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Ohm's law
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This article is about the law related to electricity. For other uses, see Ohm's acoustic law.
V, I, and R, the parameters of Ohm's law.
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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,[1] one arrives at the usual mathematical equation that describes this relationship:[2]
I = V R , {\displaystyle I={\frac {V}{R}},}
where I is the current through the conductor in units of amperes, V is the voltage 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.[3]
The law was named after the German physicist Georg Ohm, who, in a treatise published in 1827, described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire. Ohm explained his experimental results by a slightly more complex equation than the modern form above (see History).
In physics, the term Ohm's law is also used to refer to various generalizations of the law originally formulated by Ohm. The simplest example of this is:
J = σ E , {\displaystyle \mathbf {J} =\sigma \mathbf {E} ,}
where J is the current density at a given location in a resistive material, E is the electric field at that location, and σ (sigma) is a material-dependent parameter called the conductivity. This reformulation of Ohm's law is due to Gustav Kirchhoff.[4]
Contents
[hide]
1 History
2 Scope
3 Microscopic origins
4 Hydraulic analogy
5 Circuit analysis
5.1 Resistive circuits
5.2 Reactive circuits with time-varying signals
5.3 Linear approximations
6 Temperature effects
7 Relation to heat conductions
8 Other versions
8.1 Magnetic effects
8.2 Conductive fluids
9 See also
10 References
11 External links
History
Georg Ohm
In January 1781, before Georg Ohm's work, Henry Cavendish experimented with Leyden jars and glass tubes of varying diameter and length filled with salt solution. He measured the current by noting how strong a shock he felt as he completed the circuit with his body. Cavendish wrote that the "velocity" (current) varied directly as the "degree of electrification" (voltage). He did not communicate his results to other scientists at the time,[5] and his results were unknown until Maxwell published them in 1879.[6]
Francis Ronalds delineated “intensity” (voltage) and “quantity” (current) for the dry pile – a high voltage source – in 1814 using a gold-leaf electrometer. He found for a dry pile that the relationship between the two parameters was not proportional under certain meteorological conditions.[7][8]
Ohm's law in Georg Ohm's lab book.
Ohm did his work on resistance in the years 1825 and 1826, and published his results in 1827 as the book Die galvanische Kette, mathematisch bearbeitet ("The galvanic circuit investigated mathematically").[9] He drew considerable inspiration from Fourier's work on heat conduction in the theoretical explanation of his work. For experiments, he initially used voltaic piles, but later used a thermocouple as this provided a more stable voltage source in terms of internal resistance and constant voltage. He used a galvanometer to measure current, and knew that the voltage between the thermocouple terminals was proportional to the junction temperature. He then added test wires of varying length, diameter, and material to complete the circuit. He found that his data could be modeled through the equation
x = a b + l , {\displaystyle x={\frac {a}{b+l}},}
where x was the reading from the galvanometer, l was the length of the test conductor, a depended only on the thermocouple junction temperature, and b was a constant of the entire setup. From this, Ohm determined his law of proportionality and published his results.
Ohm's law was probably the most important of the early quantitative descriptions of the physics of electricity. We consider it almost obvious today. When Ohm first published his work, this was not the case; critics reacted to his treatment of the subject with hostility. They called his work a "web of naked fancies"[10] and the German Minister of Education proclaimed that "a professor who preached such heresies was unworthy to teach science."[11] The prevailing scientific philosophy in Germany at the time asserted that experiments need not be performed to develop an understanding of nature because nature is so well ordered, and that scientific truths may be deduced through reasoning alone.[12] Also, Ohm's brother Martin, a mathematician, was battling the German educational system. These factors hindered the acceptance of Ohm's work, and his work did not become widely accepted until the 1840s. Fortunately, Ohm received recognition for his contributions to science well before he died.
In the 1850s, Ohm's law was known as such and was widely considered proved, and alternatives, such as "Barlow's law", were discredited, in terms of real applications to telegraph system design, as discussed by Samuel F. B. Morse in 1855.[13]
While the old term for electrical conductance, the mho (the inverse of the resistance unit ohm), is still used, a new name, the siemens, was adopted in 1971, honoring Ernst Werner von Siemens. The siemens is preferred in formal papers.
In the 1920s, it was discovered that the current through a practical resistor actually has statistical fluctuations, which depend on temperature, even when voltage and resistance are exactly constant; this fluctuation, now known as Johnson–Nyquist noise, is due to the discrete nature of charge. This thermal effect implies that measurements of current and voltage that are taken over sufficiently short periods of time will yield ratios of V/I that fluctuate from the value of R implied by the time average or ensemble average of the measured current; Ohm's law remains correct for the average current, in the case of ordinary resistive materials.
Ohm's work long preceded Maxwell's equations and any understanding of frequency-dependent effects in AC circuits. Modern developments in electromagnetic theory and circuit theory do not contradict Ohm's law when they are evaluated within the appropriate limits.
Scope
Ohm's law is an empirical law, a generalization from many experiments that have shown that current is approximately proportional to electric field for most materials. It is less fundamental than Maxwell's equations and is not always obeyed. Any given material will break down under a strong-enough electric field, and some materials of interest in electrical engineering are "non-ohmic" under weak fields.[14][15]
Ohm's law has been observed on a wide range of length scales. In the early 20th century, it was thought that Ohm's law would fail at the atomic scale, but experiments have not borne out this expectation. As of 2012, researchers have demonstrated that Ohm's law works for silicon wires as small as four atoms wide and one atom high.[16]
Microscopic origins
Drude Model electrons (shown here in blue) constantly bounce among heavier, stationary crystal ions (shown in red).
Main articles: Drude model and Classical and quantum conductivity
The dependence of the current density on the applied electric field is essentially quantum mechanical in nature; (see Classical and quantum conductivity.) A qualitative description leading to Ohm's law can be based upon classical mechanics using the Drude model developed by Paul Drude in 1900.[17][18]
The Drude model treats electrons (or other charge carriers) like pinballs bouncing among the ions that make up the structure of the material. Electrons will be accelerated in the opposite direction to the electric field by the average electric field at their location. With each collision, though, the electron is deflected in a random direction with a velocity that is much larger than the velocity gained by the electric field. The net result is that electrons take a zigzag path due to the collisions, but generally drift in a direction opposing the electric field.
The drift velocity then determines the electric current density and its relationship to E and is independent of the collisions. Drude calculated the average drift velocity from p = −eEτ where p is the average momentum, −e is the charge of the electron and τ is the average time between the collisions. Since both the momentum and the current density are proportional to the drift velocity, the current density becomes proportional to the applied electric field; this leads to Ohm's law.
Hydraulic analogy
A hydraulic analogy is sometimes used to describe Ohm's law. Water pressure, measured by pascals (or PSI), is the analog of voltage because establishing a water pressure difference between two points along a (horizontal) pipe causes water to flow. Water flow rate, as in liters per second, is the analog of current, as in coulombs per second. Finally, flow restrictors—such as apertures placed in pipes between points where the water pressure is measured—are the analog of resistors. We say that the rate of water flow through an aperture restrictor is proportional to the difference in water pressure across the restrictor. Similarly, the rate of flow of electrical charge, that is, the electric current, through an electrical resistor is proportional to the difference in voltage measured across the resistor.
Flow and pressure variables can be calculated in fluid flow network with the use of the hydraulic ohm analogy.[19][20] The method can be applied to both steady and transient flow situations. In the linear laminar flow region, Poiseuille's law describes the hydraulic resistance of a pipe, but in the turbulent flow region the pressure–flow relations become nonlinear.
The hydraulic analogy to Ohm's law has been used, for example, to approximate blood flow through the circulatory system.[21]
Circuit analysis
Ohm's law triangle
Ohm’s law wheel with international unit symbols
In circuit analysis, three equivalent expressions of Ohm's law are used interchangeably:
I = V R or V = I R or R = V I . {\displaystyle I={\frac {V}{R}}\quad {\text{or}}\quad V=IR\quad {\text{or}}\quad R={\frac {V}{I}}.}
Each equation is quoted by some sources as the defining relationship of Ohm's law,[2][22][23] or all three are quoted,[24] or derived from a proportional form,[25] or even just the two that do not correspond to Ohm's original statement may sometimes be given.[26][27]
The interchangeability of the equation may be represented by a triangle, where V (voltage) is placed on the top section, the I (current) is placed to the left section, and the R (resistance) is placed to the right. The line that divides the left and right sections indicate multiplication, and the divider between the top and bottom sections indicates division (hence the division bar).
Resistive circuits
Resistors are circuit elements that impede the passage of electric charge in agreement with Ohm's law, and are designed to have a specific resistance value R. In a schematic diagram the resistor is shown as a zig-zag symbol. An element (resistor or conductor) that behaves according to Ohm's law over some operating range is referred to as an ohmic device (or an ohmic resistor) because Ohm's law and a single value for the resistance suffice to describe the behavior of the device over that range.
Ohm's law holds for circuits containing only resistive elements (no capacitances or inductances) for all forms of driving voltage or current, regardless of whether the driving voltage or current is constant (DC) or time-varying such as AC. At any instant of time Ohm's law is valid for such circuits.
Resistors which are in series or in parallel may be grouped together into a single "equivalent resistance" in order to apply Ohm's law in analyzing the circuit.
Reactive circuits with time-varying signals
When reactive elements such as capacitors, inductors, or transmission lines are involved in a circuit to which AC or time-varying voltage or current is applied, the relationship between voltage and current becomes the solution to a differential equation, so Ohm's law (as defined above) does not directly apply since that form contains only resistances having value R, not complex impedances which may contain capacitance ("C") or inductance ("L").
Equations for time-invariant AC circuits take the same form as Ohm's law. However, the variables are generalized to complex numbers and the current and voltage waveforms are complex exponentials.[28]
In this approach, a voltage or current waveform takes the form A e s t {\displaystyle Ae^{st}} , where t is time, s is a complex parameter, and A is a complex scalar. In any linear time-invariant system, all of the currents and voltages can be expressed with the same s parameter as the input to the system, allowing the time-varying complex exponential term to be canceled out and the system described algebraically in terms of the complex scalars in the current and voltage waveforms.
The complex generalization of resistance is impedance, usually denoted Z; it can be shown that for an inductor,
Z = s L {\displaystyle Z=sL\,}
and for a capacitor,
Z = 1 s C . {\displaystyle Z={\frac {1}{sC}}.}
We can now write,
V = I ⋅ Z {\displaystyle {\boldsymbol {V}}={\boldsymbol {I}}\cdot {\boldsymbol {Z}}}
where V and I are the complex scalars in the voltage and current respectively and Z is the complex impedance.
This form of Ohm's law, with Z taking the place of R, generalizes the simpler form. When Z is complex, only the real part is responsible for dissipating heat.
In the general AC circuit, Z varies strongly with the frequency parameter s, and so also will the relationship between voltage and current.
For the common case of a steady sinusoid, the s parameter is taken to be j ω {\displaystyle j\omega } , corresponding to a complex sinusoid A e j ω t {\displaystyle Ae^{{\mbox{ }}j\omega t}} . The real parts of such complex current and voltage waveforms describe the actual sinusoidal currents and voltages in a circuit, which can be in different phases due to the different complex scalars.
Linear approximations
See also: Small-signal modeling and Network analysis (electrical circuits) § Small signal equivalent circuit
Ohm's law is one of the basic equations used in the analysis of electrical circuits. It applies to both metal conductors and circuit components (resistors) specifically made for this behaviour. Both are ubiquitous in electrical engineering. Materials and components that obey Ohm's law are described as "ohmic" [29] which means they produce the same value for resistance (R = V/I) regardless of the value of V or I which is applied and whether the applied voltage or current is DC (direct current) of either positive or negative polarity or AC (alternating current).
In a true ohmic device, the same value of resistance will be calculated from R = V/I regardless of the value of the applied voltage V. That is, the ratio of V/I is constant, and when current is plotted as a function of voltage the curve is linear (a straight line). If voltage is forced to some value V, then that voltage V divided by measured current I will equal R. Or if the current is forced to some value I, then the measured voltage V divided by that current I is also R. Since the plot of I versus V is a straight line, then it is also true that for any set of two different voltages V1 and V2 applied across a given device of resistance R, producing currents I1 = V1/R and I2 = V2/R, that the ratio (V1−V2)/(I1−I2) is also a constant equal to R. The operator "delta" (Δ) is used to represent a difference in a quantity, so we can write ΔV = V1−V2 and ΔI = I1−I2. Summarizing, for any truly ohmic device having resistance R, V/I = ΔV/ΔI = R for any applied voltage or current or for the difference between any set of applied voltages or currents.
The I–V curves of four devices: Two resistors, a diode, and a battery. The two resistors follow Ohm's law: The plot is a straight line through the origin. The other two devices do not follow Ohm's law.
There are, however, components of electrical circuits which do not obey Ohm's law; that is, their relationship between current and voltage (their I–V curve) is nonlinear (or non-ohmic). An example is the p-n junction diode (curve at right). As seen in the figure, the current does not increase linearly with applied voltage for a diode. One can determine a value of current (I) for a given value of applied voltage (V) from the curve, but not from Ohm's law, since the value of "resistance" is not constant as a function of applied voltage. Further, the current only increases significantly if the applied voltage is positive, not negative. The ratio V/I for some point along the nonlinear curve is sometimes called the static, or chordal, or DC, resistance,[30][31] but as seen in the figure the value of total V over total I varies depending on the particular point along the nonlinear curve which is chosen. This means the "DC resistance" V/I at some point on the curve is not the same as what would be determined by applying an AC signal having peak amplitude ΔV volts or ΔI amps centered at that same point along the curve and measuring ΔV/ΔI. However, in some diode applications, the AC signal applied to the device is small and it is possible to analyze the circuit in terms of the dynamic, small-signal, or incremental resistance, defined as the one over the slope of the V–I curve at the average value (DC operating point) of the voltage (that is, one over the derivative of current with respect to voltage). For sufficiently small signals, the dynamic resistance allows the Ohm's law small signal resistance to be calculated as approximately one over the slope of a line drawn tangentially to the V-I curve at the DC operating point.[32]
Temperature effects
Ohm's law has sometimes been stated as, "for a conductor in a given state, the electromotive force is proportional to the current produced." That is, that the resistance, the ratio of the applied electromotive force (or voltage) to the current, "does not vary with the current strength ." The qualifier "in a given state" is usually interpreted as meaning "at a constant temperature," since the resistivity of materials is usually temperature dependent. Because the conduction of current is related to Joule heating of the conducting body, according to Joule's first law, the temperature of a conducting body may change when it carries a current. The dependence of resistance on temperature therefore makes resistance depend upon the current in a typical experimental setup, making the law in this form difficult to directly verify. Maxwell and others worked out several methods to test the law experimentally in 1876, controlling for heating effects.[33]
Relation to heat conductions
See also: Conduction (heat)
Ohm's principle predicts the flow of electrical charge (i.e. current) in electrical conductors when subjected to the influence of voltage differences; Jean-Baptiste-Joseph Fourier's principle predicts the flow of heat in heat conductors when subjected to the influence of temperature differences.
The same equation describes both phenomena, the equation's variables taking on different meanings in the two cases. Specifically, solving a heat conduction (Fourier) problem with temperature (the driving "force") and flux of heat (the rate of flow of the driven "quantity", i.e. heat energy) variables also solves an analogous electrical conduction (Ohm) problem having electric potential (the driving "force") and electric current (the rate of flow of the driven "quantity", i.e. charge) variables.
The basis of Fourier's work was his clear conception and definition of thermal conductivity. He assumed that, all else being the same, the flux of heat is strictly proportional to the gradient of temperature. Although undoubtedly true for small temperature gradients, strictly proportional behavior will be lost when real materials (e.g. ones having a thermal conductivity that is a function of temperature) are subjected to large temperature gradients.
A similar assumption is made in the statement of Ohm's law: other things being alike, the strength of the current at each point is proportional to the gradient of electric potential. The accuracy of the assumption that flow is proportional to the gradient is more readily tested, using modern measurement methods, for the electrical case than for the heat case.
Other versions
Ohm's law, in the form above, is an extremely useful equation in the field of electrical/electronic engineering because it describes how voltage, current and resistance are interrelated on a "macroscopic" level, that is, commonly, as circuit elements in an electrical circuit. Physicists who study the electrical properties of matter at the microscopic level use a closely related and more general vector equation, sometimes also referred to as Ohm's law, having variables that are closely related to the V, I, and R scalar variables of Ohm's law, but which are each functions of position within the conductor. Physicists often use this continuum form of Ohm's Law:[34]
E = ρ J {\displaystyle \mathbf {E} =\rho \mathbf {J} }
where "E" is the electric field vector with units of volts per meter (analogous to "V" of Ohm's law which has units of volts), "J" is the current density vector with units of amperes per unit area (analogous to "I" of Ohm's law which has units of amperes), and "ρ" (Greek "rho") is the resistivity with units of ohm·meters (analogous to "R" of Ohm's law which has units of ohms). The above equation is sometimes written[35] as J = σ {\displaystyle \sigma } E where "σ" (Greek "sigma") is the conductivity which is the reciprocal of ρ.
Current flowing through a uniform cylindrical conductor (such as a round wire) with a uniform field applied.
The voltage between two points is defined as:[36]
Δ V = − ∫ E ⋅ d l {\displaystyle {\Delta V}=-\int {\mathbf {E} \cdot d\mathbf {l} }}
with d l {\displaystyle d\mathbf {l} } the element of path along the integration of electric field vector E. If the applied E field is uniform and oriented along the length of the conductor as shown in the figure, then defining the voltage V in the usual convention of being opposite in direction to the field (see figure), and with the understanding that the voltage V is measured differentially across the length of the conductor allowing us to drop the Δ symbol, the above vector equation reduces to the scalar equation:
V = E l or E = V l . {\displaystyle V={E}{l}\ \ {\text{or}}\ \ E={\frac {V}{l}}.}
Since the E field is uniform in the direction of wire length, for a conductor having uniformly consistent resistivity ρ, the current density J will also be uniform in any cross-sectional area and oriented in the direction of wire length, so we may write:[37]
J = I a . {\displaystyle J={\frac {I}{a}}.}
Substituting the above 2 results (for E and J respectively) into the continuum form shown at the beginning of this section:
V l = I a ρ or V = I ρ l a . {\displaystyle {\frac {V}{l}}={\frac {I}{a}}\rho \qquad {\text{or}}\qquad V=I\rho {\frac {l}{a}}.}
The electrical resistance of a uniform conductor is given in terms of resistivity by:[37]
R = ρ l a {\displaystyle {R}=\rho {\frac {l}{a}}}
where l is the length of the conductor in SI units of meters, a is the cross-sectional area (for a round wire a = πr2 if r is radius) in units of meters squared, and ρ is the resistivity in units of ohm·meters.
After substitution of R from the above equation into the equation preceding it, the continuum form of Ohm's law for a uniform field (and uniform current density) oriented along the length of the conductor reduces to the more familiar form:
V = I R . {\displaystyle {V}={I}{R}.\ }
A perfect crystal lattice, with low enough thermal motion and no deviations from periodic structure, would have no resistivity,[38] but a real metal has crystallographic defects, impurities, multiple isotopes, and thermal motion of the atoms. Electrons scatter from all of these, resulting in resistance to their flow.
The more complex generalized forms of Ohm's law are important to condensed matter physics, which studies the properties of matter and, in particular, its electronic structure. In broad terms, they fall under the topic of constitutive equations and the theory of transport coefficients.
Magnetic effects
If an external B-field is present and the conductor is not at rest but moving at velocity v, then an extra term must be added to account for the current induced by the Lorentz force on the charge carriers.
J = σ ( E + v × B ) {\displaystyle \mathbf {J} =\sigma (\mathbf {E} +\mathbf {v} \times \mathbf {B} )}
In the rest frame of the moving conductor this term drops out because v= 0. There is no contradiction because the electric field in the rest frame differs from the E-field in the lab frame: E′ = E + v×B. Electric and magnetic fields are relative, see Lorentz transformation.
If the current J is alternating because the applied voltage or E-field varies in time, then reactance must be added to resistance to account for self-inductance, see electrical impedance. The reactance may be strong if the frequency is high or the conductor is coiled.
Conductive fluids
In a conductive fluid, such as a plasma, there is a similar effect. Consider a fluid moving with the velocity v → {\displaystyle {\vec {v}}} in a magnetic field B → {\displaystyle {\vec {B}}} . The relative motion induces an electric field E → {\displaystyle {\vec {E}}} which exerts electric force on the charged particles giving rise to an electric current J → {\displaystyle {\vec {J}}} . The equation of motion for the electron gas, with a number density n e {\displaystyle n_{e}} , is written as
m e n e d v → e d t = − n e e E → + n e m e ν ( v i − v e ) − e n e v → e × B → , {\displaystyle m_{e}n_{e}{d{\vec {v}}_{e} \over dt}=-n_{e}e{\vec {E}}+n_{e}m_{e}\nu (v_{i}-v_{e})-en_{e}{\vec {v}}_{e}\times {\vec {B}},}
where e {\displaystyle e} , m e {\displaystyle m_{e}} and v → e {\displaystyle {\vec {v}}_{e}} are the charge, mass and velocity of the electrons, respectively. Also, ν {\displaystyle \nu } is the frequency of collisions of the electrons with ions which have a velocity field v → i {\displaystyle {\vec {v}}_{i}} . Since, the electron has a very small mass compared with that of ions, we can ignore the left hand side of the above equation to write
σ ( E → + v → × B → ) = J → , {\displaystyle \sigma ({\vec {E}}+{\vec {v}}\times {\vec {B}})={\vec {J}},}
where we have used the definition of the current density, and also put σ = n e e 2 ν m e {\displaystyle \sigma ={n_{e}e^{2} \over \nu m_{e}}} which is the electrical conductivity. This equation can also be equivalently written as
E → + v → × B → = ρ J → , {\displaystyle {\vec {E}}+{\vec {v}}\times {\vec {B}}=\rho {\vec {J}},}
where ρ = σ − 1 {\displaystyle \rho =\sigma ^{-1}} is the electrical resistivity. It is also common to write η {\displaystyle \eta } instead of ρ {\displaystyle \rho } which can be confusing since it is the same notation used for the magnetic diffusivity defined as η = 1 / μ 0 σ {\displaystyle \eta =1/\mu _{0}\sigma } .
See also
Electronics portal
Fick's law of diffusion
Hopkinson's law ("Ohm's law for magnetics")
Maximum power transfer theorem
Norton's theorem
Sheet resistance
Superposition theorem
Thermal noise
Thévenin's theorem
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Jump up ^ Linnaeus Cumming (1902). Electricity treated experimentally for the use of schools and students. Longman's Green and Co. p. 220.
Jump up ^ Benjamin Stein (1997). Building technology (2nd ed.). John Wiley and Sons. p. 169. ISBN 978-0-471-59319-5.
Jump up ^ Rajendra Prasad (2006). Fundamentals of Electrical Engineering. Prentice-Hall of India. ISBN 978-81-203-2729-0.
Jump up ^ Hughes, E, Electrical Technology, pp10, Longmans, 1969.
Jump up ^ Forbes T. Brown (2006). Engineering System Dynamics. CRC Press. p. 43. ISBN 978-0-8493-9648-9.
Jump up ^ Kenneth L. Kaiser (2004). Electromagnetic Compatibility Handbook. CRC Press. pp. 13–52. ISBN 978-0-8493-2087-3.
Jump up ^ Horowitz, Paul; Winfield Hill (1989). The Art of Electronics (2nd ed.). Cambridge University Press. p. 13. ISBN 0-521-37095-7.
Jump up ^ Normal Lockyer, ed. (September 21, 1876). "Reports". Nature. Macmillan Journals Ltd. 14: 451–9 [452]. Bibcode:1876Natur..14..451.. doi:10.1038/014451a0.
Jump up ^ Lerner, Lawrence S. (1977). Physics for scientists and engineers. Jones & Bartlett. p. 736. ISBN 978-0-7637-0460-5.
Jump up ^ Seymour J, Physical Electronics, Pitman, 1972, pp 53–54
Jump up ^ Lerner L, Physics for scientists and engineers, Jones & Bartlett, 1997, pp. 685–686
^ Jump up to: a b Lerner L, Physics for scientists and engineers, Jones & Bartlett, 1997, pp. 732–733
Jump up ^ Seymour J, Physical Electronics, pp 48–49, Pitman, 1972
External links
Wikimedia Commons has media related to Ohm's law.
Ohm's Law chapter from Lessons In Electric Circuits Vol 1 DC book and series.
John C. Shedd and Mayo D. Hershey,"The History of Ohm's Law", Popular Science, December 1913, pages 599-614, Bonnier Corporation ISSN 0161-7370, gives the history of Ohm's investigations, prior work, Ohm's false equation in the first paper, illustration of Ohm's experimental apparatus.
Morton L. Schagrin, "Resistance to Ohm's Law", American Journal of Physics, July 1963, Volume 31, Issue 7, pp. 536–47. Explores the conceptual change underlying Ohm's experimental work.
Kenneth L. Caneva, "Ohm, Georg Simon." Complete Dictionary of Scientific Biography. 2008
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Enlightenment (Van Morrison album)
From Wikipedia, the free encyclopedia
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Enlightenment
Studio album by Van Morrison
Released
October 1990
Reissued June 2008
Recorded
February 1990
Wool Hall Studios, Real World Studio, Box Studio and Pavilion Studios, London, England; The Kirk, Somerset, England
Genre
Celtic, folk rock
Length
50:30
Label
Polydor
Producer
Van Morrison
Van Morrison chronology
The Best of Van Morrison
(1990) Enlightenment
(1990) Hymns to the Silence
(1991)
Singles from Enlightenment
"Real Real Gone" b/w "Start All Over Again"
Released: September 1990
"In the Days Before Rock 'N' Roll" b/w "I'd Love to Write Another Song"
Released: November 1990
"Enlightenment b/w "Avalon of the Heart"
Released: January 1991
Professional ratings
Review scores
Source
Rating
AllMusic [1]
Robert Christgau B+[2]
Entertainment Weekly A[3]
MusicHound 3.5/5[4]
Rolling Stone [5]
Select [6]
Enlightenment is the twentieth studio album by Northern Irish singer-songwriter Van Morrison. It was released in 1990 and reached #5 in the UK charts and "Real Real Gone" charted at #18 in Mainstream Rock Tracks.
The June 2008 re-issued and re-mastered version of the album contains alternative takes of "Enlightenment" and "So Quiet in Here"."Start All Over Again" from this album was listed as one of the standout tracks from the six album reissue.[7]
Contents
1 Recording
2 Composition
3 Track listing
3.1 Bonus tracks (2008 CD reissue)
4 Personnel
4.1 Musicians
4.2 Production
5 Charts
5.1 Album
5.2 Singles
6 Notes
7 References
8 External links
Recording[edit]
The album was recorded in London, England, and Real World in Box. The arrangements were by Fiachra Trench and Micheal O'Suilleabhain played piano with a brass section made up of British jazz musicians from the late sixties: Frank Ricotti, Henry Lowther and Malcolm Griffiths. One of the songs "So Quiet in Here" was recorded at the Kirk, Rode, Somerset, a setting which served as both church or studio.[8]
Composition[edit]
The song "Enlightenment" contains the words: "I'm in the here and now and I'm meditating/ And still I'm suffering but that's my problem/ Enlightenment, don't know what it is". "So Quiet in Here" is a continuation of the song "Into the Mystic" from the Moondance album.[citation needed] The single released from the album, "Real Real Gone", was originally written and meant for the 1980 album Common One.[9] The song "In the Days Before Rock 'N' Roll" was a collaboration between Morrison and the Irish poet Paul Durcan.
Track listing[edit]
All songs by Morrison unless noted otherwise.
"Real Real Gone" – 3:43
"Enlightenment" – 4:04
"So Quiet in Here" – 6:09
"Avalon of the Heart" – 4:45
"See Me Through" – 6:13
"Youth of 1,000 Summers" – 3:45
"In the Days Before Rock 'N' Roll" (Durcan, Morrison) – 8:13
"Start All Over Again" – 4:10
"She's My Baby" – 5:14
"Memories" – 4:14
Bonus tracks (2008 CD reissue)[edit]
"Enlightenment" – 3:29 (alternative take)
"So Quiet in Here" – 4:03 (alternative take)
Personnel[edit]
Musicians[edit]
Van Morrison - vocals, guitar, harmonica
The Ambrosian Singers - choir, with John McCarthy as choirmaster (on 4)
Dave Bishop - soprano and baritone saxophones
Paul Durcan - spoken word (on 7)
Dave Early - drums (except on 4, 10)
Georgie Fame - electric piano, hammond organ, backing vocals
Alex Gifford - synthesizers, piano
Steve Gregory - tenor saxophone, flute
Malcolm Griffiths - trombone
Bernie Holland - lead guitar (on 2, 6, 9)
Henry Lowther - trumpet (on 6, 8, 9)
Brian Odgers - bass (on 2, 9)
Mícheál Ó Súilleabháin - piano (on 3)
Steve Pearce - bass guitar (except on 2, 9)
Frank Ricotti - vibraphone (on 8)
Steve Sanger - drums (on 4, 10)
Steve Waterman - flugelhorn (on 6, 8, 9)
Production[edit]
Recorded mainly at Wool Hall Studios, Beckington
Townhouse, London, Real World, Box and Pavilion Studios, London.
("So Quiet in Here" recorded at The Kirk, Rode, Somerset)
Producer: Van Morrison
Engineers: Mick Glossop, Steve Williams
Additional engineering: Alastair McMillan
Mixing: Mick Glossop, Steve Williams
String, Brass and Choir arrangements: Fiachra Trench
String section leader: Gavin Wright
Keyboard and Synth arrangements: Neil Drinkwater
Charts[edit]
Album[edit]
UK Album Chart
Year Chart Position
1990 UK Album Chart 5
Billboard (North America)
Year
Chart
Position
1990 The Billboard 200 62
Singles[edit]
Billboard
Year
Single
Chart
Position
1990 "Real Real Gone" Mainstream Rock Tracks 18
Notes[edit]
Jump up ^ AllMusic review
Jump up ^ Robert Christgau review
Jump up ^ Entertainment Weekly review
Jump up ^ Graff, Gary; Durchholz, Daniel (eds) (1999). MusicHound Rock: The Essential Album Guide. Farmington Hills, MI: Visible Ink Press. p. 784. ISBN 1-57859-061-2. CS1 maint: Extra text: authors list (link)
Jump up ^ Rolling Stone review
Jump up ^ Brown, Glyn (November 1990). "Guiding Light". Select. p. 100.
Jump up ^ "Catalog Reissues by Van Morrison on Blurt Online". blurt-online.com. Archived from the original on 22 July 2012. Retrieved 2009-11-02.
Jump up ^ Hinton, Celtic Crossroads, pp. 292-293
Jump up ^ Hinton, Celtic Crossroads, pp 293, 294
References[edit]
Hinton, Brian (1997). Celtic Crossroads: The Art of Van Morrison, Sanctuary, ISBN 1-86074-169-X
External links[edit]
Van Morrison's Enlightenment another sign of transition
hide
v
t
e
Van Morrison
Them
The Angry Young Them
Them Again
The Story of Them Featuring Van Morrison
Studio albums
Blowin' Your Mind!
Astral Weeks
Moondance
His Band and the Street Choir
Tupelo Honey
Saint Dominic's Preview
Hard Nose the Highway
Veedon Fleece
A Period of Transition
Wavelength
Into the Music
Common One
Beautiful Vision
Inarticulate Speech of the Heart
A Sense of Wonder
No Guru, No Method, No Teacher
Poetic Champions Compose
Irish Heartbeat
Avalon Sunset
Enlightenment
Hymns to the Silence
Too Long in Exile
Days Like This
How Long Has This Been Going On
Tell Me Something: The Songs of Mose Allison
The Healing Game
Back on Top
You Win Again
Down the Road
What's Wrong with This Picture?
Magic Time
Pay the Devil
Keep It Simple
Born to Sing: No Plan B
Duets: Re-working the Catalogue
Keep Me Singing
Roll with the Punches
Versatile
You're Driving Me Crazy
Live albums
It's Too Late to Stop Now
Live at the Grand Opera House Belfast
A Night in San Francisco
The Skiffle Sessions - Live in Belfast 1998
Live at Austin City Limits Festival
Astral Weeks Live at the Hollywood Bowl
Compilations
The Best of Van Morrison
The Best of Van Morrison Volume Two
The Philosopher's Stone
Van Morrison at the Movies - Soundtrack Hits
The Best of Van Morrison Volume 3
Still on Top - The Greatest Hits
Videos
Van Morrison in Ireland
Van Morrison The Concert
DVDs
Live at Montreux 1980/1974
Astral Weeks Live at the Hollywood Bowl: The Concert Film
Unofficial Bang albums
T.B. Sheets
Bang Masters
Payin' Dues
The Complete New York Sessions '67
The Complete Bang Sessions
Tribute albums
No Prima Donna: The Songs of Van Morrison
The Van Morrison Songbook
Vanthology: A Tribute to Van Morrison
Discography
Albums
Songs
List of artists who have covered Van Morrison songs
Related topics
List of awards and nominations received by Van Morrison
Retrieved from "https://en.wikipedia.org/w/index.php?title=Enlightenment_(Van_Morrison_album)&oldid=842067107"
Categories:
Van Morrison albums
1990 albums
Mercury Records albums
Albums produced by Van Morrison
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Rings of Power
From Wikipedia, the free encyclopedia
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For other uses, see Power ring (disambiguation).
This Middle-earth-related article describes a work or element of fiction in a primarily in-universe style. Please help rewrite it to explain the fiction more clearly and provide non-fictional perspective. (February 2011) (Learn how and when to remove this template message)
The Rings of Power in J. R. R. Tolkien's Middle-earth legendarium are magic rings created by Sauron or by the Elves of Eregion under Sauron's tutelage. Sauron intended three of the rings to be worn by Elves, Seven by Dwarves, Nine by Men, and one, the One Ring, by Sauron himself in Mordor.
Sauron intended the rings to subvert these races of Middle-earth to his power, since the One Ring controlled the others. Sauron's plan was not completely successful, for the Elves hid their rings and did not use them while Sauron held the One, and the Dwarves did not respond to the One's control as Sauron expected. But the Men who wore the Nine were enslaved by Sauron, and became the Nazgûl ("ringwraiths").
Tolkien's The Lord of the Rings is largely concerned with the attempt of Sauron to recover the One and the efforts of the West to forestall him by destroying it. The One is destroyed near the end of the War of the Ring when it falls into the Cracks of Doom in Orodruin, along with Gollum, who had bitten off Frodo’s finger on which he was wearing the Ring. Tolkien is not entirely clear about what happened to the other rings, though he implied that the power of any that survived came to an end. After the War of the Ring, the three Elven Rings were taken by their bearers over the sea to the Undying Lands.
Contents
[hide]
1 Literature
1.1 The making of the rings
1.1.1 The Verse of the Rings
1.2 The Nine
1.3 The Seven
1.4 The Three
1.5 The One
2 Adaptations
3 See also
4 References
4.1 General references
Literature[edit]
The making of the rings[edit]
Tolkien's essay "Of the Rings of Power and the Third Age" in The Silmarillion gives the background of the making of the rings.[1] At the end of the First Age, Sauron evaded the call of the Valar to surrender, and fled to Middle-earth. Midway through the Second Age he came in disguise as Annatar ("Lord of Gifts") to the Elven-smiths of Eregion, who were led by Celebrimbor, and taught them the craft of forging magic rings. Tolkien writes that the Elves made many lesser rings as essays in the craft,[2] but eventually with Sauron's assistance they forged the Seven and the Nine. The Three were made by Celebrimbor himself without Sauron's assistance; they remained unsullied by his touch.
Sauron returned to Mordor, and in his forge in Mount Doom he made the One Ring, imbuing it with a large portion of his power. Its purpose was to dominate and command the wearers of the other Rings. However, when Sauron put on the One Ring and recited the incantation inscribed on it, the Elves became aware of him, and understood who he was and his purpose. The words he spoke are in the language that Westron speakers call the Black Speech:
The inscription on the One Ring is a Tengwar rendering of the language known as Black Speech.
Ash nazg durbatulûk,
Ash nazg gimbatul,
Ash nazg thrakatulûk
Agh burzum-ishi krimpatul.
One Ring to rule them all,
One Ring to find them,
One Ring to bring them all,
And in the darkness bind them.
When the Elves wearing the rings discerned Sauron's intention, they immediately removed them and hid them. Sauron invaded the West to recover the rings that the Elves had made; much of the West, including Eregion, was destroyed before he was driven back to Mordor. Sauron recovered the Nine and three of the Seven, but not the Three Elven Rings, which remained hidden.
The Verse of the Rings[edit]
The words inscribed on the One Ring come from the following verse, which describes 20 of the Rings of Power:
Three Rings for the Elven-kings under the sky,
Seven for the Dwarf-lords in their halls of stone,
Nine for Mortal Men doomed to die,
One for the Dark Lord on his dark throne,
In the Land of Mordor where the Shadows lie,
One ring to rule them all, one ring to find them,
One ring to bring them all and in the darkness bind them
In the Land of Mordor where the Shadows lie.
— The Lord of the Rings, Epigraph
The Nine[edit]
Main article: Nazgûl
Later in the Second Age, Sauron gave the Nine to powerful men, "kings, sorcerers, and warriors of old".[3] All of them fell under the rings' dominance, and they became the Nazgûl (Ringwraiths), spirits of terror whom Sauron could command even without the One. Their lives were extended indefinitely by the rings, and they became Sauron's chief servants.
To mortal observers who were not themselves wearing a Ring, a Ring of Power seemed to render the wearer invisible.[2] Although the Nazgûl could not be seen, they emanated an evil presence;[4] their steeds were also visible. When they wished to adopt a noticeable form, they wore dark cloaks over their invisible bodies.
It is not clear whether the Nazgûl kept their rings. Tolkien says both "the Nine the Nazgûl keep"[5] and that Sauron had gathered the Nine to himself,[2] though in the latter case his meaning may be metaphorical. When the Nazgûl are destroyed, no mention is made of their rings.
Only two of the Nazgûl are identified in the texts: the Witch-king of Angmar was the leader of the nine, and his second in command was Khamûl, an Easterling.[6] Khamûl is the only Nazgûl identified by name. Three of the Nine were Númenórean.[7]
The Seven[edit]
Also in the Second Age Sauron gave the Seven to the seven Dwarf-lords (though the Dwarves of Moria maintained a tradition that the ring given to Durin III came directly from the Elven-smiths).[8][9] Gandalf mentions a rumour that the seven hoards of the Dwarves began each with a single golden ring, and although the Dwarves used their rings to increase their treasure, Tolkien does not explain how the rings accomplished this (save for a reference that the rings "need gold to breed gold"). The main power of the Seven on their wearers was to excite their sense of avarice. The wearers did not become invisible, did not get extended life-spans, nor succumb directly to Sauron's control – though he could still influence them to anger and greed.[1]
Over the years, Sauron recovered three rings from the Dwarves, the last from Thráin II during his final captivity in Dol Guldur, some years before the beginning of The Hobbit. The remaining four, according to Gandalf, were consumed by dragons.[2]
Until the Council of Elrond, the Dwarves did not know that Thráin had held the ring of Durin's line and had lost it to Sauron. They thought instead that it might have been lost when Thrór was killed by Azog in Moria.[5] One of the motivations for Balin's doomed expedition to Moria was the possibility of recovering the ring. Sauron's messenger attempted to bribe the Dwarves of Erebor for news of Bilbo (the last known bearer of the One) with the promise of the return of the remaining three of the Seven and control over the Mines of Moria.
The Three[edit]
Main article: Three Rings
The Three Rings of the Elves were called Narya, the Ring of Fire (set with a ruby); Nenya, the Ring of Water or Ring of Adamant (made of mithril and set with a "white stone"), and Vilya, the Ring of Air, the "mightiest of the Three" (made of gold and set with a sapphire).[10]
Before the sack of Eregion, Celebrimbor gave Vilya and Narya to Gil-galad and Nenya to Galadriel. Gil-galad later gave Narya to Círdan, and gave Vilya to Elrond.
The Three remained hidden from Sauron and untouched by him. During the Third Age, after he lost the One, they were used for the preservation and enhancement of three remaining realms of the Eldar. Vilya was used by Elrond in Rivendell, Nenya by Galadriel in Lothlórien, and Narya by Círdan in Lindon. When the Istari, or wizards, arrived about T.A. 1100, Círdan gave Narya to Gandalf, who bore it until the end of the Third Age.
During the period of The Lord of the Rings, the Three were borne by Elrond, Galadriel, and Gandalf; but until the end of the book their rings are not seen. Only Frodo, the bearer of the One, sees Galadriel's ring, and only when she draws his attention to it. At the end of the book, these three take their rings, now visible and powerless, over the sea to the Undying Lands.
Although the Verse of the Rings describes Three Rings for the Elven-kings, the only Elven king who actually held a ring was Gil-galad. He held both Vilya and Narya, but entrusted them to Elrond and Círdan before perishing in Mordor.
The One[edit]
Main article: One Ring
Unlike the other Rings of Power, the One was unadorned. It bore only the inscription of the incantation Sauron spoke when he made it, and even that was invisible unless the ring was heated.[2] Though the other rings could be destroyed in dragon-fire, the One could be unmade only in the unyielding fires of Mount Doom where it was forged.[2]
When Sauron made the ring, he was obliged to transfer much of his power into it so that it could control the other rings, themselves objects of great potency. With the ring, Sauron remained very powerful, and he could use it to dominate the will of others; he very quickly corrupted Númenor into the worship of Melkor and open rebellion against the Valar.
When Isildur cut the ring from his hand, Sauron became much weaker. He required the ring to effect his conquest of Middle-earth, and spent most of the Third Age attempting to get it back.
The ring had a great effect on the human bearers who held it in the interim. It granted them indefinite life; though the effort of living became more difficult as time went on, for it did not grant new life.[2] If they wore it, it made them invisible, enhanced their hearing, and made the shadowy world of the wraiths visible to them. It exerted a malicious influence; Gandalf mentions that though a bearer might begin with good intentions, the good intentions would not last.[2] The Ring would give its bearer a fraction of Sauron's power, proportionate with the bearer's strength and force of will. Gollum, Bilbo, Sam, and Frodo only became invisible, although when Frodo bound Gollum to his service in The Two Towers, he indicated that he could use the Ring to control Gollum (because the Ring had mastered Gollum long ago). Gandalf and Galadriel, however, recognized that they could use the full power of the Ring, becoming even more powerful than Sauron himself, but they resisted, knowing that in the end, the Ring would corrupt them. Gandalf explained to Frodo that, with great concentration and training, even he could tap into the Ring's power, but probably at the cost of his sanity.
The One Ring possessed something of a will of its own. Its only accepted master was Sauron himself, and it would seek to leave any other bearer when it would cause the greatest harm, or when it might return to Sauron. Bilbo warned Frodo of this, and Frodo kept it on a chain so that it would not slip off unnoticed. In the end, Gollum succumbs to the malevolent influence of the ring, defies Frodo, and takes the ring for himself. While dancing with joy over the recovery of the ring, Gollum falls into the Cracks of Doom in Orodruin, where the ring is destroyed. With the destruction of the Ring, Gandalf explains that Sauron is weakened to the point that he will never be able to materialize again.[11]
Adaptations[edit]
Ralph Bakshi's 1978 animated film begins with the forging of the Rings of Power and the events of the Last Alliance's war against Sauron, all portrayed in silhouette against a red background.
Peter Jackson's The Lord of the Rings: The Fellowship of the Ring begins with a similar prologue, though longer and more detailed. The three Elven rings are shown being cast using a cuttlebone mold, an ancient primitive casting technique. Additionally, Tolkien illustrators John Howe and Alan Lee, employed as conceptual designers for the films, have cameos as two of the nine human Ring-bearers who become Nazgûl.
See also[edit]
Middle-earth portal
"Of the Rings of Power and the Third Age"
Magic ring
References[edit]
^ Jump up to: a b Silmarillion, Of the Rings of Power and the Third Age
^ Jump up to: a b c d e f g h Fellowship, The Shadow of the Past
Jump up ^ The Silmarillion, "Of the Rings of Power and the Third Age", p. 289.
Jump up ^ Unfinished Tales, "The Hunt for the Ring", p. 338.
^ Jump up to: a b Tolkien, John Ronald Reuel, "The Council of Elrond", The Fellowship of the Ring .
Jump up ^ Unfinished Tales, "The Hunt for the Ring", p. 338.
Jump up ^ The Silmarillion, "Akallabêth, p. 267.
Jump up ^ The Lord of the Rings, Appendix A, "III. Durin's Folk".
Jump up ^ Unfinished Tales, "The History of Galadriel and Celeborn", p. 238.
Jump up ^ The Return of the King, "The Grey Havens", passim.
Jump up ^ Return of the King, The Last Debate
General references[edit]
Tolkien, J. R. R. (1954), The Fellowship of the Ring, The Lord of the Rings, Boston: Houghton Mifflin (published 1987), ISBN 0-395-08254-4
Tolkien, J. R. R. (1955), The Return of the King, The Lord of the Rings, Boston: Houghton Mifflin (published 1987), ISBN 0-395-08256-0
Tolkien, J. R. R. (1977), Christopher Tolkien, ed., The Silmarillion, Boston: Houghton Mifflin, ISBN 0-395-25730-1
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