The electrical resistance of an object is a measure of its opposition to the flow of
electric current
An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving pa ...
. Its
reciprocal
Reciprocal may refer to:
In mathematics
* Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal''
* Reciprocal polynomial, a polynomial obtained from another pol ...
quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with mechanical
friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction:
*Dry friction is a force that opposes the relative lateral motion of t ...
. The
SI unit of electrical resistance is the
ohm
Ohm (symbol Ω) is a unit of electrical resistance named after Georg Ohm.
Ohm or OHM may also refer to:
People
* Georg Ohm (1789–1854), German physicist and namesake of the term ''ohm''
* Germán Ohm (born 1936), Mexican boxer
* Jörg Ohm (b ...
(), while electrical conductance is measured in
siemens
Siemens AG ( ) is a German multinational conglomerate corporation and the largest industrial manufacturing company in Europe headquartered in Munich with branch offices abroad.
The principal divisions of the corporation are ''Industry'', '' ...
(S) (formerly called the 'mho' and then represented by ).
The resistance of an object depends in large part on the material it is made of. Objects made of
electrical insulator
An electrical insulator is a material in which electric current does not flow freely. The atoms of the insulator have tightly bound electrons which cannot readily move. Other materials—semiconductors and conductors—conduct electric current ...
s like
rubber
Rubber, also called India rubber, latex, Amazonian rubber, ''caucho'', or ''caoutchouc'', as initially produced, consists of polymers of the organic compound isoprene, with minor impurities of other organic compounds. Thailand, Malaysia, and ...
tend to have very high resistance and low conductance, while objects made of
electrical conductor
In physics and electrical engineering, a conductor is an object or type of material that allows the flow of charge (electric current) in one or more directions. Materials made of metal are common electrical conductors. Electric current is gener ...
s like metals tend to have very low resistance and high conductance. This relationship is quantified by
resistivity or conductivity. The nature of a material is not the only factor in resistance and conductance, however; it also depends on the size and shape of an object because these properties are
extensive rather than intensive. For example, a wire's resistance is higher if it is long and thin, and lower if it is short and thick. All objects resist electrical current, except for
superconductors, which have a resistance of zero.
The resistance of an object is defined as the ratio of
voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
across it to
current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (stre ...
through it, while the conductance is the reciprocal:
For a wide variety of materials and conditions, and are directly proportional to each other, and therefore and 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
Strain may refer to:
Science and technology
* Strain (biology), variants of plants, viruses or bacteria; or an inbred animal used for experimental purposes
* Strain (chemistry), a chemical stress of a molecule
* Strain (injury), an injury to a mu ...
). This proportionality is called
Ohm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equat ...
, and materials that satisfy it are called ''ohmic'' materials.
In other cases, such as a
transformer
A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...
,
diode
A diode is a two-terminal electronic component that conducts current primarily in one direction (asymmetric conductance); it has low (ideally zero) resistance in one direction, and high (ideally infinite) resistance in the other.
A diode ...
or
battery
Battery most often refers to:
* Electric battery, a device that provides electrical power
* Battery (crime), a crime involving unlawful physical contact
Battery may also refer to:
Energy source
*Automotive battery, a device to provide power t ...
, and are not directly proportional. The ratio 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
– curve. In other situations, the
derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. F ...
may be most useful; this is called the ''differential resistance''.
Introduction
![ResistanceHydraulicAnalogy](https://upload.wikimedia.org/wikipedia/commons/d/d0/ResistanceHydraulicAnalogy.svg)
In the
hydraulic analogy
The electronic–hydraulic analogy (derisively referred to as the drain-pipe theory by Oliver Lodge) is the most widely used analogy for "electron fluid" in a metal conductor. Since electric current is invisible and the processes in play in ...
, current flowing through a wire (or
resistor
A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active el ...
) is like water flowing through a pipe, and the
voltage drop
Voltage drop is the decrease of electrical potential along the path of a current flowing in an electrical circuit. Voltage drops in the internal resistance of the source, across conductors, across contacts, and across connectors are undesirable ...
across the wire is like the
pressure drop
Pressure drop is defined as the difference in total pressure between two points of a fluid carrying network. A pressure drop occurs when frictional forces, caused by the resistance to flow, act on a fluid as it flows through the tube. The main det ...
that pushes water through the pipe. Conductance is proportional to how much flow occurs for a given pressure, and resistance is proportional to how much pressure is required to achieve a given flow.
The
voltage drop
Voltage drop is the decrease of electrical potential along the path of a current flowing in an electrical circuit. Voltage drops in the internal resistance of the source, across conductors, across contacts, and across connectors are undesirable ...
(i.e., difference between voltages on one side of the resistor and the other), not the
voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
itself, provides the driving force pushing current through a resistor. In hydraulics, it is similar: the pressure difference between two sides of a pipe, not the pressure itself, determines the flow through it. For example, there may be a large water pressure above the pipe, which tries to push water down through the pipe. But there may be an equally large water pressure below the pipe, which tries to push water back up through the pipe. If these pressures are equal, no water flows. (In the image at right, the water pressure below the pipe is zero.)
The resistance and conductance of a wire, resistor, or other element is mostly determined by two properties:
* geometry (shape), and
* material
Geometry is important because it is more difficult to push water through a long, narrow pipe than a wide, short pipe. In the same way, a long, thin copper wire has higher resistance (lower conductance) than a short, thick copper wire.
Materials are important as well. A pipe filled with hair restricts the flow of water more than a clean pipe of the same shape and size. Similarly,
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
s can flow freely and easily through a
copper
Copper is a chemical element with the symbol Cu (from la, cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pinkis ...
wire, but cannot flow as easily through a
steel
Steel is an alloy made up of iron with added carbon to improve its strength and fracture resistance compared to other forms of iron. Many other elements may be present or added. Stainless steels that are corrosion- and oxidation-resistant ty ...
wire of the same shape and size, and they essentially cannot flow at all through an
insulator like
rubber
Rubber, also called India rubber, latex, Amazonian rubber, ''caucho'', or ''caoutchouc'', as initially produced, consists of polymers of the organic compound isoprene, with minor impurities of other organic compounds. Thailand, Malaysia, and ...
, regardless of its shape. The difference between copper, steel, and rubber is related to their microscopic structure and
electron configuration
In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. For example, the electron configuration of the neon atom ...
, and is quantified by a property called
resistivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
.
In addition to geometry and material, there are various other factors that influence resistance and conductance, such as temperature; see
below
Below may refer to:
*Earth
*Ground (disambiguation)
*Soil
*Floor
*Bottom (disambiguation)
Bottom may refer to:
Anatomy and sex
* Bottom (BDSM), the partner in a BDSM who takes the passive, receiving, or obedient role, to that of the top or ...
.
Conductors and resistors
![Metal film resistor](https://upload.wikimedia.org/wikipedia/commons/e/e4/Metal_film_resistor.jpg)
Substances in which electricity can flow are called
conductors. A piece of conducting material of a particular resistance meant for use in a circuit is called a
resistor
A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active el ...
. Conductors are made of high-
conductivity
Conductivity may refer to:
*Electrical conductivity, a measure of a material's ability to conduct an electric current
**Conductivity (electrolytic), the electrical conductivity of an electrolyte in solution
**Ionic conductivity (solid state), elec ...
materials such as metals, in particular copper and aluminium. Resistors, on the other hand, are made of a wide variety of materials depending on factors such as the desired resistance, amount of energy that it needs to dissipate, precision, and costs.
Ohm's law
![FourIVcurves](https://upload.wikimedia.org/wikipedia/commons/d/d7/FourIVcurves.svg)
For many materials, the current through the material is proportional to the voltage applied across it:
over a wide range of voltages and currents. Therefore, the resistance and conductance of objects or electronic components made of these materials is constant. This relationship is called
Ohm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equat ...
, and materials which obey it are called ''ohmic'' materials. Examples of ohmic components are wires and
resistor
A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active el ...
s. The
current–voltage graph of an ohmic device consists of a straight line through the origin with positive
slope
In mathematics, the slope or gradient of a line is a number that describes both the ''direction'' and the ''steepness'' of the line. Slope is often denoted by the letter ''m''; there is no clear answer to the question why the letter ''m'' is use ...
.
Other components and materials used in electronics do not obey Ohm's law; the current is not proportional to the voltage, so the resistance varies with the voltage and current through them. These are called ''nonlinear'' or ''non-ohmic''. Examples include
diode
A diode is a two-terminal electronic component that conducts current primarily in one direction (asymmetric conductance); it has low (ideally zero) resistance in one direction, and high (ideally infinite) resistance in the other.
A diode ...
s and
fluorescent lamp
A fluorescent lamp, or fluorescent tube, is a low-pressure mercury-vapor gas-discharge lamp that uses fluorescence to produce visible light. An electric current in the gas excites mercury vapor, which produces short-wave ultraviolet lig ...
s. The current-voltage curve of a nonohmic device is a curved line.
Relation to resistivity and conductivity
![Resistivity geometry](https://upload.wikimedia.org/wikipedia/commons/6/68/Resistivity_geometry.png)
The resistance of a given object depends primarily on two factors: what material it is made of, and its shape. For a given material, the resistance is inversely proportional to the cross-sectional area; for example, a thick copper wire has lower resistance than an otherwise-identical thin copper wire. Also, for a given material, the resistance is proportional to the length; for example, a long copper wire has higher resistance than an otherwise-identical short copper wire. The resistance and conductance of a conductor of uniform cross section, therefore, can be computed as
where
is the length of the conductor, measured in
metre
The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pref ...
s (m), is the cross-sectional area of the conductor measured in
square metre
The square metre ( international spelling as used by the International Bureau of Weights and Measures) or square meter (American spelling) is the unit of area in the International System of Units (SI) with symbol m2. It is the area of a square w ...
s (m
2), (
sigma
Sigma (; uppercase Σ, lowercase σ, lowercase in word-final position ς; grc-gre, σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ is used as ...
) is the
electrical conductivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allow ...
measured in
siemens
Siemens AG ( ) is a German multinational conglomerate corporation and the largest industrial manufacturing company in Europe headquartered in Munich with branch offices abroad.
The principal divisions of the corporation are ''Industry'', '' ...
per meter (S·m
−1), and (
rho
Rho (uppercase Ρ, lowercase ρ or ; el, ρο or el, ρω, label=none) is the 17th letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Phoenician letter res . Its uppercase form uses the sa ...
) is the
electrical resistivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
(also called ''specific electrical resistance'') of the material, measured in ohm-metres (Ω·m). The resistivity and conductivity are proportionality constants, and therefore depend only on the material the wire is made of, not the geometry of the wire. Resistivity and conductivity are
reciprocals:
. Resistivity is a measure of the material's ability to oppose electric current.
This formula is not exact, as it assumes the
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 ar ...
is totally uniform in the conductor, which is not always true in practical situations. However, this formula still provides a good approximation for long thin conductors such as wires.
Another situation for which this formula is not exact is with
alternating current
Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in whic ...
(AC), because the
skin effect
Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases exponentially with greater depths in the co ...
inhibits current flow near the center of the conductor. For this reason, the ''geometrical'' cross-section is different from the ''effective'' cross-section in which current actually flows, so resistance is higher than expected. Similarly, if two conductors near each other carry AC current, their resistances increase due to the
proximity effect Proximity effect may refer to:
* Proximity effect (atomic physics)
* Proximity effect (audio), an increase in bass or low frequency response when a sound source is close to a microphone
* ''Proximity Effect'' (comics), a comic book series written by ...
. At
commercial power frequency, these effects are significant for large conductors carrying large currents, such as
busbar
In electric power distribution, a busbar (also bus bar) is a metallic strip or bar, typically housed inside switchgear, panel boards, and busway enclosures for local high current power distribution. They are also used to connect high volt ...
s in an
electrical substation
A substation is a part of an electrical generation, transmission, and distribution system. Substations transform voltage from high to low, or the reverse, or perform any of several other important functions. Between the generating station and ...
, or large power cables carrying more than a few hundred amperes.
The resistivity of different materials varies by an enormous amount: For example, the conductivity of
teflon
Polytetrafluoroethylene (PTFE) is a synthetic fluoropolymer of tetrafluoroethylene that has numerous applications. It is one of the best-known and widely applied PFAS. The commonly known brand name of PTFE-based composition is Teflon by Chemou ...
is about 10
30 times lower than the conductivity of copper. Loosely speaking, this is because metals have large numbers of "delocalized" electrons that are not stuck in any one place, so they are free to move across large distances. In an insulator, such as Teflon, each electron is tightly bound to a single molecule so a great force is required to pull it away.
Semiconductor
A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
s lie between these two extremes. More details can be found in the article:
Electrical resistivity and conductivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
. For the case of
electrolyte
An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electrons. This includes most soluble salts, acids, and bases dissolved in a polar solvent, such as water. Upon dis ...
solutions, see the article:
Conductivity (electrolytic)
Conductivity (or specific conductance) of an electrolyte solution is a measure of its ability to conduct electricity. The SI unit of conductivity is Siemens per meter (S/m).
Conductivity measurements are used routinely in many industrial and en ...
.
Resistivity varies with temperature. In semiconductors, resistivity also changes when exposed to light. See
below
Below may refer to:
*Earth
*Ground (disambiguation)
*Soil
*Floor
*Bottom (disambiguation)
Bottom may refer to:
Anatomy and sex
* Bottom (BDSM), the partner in a BDSM who takes the passive, receiving, or obedient role, to that of the top or ...
.
Measurement
![Sanwa SM-1005s](https://upload.wikimedia.org/wikipedia/commons/a/a7/Sanwa_SM-1005s.jpg)
An instrument for measuring resistance is called an
ohmmeter
An analog ohmmeter
An ohmmeter is an electrical instrument that measures electrical resistance (the opposition offered by a circuit or component to the flow of electric current). Multimeters also function as ohmmeters when in resistance-measu ...
. Simple ohmmeters cannot measure low resistances accurately because the resistance of their measuring leads causes a voltage drop that interferes with the measurement, so more accurate devices use
four-terminal sensing
Four-terminal sensing (4T sensing), 4-wire sensing, or 4-point probes method is an electrical impedance measuring technique that uses separate pairs of current-carrying and voltage-sensing electrodes to make more accurate measurements than the si ...
.
Typical values
Static and differential resistance
Many electrical elements, such as
diode
A diode is a two-terminal electronic component that conducts current primarily in one direction (asymmetric conductance); it has low (ideally zero) resistance in one direction, and high (ideally infinite) resistance in the other.
A diode ...
s and
batteries do satisfy
Ohm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equat ...
. These are called ''non-ohmic'' or ''non-linear'', and their
current–voltage curves are straight lines through the origin.
Resistance and conductance can still be defined for non-ohmic elements. However, unlike ohmic resistance, non-linear resistance is not constant but varies with the voltage or current through the device; i.e., its
operating point
{{unreferenced, date=April 2013
The operating point is a specific point within the operation characteristic of a technical device. This point will be engaged because of the properties of the system and the outside influences and parameters. In el ...
. There are two types of resistance:
[
]
AC circuits
Impedance and admittance
When an alternating current flows through a circuit, the relation between current and voltage across a circuit element is characterized not only by the ratio of their magnitudes, but also the difference in their phases. For example, in an ideal resistor
A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active el ...
, the moment when the voltage reaches its maximum, the current also reaches its maximum (current and voltage are oscillating in phase). But for a capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of ...
or inductor
An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
, the maximum current flow occurs as the voltage passes through zero and vice versa (current and voltage are oscillating 90° out of phase, see image below). Complex number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form ...
s are used to keep track of both the phase and magnitude of current and voltage:
where:
* is time;
* and are the voltage and current as a function of time, respectively;
* and indicate the amplitude of the voltage and current, respectively;
* is the angular frequency
In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...
of the AC current;
* is the displacement angle;
* and are the complex-valued voltage and current, respectively;
* and are the complex impedance and admittance
In electrical engineering, admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the reciprocal of impedance, analogous to how conductance & resistance are defined. The SI unit of admittance ...
, respectively;
* indicates the real part
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a ...
of a complex number; and
* is the imaginary unit
The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition an ...
.
The impedance and admittance may be expressed as complex numbers that can be broken into real and imaginary parts:
where is resistance, is conductance, is reactance, and is susceptance In electrical engineering, susceptance (''B'') is the imaginary part of admittance, where the real part is conductance. The reciprocal of admittance is impedance, where the imaginary part is reactance and the real part is resistance. In SI unit ...
.
The complex angle is the phase difference between the voltage and current passing through a component with impedance . For capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of ...
s and inductor
An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
s, this angle is exactly -90° or +90°, respectively, and and are nonzero. Ideal resistors have an angle of 0°, since (and ) are zero, and and reduce to and respectively. In general, AC systems are designed to keep the phase angle close to 0° as much as possible, since it reduces the reactive power
Reactive may refer to:
*Generally, capable of having a reaction (disambiguation)
*An adjective abbreviation denoting a bowling ball coverstock made of reactive resin
*Reactivity (chemistry)
*Reactive mind
*Reactive programming
See also
*Reactanc ...
, which does no useful work at a load. In a simple case with an inductive load (causing the phase to increase), a capacitor may be added for compensation, since the capacitors phase is negative, bringing the total impedance phase closer to 0° again.
is the inverse of () for AC circuits, just as for DC circuits containing only resistors.
Frequency dependence
A key feature of AC circuits is that the resistance and conductance can be frequency-dependent, a phenomenon known as the universal dielectric response
In physics and electrical engineering, the universal dielectric response, or UDR, refers to the observed emergent behaviour of the dielectric properties exhibited by diverse solid state systems. In particular this widely observed response involve ...
. One reason, mentioned above is the skin effect
Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases exponentially with greater depths in the co ...
(and the related proximity effect Proximity effect may refer to:
* Proximity effect (atomic physics)
* Proximity effect (audio), an increase in bass or low frequency response when a sound source is close to a microphone
* ''Proximity Effect'' (comics), a comic book series written by ...
). Another reason is that the resistivity itself may depend on frequency (see Drude model
The Drude model of electrical conduction was proposed in 1900 by Paul Drude to explain the transport properties of electrons in materials (especially metals). Basically, Ohm's law was well established and stated that the current ''J'' and voltage ...
, deep-level trap
Deep-level traps or deep-level defects are a generally undesirable type of electronic defect in semiconductors. They are "deep" in the sense that the energy required to remove an electron or hole from the trap to the valence or conduction band is ...
s, resonant frequency
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...
, Kramers–Kronig relations
The Kramers–Kronig relations are bidirectional mathematical relations, connecting the real and imaginary parts of any complex function that is analytic in the upper half-plane. The relations are often used to compute the real part from the imag ...
, etc.)
Energy dissipation and Joule heating
Resistors (and other elements with resistance) oppose the flow of electric current; therefore, electrical energy is required to push current through the resistance. This electrical energy is dissipated, heating the resistor in the process. This is called ''Joule heating
Joule heating, also known as resistive, resistance, or Ohmic heating, is the process by which the passage of an electric current through a conductor (material), conductor produces heat.
Joule's first law (also just Joule's law), also known in c ...
'' (after James Prescott Joule
James Prescott Joule (; 24 December 1818 11 October 1889) was an English physicist, mathematician and brewer, born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to mechanical work (see energy). Th ...
), also called ''ohmic heating'' or ''resistive heating''.
The dissipation of electrical energy is often undesired, particularly in the case of transmission losses in power lines
Electric power transmission is the bulk movement of electrical energy from a generating site, such as a power plant, to an electrical substation. The interconnected lines that facilitate this movement form a ''transmission network''. This is d ...
. High voltage transmission helps reduce the losses by reducing the current for a given power.
On the other hand, Joule heating is sometimes useful, for example in electric stove
An electric stove or electric range is a stove with an integrated electrical heating device to cook and bake. Electric stoves became popular as replacements for solid-fuel (wood or coal) stoves which required more labor to operate and maintain. S ...
s and other electric heaters (also called ''resistive heaters''). As another example, incandescent lamp
An incandescent light bulb, incandescent lamp or incandescent light globe is an electric light with a wire filament heated until it glows. The filament is enclosed in a glass bulb with a vacuum or inert gas to protect the filament from oxid ...
s rely on Joule heating: the filament is heated to such a high temperature that it glows "white hot" with thermal radiation
Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) is ...
(also called incandescence
Incandescence is the emission of electromagnetic radiation (including visible light) from a hot body as a result of its high temperature. The term derives from the Latin verb ''incandescere,'' to glow white. A common use of incandescence is ...
).
The formula for Joule heating is:
where is the power
Power most often refers to:
* Power (physics), meaning "rate of doing work"
** Engine power, the power put out by an engine
** Electric power
* Power (social and political), the ability to influence people or events
** Abusive power
Power may a ...
(energy per unit time) converted from electrical energy to thermal energy, is the resistance, and is the current through the resistor.
Dependence on other conditions
Temperature dependence
Near room temperature, the resistivity of metals typically increases as temperature is increased, while the resistivity of semiconductors typically decreases as temperature is increased. The resistivity of insulators and electrolytes may increase or decrease depending on the system. For the detailed behavior and explanation, see Electrical resistivity and conductivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
.
As a consequence, the resistance of wires, resistors, and other components often change with temperature. This effect may be undesired, causing an electronic circuit to malfunction at extreme temperatures. In some cases, however, the effect is put to good use. When temperature-dependent resistance of a component is used purposefully, the component is called a resistance thermometer
Resistance thermometers, also called resistance temperature detectors (RTDs), are sensors used to measure temperature. Many RTD elements consist of a length of fine wire wrapped around a heat-resistant ceramic or glass core but other constructio ...
or thermistor
A thermistor is a type of resistor whose resistance is strongly dependent on temperature, more so than in standard resistors. The word thermistor is a portmanteau of ''thermal'' and ''resistor''.
Thermistors are divided based on their conduction ...
. (A resistance thermometer is made of metal, usually platinum, while a thermistor is made of ceramic or polymer.)
Resistance thermometers and thermistors are generally used in two ways. First, they can be used as thermometer
A thermometer is a device that temperature measurement, measures temperature or a temperature gradient (the degree of hotness or coldness of an object). A thermometer has two important elements: (1) a temperature sensor (e.g. the bulb of a merc ...
s: by measuring the resistance, the temperature of the environment can be inferred. Second, they can be used in conjunction with Joule heating
Joule heating, also known as resistive, resistance, or Ohmic heating, is the process by which the passage of an electric current through a conductor (material), conductor produces heat.
Joule's first law (also just Joule's law), also known in c ...
(also called self-heating): if a large current is running through the resistor, the resistor's temperature rises and therefore its resistance changes. Therefore, these components can be used in a circuit-protection role similar to fuses
Fuse or FUSE may refer to:
Devices
* Fuse (electrical), a device used in electrical systems to protect against excessive current
** Fuse (automotive), a class of fuses for vehicles
* Fuse (hydraulic), a device used in hydraulic systems to protec ...
, or for feedback
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to ''feed back'' into itself. The notion of cause-and-effect has to be handled ...
in circuits, or for many other purposes. In general, self-heating can turn a resistor into a nonlinear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
and hysteretic
Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of ...
circuit element. For more details see Thermistor#Self-heating effects.
If the temperature does not vary too much, a linear approximation
In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or a ...
is typically used: