daniell cell, as discussed below) the charge through the external circuit is:

${\displaystyle \Delta Q=-n_{0}F_{0}\ ,}$

where n₀ is the number of electrons/ion, and F₀ is the Faraday constant and the minus sign indicates discharge of the cell. Assuming constant pressure and volume, the thermodynamic properties of the cell are related strictly to the behavior of its emf by:

${\displaystyle \Delta H=-n_{0}F_{0}\left({\mathcal {E}}-T{\frac {d{\mathcal {E}}}{dT}}\right)\ ,}$

where ΔH is the enthalpy of reaction. The quantities on the right are all directly measurable.

Voltage difference

An electrical voltage difference is sometimes called an emf. The points below illustrate the more formal usage, in terms of the distinction between emf and the voltage it generates:

1. For a circuit as a whole, such as one containing a resistor in series with a voltaic cell, electrical voltage does not contribute to the overall emf, because the voltage difference on going around a circuit is zero. (The ohmic IR voltage drop plus the applied electrical voltage sum to zero. The emf is due solely to the chemistry in the battery that causes charge separation, which in turn creates an electrical voltage that drives the current.
2. For a circuit consisting of an electrical generator that drives current through a resistor, the emf is due solely to a time-varying magnetic field within the generator that generates an electrical voltage that in turn drives the current. (The ohmic IR drop plus the applied electrical voltage again is zero.)
3. A transformer coupling two circuits may be considered a source of emf for one of the circuits, just as if it were caused by an electrical generator; this example illustrates the origin of the term "transformer emf".
4. A photodiode or solar cell may be considered as a source of emf, similar to a battery, resulting in an electrical voltage generated by charge separation driven by light rather than chemical reaction.
5. Other devices that produce emf are fuel cells, thermocouples, and thermopiles.

In the case of an open circuit, the electric charge that has been separated by the mechanism generating the emf creates an electric field opposing the separation mechanism. For example, the chemical reaction in a voltaic cell stops when the opposing electric field at each electrode is strong enough to arrest the reactions. A larger opposing field can reverse the reactions in what are called reversible cells.

The electric charge that has been separated creates an electric potential difference that can be measured with a voltmeter between the terminals of the device. The magnitude of the emf for the battery (or other source) is the value of this 'open circuit' voltage. When the battery is charging or discharging, the emf itself cannot be measured directly using the external voltage because some voltage is lost inside the source. It can, however, be inferred from a measurement of the current I and voltage difference V, provided that the internal resistance r already has been measured: ℰ = V + Ir.

Generation

Chemical sources

A typical reaction path requires the initial reactants to cross an energy barrier, enter an intermediate state and finally emerge in a lower energy configuration. If charge separation is involved, this energy difference can result in an emf. See Bergmann et al. and Transition state.

 

Galvanic cell using a salt bridge

The question of how batteries (galvanic cells) generate an emf is one that occupied scientists for most of the 19th century. The "seat of the electromotive force" was eventually determined by Walther Nernst to be primarily at the interfaces between the electrodes and the electrolyte.

Molecules are groups of atoms held together by chemical bonds, and these bonds consist of electrical forces between electrons (negative) and protons (positive). The molecule in isolation is a stable entity, but when different molecules are brought together, some types of molecules are able to steal electrons from others, resulting in charge separation. This redistribution of charge is accompanied by a change in energy of the system, and a reconfiguration of the atoms in the molecules. The gain of an electron is termed "reduction" and the loss of an electron is termed "oxidation". Reactions in which such electron exchange occurs (which are the basis for batteries) are called reduction-oxidation reactions or redox reactions. In a battery, one electrode is composed of material that gains electrons from the solute, and the other electrode loses electrons, because of these fundamental molecular attributes. The same behavior can be seen in atoms themselves, and their ability to steal electrons is referred to as their electronegativity.

As an example, a Daniell cell consists of a zinc anode (an electron collector), is oxidized as it dissolves into a zinc sulfate solution, the dissolving zinc leaving behind its electrons in the electrode according to the oxidation reaction (s = solid electrode; aq = aqueous solution):

${\displaystyle \mathrm {Zn_{(s)}\rightarrow Zn_{(aq)}^{2+}+2e^{-}\ } }$

The zinc sulfate is the electrolyte in that half cell. It is a solution which contains zinc cations ${\displaystyle \mathrm {Zn} _{}^{2+}}$, and sulfate anions ${\displaystyle \mathrm {SO} _{4}^{2-}\ }$ with charges that balance to zero.

In the other half cell, the copper cations in a copper sulfate electrolyte are drawn to the copper cathode to which they attach themselves as they adopt electrons from the copper electrode by the reduction reaction:

${\displaystyle \mathrm {Cu_{(aq)}^{2+}+2e^{-}\rightarrow Cu_{(s)}\ } }$

in effect leaving a deficit of electrons on the copper cathode. The difference of excess electrons on the anode and deficit of electrons on the cathode creates an electrical potential between the two electrodes. (A detailed discussion of the microscopic process of electron transfer between an electrode and the ions in an electrolyte may be found in Conway.)

If the cathode and anode are connected by an external conductor, electrons would pass through that external circuit (light bulb in figure), while the ions pass through the salt bridge to maintain charge balance until such a time as the anode and cathode reach electrical equilibrium of zero volts as chemical equilibrium is reached in the cell. In the process the zinc anode is dissolved while the copper electrode is plated with copper. The so-called "salt bridge" is not made of salt but could be made of material able to wick the cations and anions (salts) in the solutions, where the flow of positively charged cations along the "bridge" amounts to the same number of negative charges flowing in the opposite direction.

If the light bulb is removed (open circuit) the emf between the electrodes is opposed by the electric field due to charge separation, and the reactions stop.

For this particular cell chemistry, at 298 K (room temperature), the emf ℰ = 1.0934 V, with a temperature coefficient of dℰ/dT = −4.53×10⁻⁴ V/K.

Voltaic cells

Volta developed the voltaic cell about 1792, and presented his work March 20, 1800. Volta correctly identified the role of dissimilar electrodes in producing the voltage, but incorrectly dismissed any role for the electrolyte. Volta ordered the metals in a 'tension series', “that is to say in an order such that any one in the list becomes positive when in contact with any one that succeeds, but negative by contact with any one that precedes it.” A typical symbolic convention in a schematic of this circuit ( –||– ) would have a long electrode 1 and a short electrode 2, to indicate that electrode 1 dominates. Volta's law about opposing electrode emfs implies that, given ten electrodes (for example, zinc and nine other materials), 45 unique combinations of voltaic cells (10 × 9/2) can be created.

Typical values

The electromotive force produced by primary (single-use) and secondary (rechargeable) cells is usually of the order of a few volts. The figures quoted below are nominal, because emf varies according to the size of the load and the state of exhaustion of the cell.

EMF	Cell chemistry			Common name
	Anode	Solvent, electrolyte	Cathode
1.2 V	Cadmium	Water, potassium hydroxide	NiO(OH)	nickel-cadmium
1.2 V	Mischmetal (hydrogen absorbing)	Water, potassium hydroxide	Nickel	nickel–metal hydride
1.5 V	Zinc	Water, ammonium or zinc chloride	Carbon, manganese dioxide	Zinc carbon
2.1 V	Lead	Water, sulfuric acid	Lead dioxide	Lead–acid
3.6 V to 3.7 V	Graphite	Organic solvent, Li salts	LiCoO2	Lithium-ion
1.35 V	Zinc	Water, sodium or potassium hydroxide	HgO	Mercury cell

Electromagnetic induction

The principle of electromagnetic induction, noted above, states that a time-dependent magnetic field produces a circulating electric field. A time-dependent magnetic field can be produced either by motion of a magnet relative to a circuit, by motion of a circuit relative to another circuit (at least one of these must be carrying a current), or by changing the current in a fixed circuit. The effect on the circuit itself, of changing the current, is known as self-induction; the effect on another circuit is known as mutual induction.
For a given circuit, the electromagnetically induced emf is determined purely by the rate of change of the magnetic flux through the circuit according to Faraday's law of induction.

An emf is induced in a coil or conductor whenever there is change in the flux linkages. Depending on the way in which the changes are brought about, there are two types: When the conductor is moved in a stationary magnetic field to procure a change in the flux linkage, the emf is statically induced. The electromotive force generated by motion is often referred to as motional emf. When the change in flux linkage arises from a change in the magnetic field around the stationary conductor, the emf is dynamically induced. The electromotive force generated by a time-varying magnetic field is often referred to as transformer emf.

Contact potentials

When solids of two different materials are in contact, thermodynamic equilibrium requires that one of the solids assume a higher electrical potential than the other. This is called the contact potential. Dissimilar metals in contact produce what is known also as a contact electromotive force or Galvani potential. The magnitude of this potential difference is often expressed as a difference in Fermi levels in the two solids when they are at charge neutrality, where the Fermi level (a name for the chemical potential of an electron system) describes the energy necessary to remove an electron from the body to some common point (such as ground). If there is an energy advantage in taking an electron from one body to the other, such a transfer will occur. The transfer causes a charge separation, with one body gaining electrons and the other losing electrons. This charge transfer causes a potential difference between the bodies, which partly cancels the potential originating from the contact, and eventually equilibrium is reached. At thermodynamic equilibrium, the Fermi levels are equal (the electron removal energy is identical) and there is now a built-in electrostatic potential between the bodies. The original difference in Fermi levels, before contact, is referred to as the emf. The contact potential cannot drive steady current through a load attached to its terminals because that current would involve a charge transfer. No mechanism exists to continue such transfer and, hence, maintain a current, once equilibrium is attained.

One might inquire why the contact potential does not appear in Kirchhoff's law of voltages as one contribution to the sum of potential drops. The customary answer is that any circuit involves not only a particular diode or junction, but also all the contact potentials due to wiring and so forth around the entire circuit. The sum of all the contact potentials is zero, and so they may be ignored in Kirchhoff's law.

Solar cell

The equivalent circuit of a solar cell; parasitic resistances are ignored in the discussion of the text.

 

Solar cell voltage as a function of solar cell current delivered to a load for two light-induced currents I_L; currents as a ratio with reverse saturation current I₀. Compare with Fig. 1.4 in Nelson.

 

Operation of a solar cell can be understood from the equivalent circuit at right. Light, of sufficient energy (greater than the bandgap of the material), creates mobile electron–hole pairs in a semiconductor. Charge separation occurs because of a pre-existing electric field associated with the p-n junction in thermal equilibrium (a contact potential creates the field). This charge separation between positive holes and negative electrons across a p-n junction (a diode) yields a forward voltage, the photo voltage, between the illuminated diode terminals. As has been noted earlier in the terminology section, the photo voltage is sometimes referred to as the photo emf, rather than distinguishing between the effect and the cause. The charge separation causes a photo voltage that drives current through any attached load.

The current available to the external circuit is limited by internal losses I₀=I_SH + I _D:

${\displaystyle I=I_{L}-I_{0}=I_{L}-I_{SH}-I_{D}}$

Losses limit the current available to the external circuit. The light-induced charge separation eventually creates a current (called a forward current) I_SH through the cell's junction in the direction opposite that the light is driving the current. In addition, the induced voltage tends to forward bias the junction. At high enough levels, this forward bias of the junction will cause a forward current, I _D in the diode opposite that induced by the light. Consequently, the greatest current is obtained under short-circuit conditions, and is denoted as I_L (for light-induced current) in the equivalent circuit. Approximately, this same current is obtained for forward voltages up to the point where the diode conduction becomes significant.

The current delivered by the illuminated diode, to the external circuit is:

${\displaystyle I=I_{L}-I_{0}\left(e^{qV/(mkT)}-1\right)\ ,}$

where I₀ is the reverse saturation current. Where the two parameters that depend on the solar cell construction and to some degree upon the voltage itself are m, the ideality factor, and kT/q the thermal voltage (about 0.026 V at room temperature). This relation is plotted in the figure using a fixed value m = 2. Under open-circuit conditions (that is, as I = 0), the open-circuit voltage is the voltage at which forward bias of the junction is enough that the forward current completely balances the photocurrent. Solving the above for the voltage V and designating it the open-circuit voltage of the I–V equation as:

${\displaystyle V_{\text{oc}}=m\ {\frac {kT}{q}}\ \ln \left({\frac {I_{\text{L}}}{I_{0}}}+1\right)\ ,}$

which is useful in indicating a logarithmic dependence of V_oc upon the light-induced current. Typically, the open-circuit voltage is not more than about 0.5 V.

When driving a load, the photo voltage is variable. As shown in the figure, for a load resistance R_L, the cell develops a voltage that is between the short-circuit value V = 0, I = I_L and the open-circuit value V_oc, I = 0, a value given by Ohm's law V = I R_L, where the current I is the difference between the short-circuit current and current due to forward bias of the junction, as indicated by the equivalent circuit (neglecting the parasitic resistances).

In contrast to the battery, at current levels delivered to the external circuit near I_L, the solar cell acts more like a current source rather than a voltage source( near vertical part of the two illustrated curves). The current drawn is nearly fixed over a range of load voltages, to one electron per converted photon. The quantum efficiency, or probability of getting an electron of photocurrent per incident photon, depends not only upon the solar cell itself, but upon the spectrum of the light.

The diode possesses a "built-in potential" due to the contact potential difference between the two different materials on either side of the junction. This built-in potential is established when the junction is manufactured and that voltage a by-product of thermodynamic equilibrium within the cell. Once established, this potential difference cannot drive a current, however, as connecting a load does not upset this equilibrium. In contrast, the accumulation of excess electrons in one region and of excess holes in another, due to illumination, results in a photo voltage that does drive a current when a load is attached to the illuminated diode. As noted above, this photo voltage also forward biases the junction, and so reduces the pre-existing field in the depletion region.

Electric current

From Wikipedia, the free encyclopedia

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 unit	ampere
Derivations from other quantities	${\displaystyle I={V \over R}\,,I={Q \over t}}$
Dimension	I

An electric current is a flow of electric charge. In electric circuits this charge is often carried by moving electrons in a wire. It can also be carried by ions in an electrolyte, or by both ions and electrons such as in an ionised gas (plasma).

The SI unit for measuring an electric current is the ampere, which is the flow of electric charge across a surface at the rate of one coulomb per second. Electric current is measured using a device called an ammeter.

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.

Symbol

The conventional symbol for current is I, which originates from the French phrase intensité de courant, (current intensity). Current intensity is often referred to simply as current. 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). 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.

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 are held in a fixed position, and the negatively charged electrons are free to move, carrying their charge from one place to another. 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, one arrives at the usual mathematical equation that describes this relationship:

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

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.

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.

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 a semiconductor.

Current measurement

Current can be measured using an ammeter.

At the circuit level, various techniques are used to measure current:

• Shunt resistors
• Hall effect current sensor transducers
• Transformers (however DC cannot be measured)
• Magnetoresistive field sensors

Resistive heating

Joule heating, also known as ohmic heating and resistive heating, is the process by which the passage of an electric current through a conductor produces heat. It 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.

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

This relationship is known as Joule's First Law. The SI unit of energy was subsequently named the joule and given the symbol J. The commonly known unit of power, the watt, is equivalent to one joule per second.

Electromagnetism

Electromagnet

In an electromagnet a coil, of a large number of circular turns of insulated wire, wrapped on a cylindrical core, 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 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.

Magnetism can also produce electric currents. When a changing magnetic field is applied to a conductor, an Electromotive force (EMF) is produced, and when there is a suitable path, this causes current.

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 used for this include Hall effect sensors, current clamps, current transformers, and Rogowski coils.

Radio waves

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 hydrogen ions (protons) 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. 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, absorbing 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.

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]).

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 a measure of the density of an electric current. It is defined as a vector whose magnitude is the electric current per cross-sectional area. In SI units, the current density is measured in amperes per square metre.

${\displaystyle I=\int {\vec {J}}\cdot d{\vec {A}}}$

where ${\displaystyle I}$ is current in the conductor, ${\displaystyle {\vec {J}}}$ is the current density, and ${\displaystyle d{\vec {A}}}$ is the differential cross-sectional area vector.

The current density (current per unit area) ${\displaystyle {\vec {J}}}$ in materials with finite resistance is directly proportional to the electric field ${\displaystyle {\vec {E}}}$ in the medium. The proportionality constant is called the conductivity ${\displaystyle \sigma }$ of the material, whose value depends on the material concerned and, in general, is dependent on the temperature of the material:

${\displaystyle {\vec {J}}=\sigma {\vec {E}}\,}$

The reciprocal of the conductivity ${\displaystyle \sigma }$ of the material is called the resistivity ${\displaystyle \rho }$ of the material and the above equation, when written in terms of resistivity becomes:

${\displaystyle {\vec {J}}={\frac {\vec {E}}{\rho }}}$ or

${\displaystyle {\vec {E}}=\rho {\vec {J}}}$

Conduction in semiconductor devices may occur by a combination of drift and diffusion, which is proportional to diffusion constant ${\displaystyle D}$ and charge density ${\displaystyle \alpha _{q}}$. The current density is then:

${\displaystyle J=\sigma E+Dq\nabla n,}$

with ${\displaystyle q}$ being the elementary charge and ${\displaystyle n}$ the electron density. The carriers move in the direction of decreasing concentration, so for electrons a positive current results for a positive density gradient. If the carriers are holes, replace electron density ${\displaystyle n}$ by the negative of the hole density ${\displaystyle p}$.

In linear anisotropic materials, σ, ρ and D are tensors.

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:

• 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.