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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] Ohm's law is an empirical relation which accurately describes the conductivity of the vast majority of electrically conductive materials over many orders of magnitude of current. However some materials do not obey Ohm's law, these are called non-ohmic.
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; for example the vector form of the law used in electromagnetics and material science:
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
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 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.
In modern notation we would write,
I = E r + R , {\displaystyle I={\frac {\mathcal {E}}{r+R}},}
where E {\displaystyle {\mathcal {E}}} is the open-circuit emf of the thermocouple, r {\displaystyle r} is the internal resistance of the thermocouple and R {\displaystyle R} is the resistance of the test wire. In terms of the length of the wire this becomes,
I = E r + R l , {\displaystyle I={\frac {\mathcal {E}}{r+{\mathcal {R}}l}},}
where R {\displaystyle {\mathcal {R}}} is the resistance of the test wire per unit length. Thus, Ohm's coefficients are,
a = E R , b = r R . {\displaystyle a={\frac {\mathcal {E}}{\mathcal {R}}},\quad b={\frac {\mathcal {r}}{\mathcal {R}}}.}
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]
The electron was discovered in 1897 by J. J. Thomson, and it was quickly realized that it is the particle (charge carrier) that carries electric currents in electric circuits. In 1900 the first (classical) model of electrical conduction, the Drude model, was proposed by Paul Drude, which finally gave a scientific explanation for Ohm's law. In this model, a solid conductor consists of a stationary lattice of atoms (ions), with conduction electrons moving randomly in it. A voltage across a conductor causes an electric field, which accelerates the electrons in the direction of the electric field, causing a drift of electrons which is the electric current. However the electrons collide with and scatter off of the atoms, which randomizes their motion, thus converting the kinetic energy added to the electron by the field to heat (thermal energy). Using statistical distributions, it can be shown that the average drift velocity of the electrons, and thus the current, is proportional to the electric field, and thus the voltage, over a wide range of voltages.
The development of quantum mechanics in the 1920s modified this picture somewhat, but in modern theories the average drift velocity of electrons can still be shown to be proportional to the electric field, thus deriving Ohm's law. In 1927 Arnold Sommerfeld applied the quantum Fermi-Dirac distribution of electron energies to the Drude model, resulting in the free electron model. A year later, Felix Bloch showed that electrons move in waves (Bloch waves) through a solid crystal lattice, so scattering off the lattice atoms as postulated in the Drude model is not a major process; the electrons scatter off impurity atoms and defects in the material. The final successor, the modern quantum band theory of solids, showed that the electrons in a solid cannot take on any energy as assumed in the Drude model but are restricted to energy bands, with gaps between them of energies that electrons are forbidden to have. The size of the band gap is a characteristic of a particular substance which has a great deal to do with its electrical resistivity, explaining why some substances are electrical conductors, some semiconductors, and some insulators.
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 article: Drude model
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 \mathbf {v} } in a magnetic field B {\displaystyle \mathbf {B} } . The relative motion induces an electric field E {\displaystyle \mathbf {E} } which exerts electric force on the charged particles giving rise to an electric current J {\displaystyle \mathbf {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\mathbf {v} _{e} \over dt}=-n_{e}e\mathbf {E} +n_{e}m_{e}\nu (v_{i}-v_{e})-en_{e}\mathbf {v} _{e}\times \mathbf {B} ,}
where e {\displaystyle e} , m e {\displaystyle m_{e}} and v e {\displaystyle \mathbf {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 \mathbf {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 (\mathbf {E} +\mathbf {v} \times \mathbf {B} )=\mathbf {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 \mathbf {E} +\mathbf {v} \times \mathbf {B} =\rho \mathbf {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 ^ Weber, B.; Mahapatra, S.; Ryu, H.; Lee, S.; Fuhrer, A.; Reusch, T. C. G.; Thompson, D. L.; Lee, W. C. T.; Klimeck, G.; Hollenberg, L. C. L.; Simmons, M. Y. (2012). "Ohm's Law Survives to the Atomic Scale". Science. 335 (6064): 64–67. Bibcode:2012Sci...335...64W. doi:10.1126/science.1214319. PMID 22223802.
Jump up ^ Drude, Paul (1900). "Zur Elektronentheorie der Metalle". Annalen der Physik. 306 (3): 566. Bibcode:1900AnP...306..566D. doi:10.1002/andp.19003060312.
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Jump up ^ A. Akers; M. Gassman & R. Smith (2006). Hydraulic Power System Analysis. New York: Taylor & Francis. Chapter 13. ISBN 0-8247-9956-9.
Jump up ^ A. Esposito, "A Simplified Method for Analyzing Circuits by Analogy", Machine Design, October 1969, pp. 173–177.
Jump up ^ Guyton, Arthur; Hall, John (2006). "Chapter 14: Overview of the Circulation; Medical Physics of Pressure, Flow, and Resistance". In Gruliow, Rebecca. Textbook of Medical Physiology (11th ed.). Philadelphia, Pennsylvania: Elsevier Inc. p. 164. ISBN 0-7216-0240-1.
Jump up ^ James William Nilsson & Susan A. Riedel (2008). Electric circuits. Prentice Hall. p. 29. ISBN 978-0-13-198925-2.
Jump up ^ Alvin M. Halpern & Erich Erlbach (1998). Schaum's outline of theory and problems of beginning physics II. McGraw-Hill Professional. p. 140. ISBN 978-0-07-025707-8.
Jump up ^ Dale R. Patrick & Stephen W. Fardo (1999). Understanding DC circuits. Newnes. p. 96. ISBN 978-0-7506-7110-1.
Jump up ^ Thomas O'Conor Sloane (1909). Elementary electrical calculations. D. Van Nostrand Co. p. 41.
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.
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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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Lady Sings the Blues (film)
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Lady Sings the Blues
Theatrical release poster
Directed by
Sidney J. Furie
Produced by
Brad Dexter
Berry Gordy
Jay Weston
James S. White
Screenplay by
Suzanne de Passe
Chris Clark
Terence McCloy
Based on
Lady Sings the Blues
by Billie Holiday
William Dufty
Starring
Diana Ross
Billy Dee Williams
Richard Pryor
Music by
Gil Askey
Michel Legrand
Cinematography
John A. Alonzo
Edited by
Argyle Nelson
Production
company
Motown Productions
Distributed by
Paramount Pictures
Release date
October 12, 1972 (1972-10-12)
Running time
144 minutes[1]
Country
United States
Language
English
Budget
$14 million
Box office
$19,726,490[2]
Lady Sings the Blues is a 1972 American biographical drama film directed by Sidney J. Furie about jazz singer Billie Holiday, loosely based on her 1956 autobiography which, in turn, took its title from one of Holiday's most popular songs. It was produced by Motown Productions for Paramount Pictures. Diana Ross portrayed Holiday, alongside a cast including Billy Dee Williams, Richard Pryor, James T. Callahan, and Scatman Crothers.[3]
Contents
[hide]
1 Plot
2 Cast
3 Box office
4 Awards and honors
5 Soundtrack
6 See also
7 References
8 External links
Plot[edit]
In 1945 New York City, Billie Holiday is arrested on a drugs charge.
In a flashback to 1928, Billie is working as a housekeeper in a brothel in Baltimore where she is raped. She runs away to her mother, who sets up a job cleaning for another brothel in the Harlem section of New York. The brothel is run by an arrogant, selfish owner who pays Billie very little money.
Eventually, Billie tires of scrubbing floors and becomes a prostitute, but later quits and returns to a nightclub to unsuccessfully audition to become a showgirl. After "Piano Man" accompanies Billie when she sings "All of Me", club owner Jerry books her as a singer in the show.
Billie's debut begins unsuccessfully until Louis McKay arrives and gives her a fifty dollar tip. Billie takes the money and sings "Them There Eyes". Billie takes a liking to Louis and begins a relationship with him. Eventually she is discovered by Harry and Reg Hanley, who sign her as a soloist for their southern tour in hopes of landing a radio network gig. During the tour, Billie witnesses the aftermath of the lynching of an African-American man, which presses her to record the controversial song "Strange Fruit". The harsh experiences on the tour result in Billie taking drugs which Harry supplies. One night when Billie is performing, Louis comes to see Billie. She collapses on stage. In her dressing room, Louis notices her needle marks, knows that she is doing drugs, and tells her she is going home with him. Billie promises to stay off the drugs if Louis stays with her.
In New York, Reg and Louis arrange Billie's radio debut, but the station does not call her to sing; the radio sponsors, a soap company, object to her race. The group heads to Cafe Manhattan to drown their sorrows. Billie has too much to drink and asks Harry for drugs, saying that she does not want her family to know that the radio show upset her. He refuses and she throws her drink in his face. She is ready to leave, but Louis has arranged for her to sing at the Cafe, a club where she once aspired to sing. She obliges with one song but refuses an encore, leaving the club in urgent need of a fix. Louis, suspicious that Billie has broken her promise, takes her back to his home but refuses to allow her access to the bathroom or her kit. She fights Louis for it, pulling a razor on him. Louis leaves her to shoot up, telling her he does not want her there when he returns.
Billie returns to the Harlem nightclub, where her drug use intensifies until she hears of the death of her mother. Billie checks herself into a drug clinic, but because she cannot afford her treatment the hospital secretly calls Louis, who comes to see her and agrees to pay her bills without her knowledge. Impressed with the initiative she has taken to straighten herself out, Louis proposes to her at the hospital. Just as things are looking up, Billie is arrested for possession of narcotics and removed from the clinic.
In prison, Billie goes through crippling withdrawal. Louis brings the doctor from the hospital to treat her, but she is incoherent. He puts a ring on her finger to remind her of his promise to marry her. When she finishes her prison sentence, Billie returns home and tells her friends that she does not want to sing anymore. Billie marries Louis and pledges not to continue her career, but the lure of performing is too strong and she returns to singing with Louis as her manager. Unfortunately, her felony conviction has stripped her of her Cabaret Card, which would allow her to sing in NYC nightclubs. To restore public confidence and regain her license, Billie agrees to a cross-country tour. Billie's career takes off on the nightclub circuit.
Louis leaves for New York to arrange a comeback performance for Billie at Carnegie Hall. Despondent at Louis' absence and the never-ending stream of venues, Billie asks Piano Man to pawn the ring Louis gave her in exchange for drugs. While they are high that evening, Piano Man's drug connections arrive; he neither pawned the ring nor paid for the drugs. Piano Man is killed by the dealers. Within the hour, Louis and her promoter call Billie with news that they got Carnegie Hall. Louis returns to find a very fragile Billie who is traumatized and has fallen back into drugs. Louis takes her back to New York.
Billie plays to a packed house at Carnegie Hall. Her encore, "God Bless the Child", is overlaid with newspaper clippings highlighting subsequent events: the concert fails to sway the Commission to restore her license; subsequent appeals are denied; she is later re-arrested on drug charges and finally dies when she is 44. Nevertheless, the Carnegie triumph is frozen in time.
Cast[edit]
Diana Ross as Billie Holiday
Billy Dee Williams as Louis McKay
Richard Pryor as Piano Man
James Callahan as Reg Hanley
Paul Hampton as Harry
Sid Melton as Jerry
Virginia Capers as Sadie Fagan Holiday, Billie's mother
Yvonne Fair as Yvonne
Isabel Sanford as Madame
Jester Hairston as Fefe
Lynn Hamilton as Aunt Ida
Victor Morosco as Vic
Robert Gordy as The Hawk
Harry Caesar as The Rapist
Paulene Myers as Mrs. Edson
Scatman Crothers as Big Ben
Box office[edit]
The film earned an estimated $9,050,000 in North American rentals in 1973.[4]
Awards and honors[edit]
It was nominated for five Academy Awards.[5] The nominations were for Best Actress in a Leading Role (Diana Ross), Best Art Direction-Set Decoration (Carl Anderson and Reg Allen), Best Costume Design (Norma Koch), Best Music, Original Song Score and Adaptation (Gil Askey & Michel Legrand) and Best Writing, Story and Screenplay Based on Factual Material or Material Not Previously Published or Produced.[6] The film was also screened at the 1973 Cannes Film Festival, but was not entered into the main competition.[7]

The film is recognized by American Film Institute in these lists:
2004: AFI's 100 Years...100 Songs:
"God Bless the Child" – Nominated[8]
Soundtrack[edit]
Motown released a hugely successful soundtrack double-album of Ross' recordings of Billie Holiday songs from the film, also titled Lady Sings the Blues. The album went to number one on the Billboard Hot 200 Album Charts,[9] for the week-ending dates of April 7 and 14, 1973.
See also[edit]
List of American films of 1972
References[edit]
Jump up ^ "LADY SINGS THE BLUES (X)". British Board of Film Classification. December 22, 1972. Retrieved July 21, 2013.
Jump up ^ "Lady Sings the Blues, Box Office Information". The Numbers. Retrieved January 21, 2012.
Jump up ^ The AFI Catalog of Feature Films:Lady Sings the Blues
Jump up ^ "Big Rental Films of 1973", Variety, 9 January 1974 p 19
Jump up ^ "NY Times: Lady Sings the Blues". NY Times. Retrieved 2008-12-28.
Jump up ^ "Academy Award Official Database for 1972".
Jump up ^ "Festival de Cannes: Lady Sings the Blues". festival-cannes.com. Retrieved 2009-04-20.
Jump up ^ "AFI's 100 Years...100 Songs Nominees" (PDF). Retrieved 2016-07-30.
Jump up ^ "Article at Sulekha.biz".
External links[edit]
Lady Sings the Blues on IMDb
Lady Sings the Blues at Box Office Mojo
Lady Sings the Blues at Rotten Tomatoes
[show]
v
t
e
Billie Holiday
Discography
Awards and nominations
Albums
Billie Holiday Sings/Solitude
An Evening with Billie Holiday
Billie Holiday
Billie Holiday at JATP
Stay with Me
Music for Torching
Velvet Mood
Lady Sings the Blues
Body and Soul
Songs for Distingué Lovers
Ella Fitzgerald and Billie Holiday at Newport
All or Nothing at All
Lady in Satin
Last Recordings
The Essential Billie Holiday: Carnegie Hall Concert Recorded Live
Lady in Autumn: The Best of the Verve Years
Lady Day: The Complete Billie Holiday on Columbia 1933–1944
Remixed and Reimagined
Songs
"Ain't Nobody's Business"
"As Time Goes By"
"Billie's Blues"
"Blue Moon"
"Body and Soul"
"Do You Know What It Means to Miss New Orleans?"
"Don't Explain"
"Easy Living"
"Embraceable You"
"Everything Happens for the Best"
"Everything Happens to Me"
"Fine and Mellow"
"Gloomy Sunday"
"God Bless the Child"
"Good Morning Heartache"
"I Cover the Waterfront"
"I Loves You, Porgy"
"I Thought About You"
"I'll Be Seeing You"
"I'll Get By"
"I've Got My Love to Keep Me Warm"
"Just One of Those Things"
"Lady Sings the Blues"
"Left Alone"
"Love for Sale"
"Lover Man (Oh, Where Can You Be?)"
"Me, Myself, and I"
"Miss Brown to You"
"My Man"
"Moonlight in Vermont"
"Night and Day"
"No More"
"Now or Never"
"Our Love Is Different"
"P.S. I Love You"
"Pennies from Heaven"
"Please Don't Do It Here"
"Preacher Boy"
"Sophisticated Lady"
"Stormy Blues"
"Strange Fruit"
"Summertime"
"These Foolish Things (Remind Me of You)"
"Too Marvelous for Words"
"Trav'lin' Light"
"What a Little Moonlight Can Do"
"What Is This Thing Called Love?"
"Who Needs You (Baby)"
"Why Was I Born?"
"Willow Weep for Me"
"You Go to My Head"
Related topics
"Angel of Harlem"
Lady Sings the Blues (book)
Lady Sings the Blues (film)
Lady Sings the Blues (soundtrack)
Book
Category
[show]
v
t
e
Films directed by Sidney J. Furie
A Dangerous Age (1958)
A Cool Sound from Hell (1959)
Doctor Blood's Coffin (1961)
The Snake Woman (1961)
Three on a Spree (1961)
During One Night (1961)
The Young Ones (1961)
The Boys (1962)
The Leather Boys (1964)
Wonderful Life (1964)
The Ipcress File (1965)
The Appaloosa (1966)
The Naked Runner (1967)
The Lawyer (1970)
Little Fauss and Big Halsy (1970)
Lady Sings the Blues (1972)
Hit! (1973)
Sheila Levine Is Dead and Living in New York (1975)
Gable and Lombard (1976)
The Boys in Company C (1978)
The Entity (1981)
Purple Hearts (1984)
Iron Eagle (1986)
Superman IV: The Quest for Peace (1987)
Iron Eagle II (1988)
The Taking of Beverly Hills (1991)
Ladybugs (1992)
Iron Eagle on the Attack (1995)
Hollow Point (1996)
Top of the World (1997)
The Rage (1997)
Married to a Stranger (1997)
In Her Defense (1999)
My 5 Wives (2000)
Cord (2000)
Under Heavy Fire (2001)
The Fraternity (2002)
Global Heresy (2002)
Partners in Action (2002)
Detention (2003)
Direct Action (2004)
American Soldiers (2005)
The Veteran (2006)
Conduct Unbecoming (2011)
The Dependables (2014)
[show]
v
t
e
NAACP Image Award for Outstanding Motion Picture
1972–2000
Lady Sings the Blues (1972)
Let's Do It Again (1976)
The Greatest (1978)
Fame (1980)
Bustin' Loose (1981)
An Officer and a Gentleman (1982)
A Soldier's Story (1985)
The Color Purple (1986)
Lethal Weapon (1987)
Coming to America (1988)
Lean on Me (1989)
Glory (1990)
Boyz n the Hood (1992)
Sister Act (1993)
Malcolm X (1994)
Waiting to Exhale (1996)
A Time to Kill (1997)
Soul Food (1998)
How Stella Got Her Groove Back (1999)
The Best Man (2000)
2001–present
Remember the Titans (2001)
Ali (2002)
Antwone Fisher (2003)
The Fighting Temptations (2004)
Ray (2005)
Crash (2006)
The Pursuit of Happyness (2007)
The Great Debaters (2008)
The Secret Life of Bees (2009)
Precious (2010)
For Colored Girls (2011)
The Help (2012)
Red Tails (2013)
12 Years a Slave (2014)
Selma (2015)
Straight Outta Compton (2016)
Hidden Figures (2017)
Retrieved from "https://en.wikipedia.org/w/index.php?title=Lady_Sings_the_Blues_(film)&oldid=782344520"
Categories:
1972 films
English-language films
Billie Holiday
1970s drama films
1970s biographical films
American films
American biographical films
American drama films
African-American films
Biographical films about musicians
Films about drugs
Jazz films
Films about race and ethnicity
Films based on biographies
Films directed by Sidney J. Furie
Motown Productions films
Paramount Pictures films
Films set in New York City
Films set in the 1920s
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Royal Niger Company
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
"Central African Company" redirects here. For companies in the modern nation, see list of Central African companies.
Flag of the Royal Niger Company
The Royal Niger Company was a mercantile company chartered by the British government in the nineteenth century. It was formed in 1879 as the United African Company and renamed to National African Company in 1881 and to Royal Niger Company in 1886.
The company existed for a comparatively short time (1879–1900) but was instrumental in the formation of Colonial Nigeria, as it enabled the British Empire to establish control over the lower Niger against the German competition led by Bismarck during the 1890s. In 1900, the company-controlled territories became the Southern Nigeria Protectorate, which was in turn united with the Northern Nigeria Protectorate to form the Colony and Protectorate of Nigeria in 1914 (which eventually gained independence within the same borders as the Federal Republic of Nigeria in 1960).
Contents
1 United African Company
2 National African Company
3 Niger Company
4 See also
5 References
6 External links
United African Company[edit]
Richard Lander first explored the area of Nigeria as the servant of Hugh Clapperton. In 1830, he returned to the river with his brother John; in 1832, he returned again (without his brother) to establish a trading post for the "African Steamship Company"[1] at the confluence of the Niger and Benue rivers. The expedition failed, with 40 of the 49 members dying of fever or wounds from native attacks. One of the survivors, Macgregor Laird, subsequently remained in Britain but directed and funded expeditions to the country until his death in 1861. He opposed the failed Niger expedition of 1841 but the success of the Pleiad’s first mission in 1854 led to annual trips under Baikie and the 1857 foundation of Lokoja at the Niger–Benue confluence.
There were no voyages for the three years following Laird's death, but the establishment of the West African Company was soon followed by several other firms. The competition reduced prices to the point that profits were minimal. Arriving in the region in 1877,[2] George Goldie argued for the amalgamation of the surviving British firms into a single monopolistic chartered company, a method contemporaries supposed had been buried with the ultimate failure of the East India Company following the Sepoy Rebellion. By 1879, he had helped combine James Crowther's WAC, David Macintosh's Central African Company, and the William Brothers' and James Pinnock's firms into a single United African Company; he then acted as the combined firm's agent in the territory.[3]
Almost immediately, the firm saw renewed competition as two French firms—the French Equatorial African Association and the Senegal Company—and another English one—the Liverpool and Manchester Trading Company—begin establishing posts on the river as well.[4] A native attack on the UAC's outpost at Onitsha in 1879 was repulsed with help from HMS Pioneer[3] but the Gladstone administration subsequently denied Goldie's attempt to procure a government charter in 1881, on the grounds that the international rivalry might occasion unnecessary conflict and that the united firm was undercapitalized for the expense of genuine colonial administration.[4]
National African Company[edit]
George Goldie in 1898.
See also: Berlin Conference
Goldie first began addressing the administration's concerns by increasing the company's capitalization to £100 000. He then managed to corral £1 000 000 in investments in a new concern—the National African Company—which bought up the UAC and its interests in 1882.[5] The death of Léon Gambetta the same year deprived the French companies of their support within the French government and the strong subsidies it had been providing them.[4] Goldie's cash-flush NAC was then able to maintain 30 trading posts along the river[3] and ruin its competition in a two-year price war: by October 1884 all three had permitted him to buy out their interests in the region and the NAC's annual report for 1885 was able to crow that it "remained alone in undisputed commercial possession of the Niger–Binué region".[4]
This monopoly permitted Britain to resist French and German calls to internationalize trade on the Niger river during the negotiations at the 1884–1885 Berlin Conference on African colonization. Goldie himself attended the meetings and successfully argued for including the region of the NAC's operations within a British sphere of interest. Pledges from him and the British diplomats that free trade (or, in any case, non-discriminatory tariff rates) would be respected in their territory were dead letters: the NAC's over 400 treaties with local leaders obliged the natives to trade solely with or through the company's agents. Large tariffs and license fees eliminated competing firms from the area. The terms of these private contracts were made into general treaties by the British consuls, whose own treaties expressly incorporated them.[6] Similarly, when King Jaja of Opobo organized his own trading network and even began running his own shipments of palm oil to Britain, he was lured onto a British warship and shipped into exile on Saint Vincent on charges of "treaty breaking" and "obstructing commerce".[2]
Despite treaties extending British control over the tribes of the Cameroons, however, Britain was willing to recognize the German colony that usurped the area in 1885[6] as a check on French activity in the upper Congo and Ubangi watersheds.
The scruples of the British government being overcome, a charter was at length granted (July 1886), the National African Company becoming The Royal Niger Company Chartered and Limited[7] (normally shortened to the Royal Niger Company), with Lord Aberdare as governor and Goldie as vice-governor.[8]
Niger Company[edit]
It was, however, evidently impossible for a chartered company to hold its own against the state-supported protectorates of France and Germany, and in consequence its charter was revoked in 1899[9] and, on 1 January 1900, the Royal Niger Company transferred its territories to the British Government for the sum of £865,000. The ceded territory together with the small Niger Coast Protectorate, already under imperial control, was formed into the two protectorates of northern and southern Nigeria.[8]
The company changed its name to The Niger Company Ltd and in 1929 became part of the United Africa Company.[7] The United Africa Company came under the control of Unilever in the 1930s and continued to exist as a subsidiary of Unilever until 1987, when it was absorbed into the parent company.
See also[edit]
Alhassan Dantata
Royal Niger Company’s Medal
Postage stamps and postal history of the Niger Territories
Sokoto
References[edit]
Jump up ^ Baynes, T.S., ed. (1902). "Niger (river)". Encyclopædia Britannica (9th ed.). New York: Charles Scribner's Sons.
^ Jump up to: a b Máthé-Shires, László. "Lagos Colony and Oil Rivers Protectorate" in the Encyclopedia of African History, Vol. 3, pp. 791–792. Accessed 5 Apr 2014.
^ Jump up to: a b c Geary, Sir William N.M. (1927), pp. 174 ff.
^ Jump up to: a b c d McPhee, Allan. The Economic Revolution in British West Africa, pp. 75 ff. Frank Cass & Co. Ltd. (Abingdon), 1926 and reprinted 1971. Accessed 4 Apr 2014.
Jump up ^ "Chartered Companies" in the Encyclopædia Britannica, 10th ed.
^ Jump up to: a b Geary, Sir William Nevill Montgomerie. Nigeria under British Rule, p. 95. Frank Cass & Co, 1927. Accessed 5 Apr 2014.
^ Jump up to: a b Baker, Geoffrey L (19968). Trade Winds on the Niger: Saga of the Royal Niger Company, 1830-1971. London: Radcliffe Press. ISBN 978-1860640148. Check date values in: |year= (help)
^ Jump up to: a b One or more of the preceding sentences incorporates text from a publication now in the public domain: Chisholm, Hugh, ed. (1911a). "Goldie, Sir George Dashwood Taubman". Encyclopædia Britannica. 12 (11th ed.). Cambridge University Press. pp. 211–212.
Jump up ^ Falola, Toyin; Heaton, Matthew (2008). A History of Nigeria. Cambridge University Press. p. 101. ISBN 978-0521681575.
External links[edit]
Wikimedia Commons has media related to Royal Niger Company.
"Nigeria". Encyclopædia Britannica. 19 (11th ed.). 1911. pp. 677–684.
"Lugard, Sir Frederick John Dealtry". Encyclopædia Britannica. 17 (11th ed.). 1911. pp. 115–116.
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Retrieved from "https://en.wikipedia.org/w/index.php?title=Royal_Niger_Company&oldid=824940901"
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British West Africa
Colonial Nigeria
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Retail companies established in 1886
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