Information about Electrical Resistance
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A 750-kΩ resistor, as identified by its electronic color code. An ohmmeter could be used to verify this value.
The resistance of an object determines the amount of current through the object for a given voltage across the object.
where
- R is the resistance of the object, measured in ohms, equivalent to J·s/C2
- V is the voltage across the object, measured in volts
- I is the current through the object, measured in amperes
For a wide variety of materials and conditions, the electrical resistance does not depend on the amount of current through or the amount of voltage across the object, meaning that the resistance R is constant.
Resistive loss
When there is a current I through an object with resistance, R, electrical energy is converted to heat at a rate (power) equal to
where
- P is the power measured in watts
- I is the current measured in amperes
- R is the resistance measured in ohms
This energy conversion is useful in applications such as incandescent lighting and electric heating but is considered a loss in other applications such as power transmission. Ideally, the conductors used to connect electrical devices together should have zero resistance but in reality, only superconductors achieve this ideal. Common ways to combat resistive loss in conductors include using thicker wire and higher voltages.
Resistance of a conductor
DC resistance
As long as the current density is totally uniform in the conductor, the DC resistance R of a conductor of regular cross section can be computed as
where
- l is the length of the conductor, measured in meters
- A is the cross-sectional area, measured in square meters
- ρ (Greek: rho) is the electrical resistivity (also called specific electrical resistance) of the material, measured in ohm · meter. Resistivity is a measure of the material's ability to oppose the flow of electric current.
For practical reasons, almost any connections to a real conductor will almost certainly mean the current density is not totally uniform. However, this formula still provides a good approximation for long thin conductors such as wires.
AC resistance
If a wire conducts high-frequency alternating current then the effective cross sectional area of the wire is reduced because of the skin effect. This causes the wire resistance to increase at a rate of 10dB/decade for wire radius much greater than skin depth.In a conductor close to others, the actual resistance is higher than that predicted by the skin effect because of the proximity effect.
Causes of resistance
In metals
A metal consists of a lattice of atoms, each with a shell of electrons. This can also be known as a positive ionic lattice. The outer electrons are free to dissociate from their parent atoms and travel through the lattice, creating a 'sea' of electrons, making the metal a conductor. When an electrical potential difference (a voltage) is applied across the metal, the electrons drift from one end of the conductor to the other under the influence of the electric field.Near room temperatures, the thermal motion of ions is the primary source of scattering of electrons (due to destructive interference of free electron wave on non-correlating potentials of ions) - thus the prime cause of metal resistance. Imperfections of lattice also contribute into resistance, although their contribution in pure metals is negligible.
The larger the cross-sectional area of the conductor, the more electrons are available to carry the current, so the lower the resistance. The longer the conductor, the more scattering events occur in each electron's path through the material, so the higher the resistance. And different materials also affect the resistance.[1]
In semiconductors and insulators
In metals, the fermi level lies in the conduction band giving rise to free conduction electrons. However, in semiconductors the position of the fermi level is within the band gap, exactly half way between the conduction band minimum and valence band maximum for intrinsic (undoped) semiconductors. This means that at 0 Kelvin, there are no free conduction electrons and the resistance is infinite. However, the resistance will continue to decrease as the charge carrier density in the conduction band increases. In extrinsic (doped) semiconductors, dopant atoms increase the majority charge carrier by donating electrons to the conduction band or accepting holes in the valence band. For both types of donor or acceptor atoms, increasing the dopant density leads to a reduction in the resistance. Highly doped semiconductors hence behave metallic. At very high temperatures, the contribution of thermally generated carriers will dominate over the contribution from dopant atoms and the resistance will decrease exponentially with temperature.In ionic liquids/electrolytes
In electrolytes, electrical conduction happens not by band electrons or holes, but by full atomic species (ions) traveling, each carrying an electrical charge. The resistivity of ionic liquids varies tremendously by the salt concentration - while distilled water is almost an insulator, salt water is a very efficient electrical conductor. In biological membranes, currents are carried by ionic salts. Small holes in the membranes, called ion channels, are selective to specific ions and determine the membrane resistance.Resistance of various materials
| Material | Resistivity,  ohm-meter |
| Metals |  |
| Semiconductors | variable |
| Electrolytes | variable |
| Insulators |  |
Band theory
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Electron energy levels in an insulator.
Quantum mechanics states that the energy of an electron in an atom cannot be any arbitrary value. Rather, there are fixed energy levels which the electrons can occupy, and values in between these levels are impossible. The energy levels are grouped into two bands: the valence band and the conduction band (the latter is generally above the former). Electrons in the conduction band may move freely throughout the substance in the presence of an electrical field.
In insulators and semiconductors, the atoms in the substance influence each other so that between the valence band and the conduction band there exists a forbidden band of energy levels, which the electrons cannot occupy. In order for a current to flow, a relatively large amount of energy must be furnished to an electron for it to leap across this forbidden gap and into the conduction band. Thus, even large voltages can yield relatively small currents.
Differential resistance
When resistance may depend on voltage and current, differential resistance, incremental resistance or slope resistance is defined as the slope of the U-I graph at a particular point, thus:
This quantity is sometimes called simply resistance, although the two definitions are equivalent only for an ohmic component such as an ideal resistor. If the U-I graph is not monotonic (i.e. it has a peak or a trough), the differential resistance will be negative for some values of voltage and current. This property is often known as negative resistance, although it is more correctly called negative differential resistance, since the absolute resistance U/I is still positive.
Temperature-dependence
Near room temperature, the electric resistance of a typical metal varies linearly with the temperature. At lower temperatures (less than the Debye temperature), the resistance decreases as T5 due to the electrons scattering off of phonons. At even lower temperatures, the dominant scattering mechanism for electrons is other electrons, and the resistance decreases as T². At some point, the impurities in the metal will dominate the behavior of the electrical resistance which causes it to saturate to a constant value. Matthiessen's Rule[1][2] says that all of these different behaviors can be summed up to get the total resistance as a function of temperature,
The electric resistance of a typical intrinsic (non doped) semiconductor decreases exponentially with the temperature:
Extrinsic (doped) semiconductors have a far more complicated temperature profile. As temperature increased starting from absolute zero they first decrease steeply in resistance as the carriers leave the donors or acceptors. After most of the donors or acceptors have lost their carriers the resistance starts to increase again slightly due to the reducing mobility of carriers (much as in a metal). At higher temperatures it will behave like intrinsic semiconductors as the carriers from the donors/acceptors become insignificant compared to the thermally generated carriers.
The electric resistance of electrolytes and insulators is highly nonlinear, and case by case dependent, therefore no generalized equations are given.
Measuring resistance
An instrument for measuring resistance is called a resistance meter or 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.See also
- Resistor
- Electrical conduction for more information about the physical mechanisms for conduction in materials.
- Ohm's Law
- Voltage divider
- Voltage drop
- Current divider
- Thermal resistance
- Sheet resistance
- Electrical resistivity
- Electrical impedance
- SI electromagnetism units
- Quantum Hall effect, a new standard for measuring resistance.
- Series and parallel circuits
- Proximity effect (electromagnetism)
- Skin effect
References
External links
- Circuits
- Resistance, Reactance, and Impedance
- Calculation: Electrical resistance, voltage, current, and power
Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles.
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Electricity (from New Latin ēlectricus, "amberlike") is a general term for a variety of phenomena resulting from the presence and flow of electric charge. This includes many well-known physical phenomena such as lightning, electromagnetic fields and electric currents,
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magnetism is one of the phenomena by which materials exert attractive or repulsive forces on other materials. Some well known materials that exhibit easily detectable magnetic properties (called magnets) are nickel, iron and their alloys; however, all materials are influenced to
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Electrostatics (also known as static electricity) is the branch of physics that deals with the phenomena arising from what seem to be stationary electric charges. This includes phenomena as simple as the attraction of plastic wrap to your hand after you remove it from a
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Flavour in particle physics
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Coulomb's law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated as follows:
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- The magnitude of the electrostatic force between two points electric charges is directly proportional to the product of the magnitudes of each
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electric field. This electric field exerts a force on other electrically charged objects. The concept of electric field was introduced by Michael Faraday.
The electric field is a vector field with SI units of newtons per coulomb (N C−1
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The electric field is a vector field with SI units of newtons per coulomb (N C−1
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In physics and mathematical analysis, Gauss's law is the electrostatic application of the generalized Gauss's theorem giving the equivalence relation between any flux, e.g.
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Electric potential is the potential energy per unit of charge associated with a static (time-invariant) electric field, also called the electrostatic potential, typically measured in volts. It is a scalar quantity.
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In physics, the electric dipole moment (or electric dipole for short) is a measure of the polarity of a system of electric charges.
In the simple case of two point charges, one with charge and one with charge , the electric dipole moment is:
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In the simple case of two point charges, one with charge and one with charge , the electric dipole moment is:
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Magnetostatics is the study of static magnetic fields. In electrostatics, the charges are stationary, whereas here, the currents are stationary. As it turns out magnetostatics is a good approximation even when the currents are not static as long as the currents do not
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magnetic field is a field that permeates space and which exerts a magnetic force on moving electric charges and magnetic dipoles. Magnetic fields surround electric currents, magnetic dipoles, and changing electric fields.
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Magnetic flux, represented by the Greek letter Φ (phi), is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field.
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The Biot-Savart Law is an equation in electromagnetism that describes the magnetic field vector B in terms of the magnitude and direction of the source electric current, the distance from the source electric current, and the magnetic permeability weighting factor.
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In physics, the magnetic moment or magnetic dipole moment is a measure of the strength of a magnetic source. In the simplest case of a current loop, the magnetic moment is defined as:
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Classical electromagnetism (or classical electrodynamics) is a theory of electromagnetism that was developed over the course of the 19th century, most prominently by James Clerk Maxwell.
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Electric current is the flow (movement) of electric charge. The SI unit of electric current is the ampere (A), which is equal to a flow of one coulomb of charge per second.
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Definition
The amount of electric current (measured in amperes) through some surface, e.g...... Click the link for more information.
Lorentz force is the force exerted on a charged particle in an electromagnetic field. The particle will experience a force due to electric field of qE, and due to the magnetic field qv × B.
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Electromotive force (emf, ) is a term used to characterize electrical devices, such as voltaic cells, thermoelectric devices, electrical generators and transformers, and even resistors.
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For magnetic induction, see .
Electromagnetic induction is the production of voltage across a conductor situated in a changing magnetic field or a conductor moving through a stationary magnetic field...... Click the link for more information.
Faraday's law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop.
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Displacement current is a quantity related to changing electric field. It occurs in dielectric materials and also in free space.
In the particular case of when it occurs in free space, it is not believed to involve the motion of electric charge as is the case with
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In the particular case of when it occurs in free space, it is not believed to involve the motion of electric charge as is the case with
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For thermodynamic relations, see .
In electromagnetism, Maxwell's equations are a set of four equations that were first presented as a distinct group in 1884 by Oliver Heaviside in conjunction with Willard Gibbs...... Click the link for more information.
The electromagnetic field is a physical field produced by electrically charged objects. It affects the behaviour of charged objects in the vicinity of the field.
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Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. These components oscillate at right angles to each other and to the direction of propagation, and are in phase with each other.
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Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. The most common form of charge storage device is a two-plate capacitor.
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inductance, or more accurately self-inductance of the circuit. The term was coined by Oliver Heaviside in February 1886. It is customary to use the symbol for inductance, possibly in honour of the physicist Heinrich Lenz.
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Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current (AC). Electrical impedance extends the concept of resistance to AC circuits, describing not only the relative magnitudes of the voltage and current, but also the
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A resonator is a device or system that exhibits resonance or resonant behavior. Many objects that use resonant effects are referred to simply as resonators. Examples of resonators are discussed in this article.
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theory of relativity, or simply relativity, refers specifically to two theories: Albert Einstein's special relativity and general relativity.
The term "relativity" was coined by Max Planck in 1908 to emphasize how special relativity (and later, general relativity)
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The term "relativity" was coined by Max Planck in 1908 to emphasize how special relativity (and later, general relativity)
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