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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 movin ...
. Its reciprocal 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 (motion), sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative la ...
. The SI unit of electrical resistance is the ohm (), while electrical conductance is measured in siemens (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 insulators 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, a ...
tend to have very high resistance and low conductance, while objects made of electrical conductors 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 t ...
across it to current through it, while the conductance is the reciprocal: R = \frac, \qquad G = \frac = \frac For a wide variety of materials and conditions, and are directly proportional to each other, and therefore and are
constants Constant or The Constant may refer to: Mathematics * Constant (mathematics), a non-varying value * Mathematical constant, a special number that arises naturally in mathematics, such as or Other concepts * Control variable or scientific const ...
(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, 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 Chord may refer to: * Chord (music), an aggregate of musical pitches sounded simultaneously ** Guitar chord a chord played on a guitar, which has a particular tuning * Chord (geometry), a line segment joining two points on a curve * 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. ...
\frac may be most useful; this is called the ''differential resistance''.


Introduction

In the hydraulic analogy, 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 activ ...
) is like water flowing through a pipe, and the voltage drop across the wire is like the pressure drop 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 (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 t ...
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 in nuclear reactions) 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 partic ...
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 pinkish ...
wire, but cannot flow as easily through a steel 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, a ...
, 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 at ...
, and is quantified by a property called resistivity. 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) * Less than *Temperatures below freezing * Hell or underworld People with the surname * Ernst von Below (1863–1955), German World War I general * Fr ...
.


Conductors and resistors

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 activ ...
. Conductors are made of high- conductivity 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

For many materials, the current through the material is proportional to the voltage applied across it: I \propto V 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, 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 activ ...
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 used ...
. 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 diodes and fluorescent lamps. The current-voltage curve of a nonohmic device is a curved line.


Relation to resistivity and conductivity

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 \begin R &= \rho \frac, \\ pt G &= \sigma \frac \,. \end where \ell 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 p ...
s (m), is the cross-sectional area of the conductor measured in square metres (m2), (
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 ...
) is the electrical conductivity measured in siemens 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 (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: \rho=1/\sigma. 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 a ...
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 (AC), because the skin effect 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. 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, 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 is about 1030 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. Semiconductors lie between these two extremes. More details can be found in the article: Electrical resistivity and conductivity. For the case of electrolyte 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 ...
. Resistivity varies with temperature. In semiconductors, resistivity also changes when exposed to light. See
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.


Measurement

An instrument for measuring resistance is called an ohmmeter. 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.


Typical values


Static and differential resistance

Many electrical elements, such as diodes and
batteries 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 ...
do satisfy Ohm's law. 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. 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 activ ...
, 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 a ...
or inductor, 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 for ...
s are used to keep track of both the phase and magnitude of current and voltage: \begin u(t) &= \mathfrak\left(U_0 \cdot e^\right) \\ i(t) &= \mathfrak\left(I_0 \cdot e^\right) \\ Z &= \frac \\ Y &= \frac = \frac \end 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; * \omega is the angular frequency of the AC current; * \varphi is the displacement angle; * and are the complex-valued voltage and current, respectively; * and are the complex impedance and admittance, respectively; * \mathfrak indicates the real part of a complex number; and * j=\sqrt is the imaginary unit. The impedance and admittance may be expressed as complex numbers that can be broken into real and imaginary parts: \begin Z &= R + jX \\ Y &= G + jB \end 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 un ...
. The complex angle \theta = \arg(Z) = -\arg(Y) 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 a ...
s and inductors, 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, 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 (Z = 1/Y) for AC circuits, just as R = 1/G 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. One reason, mentioned above is the skin effect (and the related proximity effect). Another reason is that the resistivity itself may depend on frequency (see Drude model, deep-level traps, resonant frequency, Kramers–Kronig relations, 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'' (after James Prescott Joule), 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. 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 stoves and other
electric heaters Electric heating is a process in which electrical energy is converted directly to heat energy at around 100% efficiency, using rather cheap devices. Common applications include space heating, cooking, water heating and industrial processes. An ...
(also called ''resistive heaters''). As another example, incandescent lamps 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). The formula for Joule heating is: P=I^2R where is the power (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. 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 or thermistor. (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 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 mercury-in-glass thermomete ...
s: by measuring the resistance, the temperature of the environment can be inferred. Second, they can be used in conjunction with Joule heating (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, 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 and hysteretic circuit element. For more details see Thermistor#Self-heating effects. If the temperature does not vary too much, a linear approximation is typically used: R(T) = R_0 +\alpha (T - T_0)/math> where \alpha is called the ''temperature coefficient of resistance'', T_0 is a fixed reference temperature (usually room temperature), and R_0 is the resistance at temperature T_0. The parameter \alpha is an empirical parameter fitted from measurement data. Because the linear approximation is only an approximation, \alpha is different for different reference temperatures. For this reason it is usual to specify the temperature that \alpha was measured at with a suffix, such as \alpha_, and the relationship only holds in a range of temperatures around the reference. The temperature coefficient \alpha is typically to for metals near room temperature. It is usually negative for semiconductors and insulators, with highly variable magnitude.


Strain dependence

Just as the resistance of a conductor depends upon temperature, the resistance of a conductor depends upon strain. By placing a conductor under tension (a form of stress that leads to strain in the form of stretching of the conductor), the length of the section of conductor under tension increases and its cross-sectional area decreases. Both these effects contribute to increasing the resistance of the strained section of conductor. Under compression (strain in the opposite direction), the resistance of the strained section of conductor decreases. See the discussion on strain gauges for details about devices constructed to take advantage of this effect.


Light illumination dependence

Some resistors, particularly those made from semiconductors, exhibit '' photoconductivity'', meaning that their resistance changes when light is shining on them. Therefore, they are called '' photoresistors'' (or ''light dependent resistors''). These are a common type of light detector.


Superconductivity

Superconductors are materials that have exactly zero resistance and infinite conductance, because they can have and . This also means there is no joule heating, or in other words no dissipation of electrical energy. Therefore, if superconductive wire is made into a closed loop, current flows around the loop forever. Superconductors require cooling to temperatures near with
liquid helium Liquid helium is a physical state of helium at very low temperatures at standard atmospheric pressures. Liquid helium may show superfluidity. At standard pressure, the chemical element helium exists in a liquid form only at the extremely low t ...
for most metallic superconductors like niobium–tin alloys, or cooling to temperatures near with
liquid nitrogen Liquid nitrogen—LN2—is nitrogen in a liquid state at low temperature. Liquid nitrogen has a boiling point of about . It is produced industrially by fractional distillation of liquid air. It is a colorless, low viscosity liquid that is wi ...
for the expensive, brittle and delicate ceramic high temperature superconductors. Nevertheless, there are many technological applications of superconductivity, including superconducting magnets.


See also

*
Conductance quantum The conductance quantum, denoted by the symbol , is the quantized unit of electrical conductance. It is defined by the elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalent ...
** Von Klitzing constant (its reciprocal) * Electrical measurements * Contact resistance * Electrical resistivity and conductivity for more information about the physical mechanisms for conduction in materials. * Johnson–Nyquist noise * Quantum Hall effect, a standard for high-accuracy resistance measurements. *
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 activ ...
* RKM code * Series and parallel circuits * Sheet resistance * SI electromagnetism units * Thermal resistance * Voltage divider * Voltage drop


Footnotes


References


External links

* * {{DEFAULTSORT:Electrical Resistance Electricity Physical quantities Electromagnetism