e.engineering 6 equations

7/29/2019 E.engineering 6 Equations

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Gustav RobertKirchhoff

Born: 12-Mar-1824Birthplace: Knigsberg, Prussia, GermanyDied: 17-Oct-1887Location of death: Berlin, GermanyCause of death: unspecified

Gender: MaleRaceorEthnicity: WhiteOccupation: Physicist

Nationality:Germany

Executive summary:Theory of spectrum

analysis

German physicist, born at Knigsberg(now Kaliningrad, Russia) on the 12th ofMarch 1824, and was educated at the university of his native town, where he graduated PhDin 1847. After acting as privat-docent at Berlin for some time, he became extraordinaryprofessor of physics at Breslau in 1850. Four years later he was appointed professor ofphysics at Heidelberg, and in 1875 he was transferred to Berlin, where he died on the 17th ofOctober 1887. Kirchhoff's contributions to mathematical physics were numerous and

important, his strength lying in his powers of stating a new physical problem in terms ofmathematics, not merely in working out the solution after it had been so formulated. Anumber of his papers were concerned with electrical questions. One of the earliest wasdevoted to electrical conduction in a thin plate, and especially in a circular one, and it alsocontained a theorem which enables the distribution of currents in a network of conductorsto be ascertained. Another discussed conduction in curved sheets; a third, the distribution ofelectricity in two influencing spheres; a fourth, the determination of the constant on whichdepends the intensity of induced currents; while others were devoted to Ohm's law, themotion of electricity in submarine cables, induced magnetism, etc. In other papers, again,various miscellaneous topics were treated -- the thermal conductivity of iron, crystalline

reflection and refraction, certain propositions in the thermodynamics of solution andvaporization, etc. An important part of his work was contained in his Vorlesungen bermathematische Physik (1876), in which the principles of dynamics, as well as various specialproblems, were treated in a somewhat novel and original manner. But his name is bestknown for the researches, experimental and mathematical, in radiation which led him, incompany with Robert Wilhelm Bunsen, to the development of spectrum analysis as acomplete system in 1859-60. He can scarcely be called its inventor, for not only had manyinvestigators already used the prism as an instrument of chemical inquiry, but considerable
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progress had been made towards the explanation of the principles upon which spectrumanalysis rests. But to him belongs the merit of having, most probably without knowing whathad already been done, enunciated a complete account of its theory, and of thus havingfirmly established it as a means by which the chemical constituents of celestial bodies can bediscovered through the comparison of their spectra with those of the various elements that

exist on this earth.


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James Clerk Maxwell

Born: 13-Jun-1831Birthplace: Edinburgh, ScotlandDied: 5-Nov-1879Location of death: Cambridge, EnglandCause of death: Cancer - unspecifiedRemains: Buried, Parton Chuchyard, Glenlair, Dumfriesand Galloway, Scotland

Gender: MaleReligion: Christian

Race or Ethnicity: WhiteSexual orientation: StraightOccupation: Physicist

Nationality: ScotlandExecutive summary: Maxwell's equations

British physicist, the last representative of a younger branch of the well-known Scottishfamily of Clerk of Penicuik, and was born at Edinburgh on the 13th of November 1831. He waseducated at the Edinburgh Academy (1840-47) and the University of Edinburgh (1847-50).Entering at Cambridge in 1850, he spent a term or two at Peter house, but afterwards

migrated to Trinity. In 1854 he took his degree as second wrangler, and was declared equalwith the senior wrangler of his year (E. J. Routh) in the higher ordeal of the Smith's prizeexamination. He held the chair of Natural Philosophy in Marischal College, Aberdeen, from1856 until the fusion of the two colleges there in 1860. For eight years subsequently he heldthe chair of Physics and Astronomy in King's College, London, but resigned in 1868 andretired to his estate of Glenlair in Kirkcudbrightshire. He was summoned from his seclusionin 1871 to become the first holder of the newly founded professorship of ExperimentalPhysics in Cambridge; and it was under his direction that the plans of the CavendishLaboratory were prepared. He superintended every step of the progress of the building andof the purchase of the very valuable collection of apparatus with which it was equipped at

the expense of its munificent founder seventh Duke of Devonshire (Chancellor of theUniversity, and one of its most distinguished alumni). He died at Cambridge on the 5th ofNovember 1879.

For more than half of his brief life he held a prominent position in the very foremost rank ofnatural philosophers. His contributions to scientific societies began in his fifteenth year,when Professor J. D. Forbes communicated to the Royal Society of Edinburgh a short paperof his on a mechanical method of tracing Cartesian ovals. In his eighteenth year, while still a
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student in Edinburgh, he contributed two valuable papers to the Transactions of the samesociety -- one of which, "On the Equilibrium of Elastic Solids", is remarkable, not only onaccount of its intrinsic power and the youth of its author, but also because in it he laid thefoundation of one of the most singular discoveries of his later life, the temporary doublerefraction produced in viscous liquids by shearing stress. Immediately after taking his

degree, he read to the Cambridge Philosophical Society a very novel paper, "On theTransformation of Surfaces by Bending." This is one of the few purely mathematical papershe published, and it exhibited at once to experts the full genius of its author. About thesame time appeared his elaborate paper, "On Faraday's Lines of Force", in which he gavethe first indication of some of those extraordinary electrical investigations which culminatedin the greatest work of his life. He obtained in 1859 the Adams prize in Cambridge for a veryoriginal and powerful essay, "On the Stability of Saturn's Rings." From 1855 to 1872 hepublished at intervals a series of valuable investigations connected with the "Perception ofColor" and "Color-Blindness", for the earlier of which he received the Rumford medal fromthe Royal Society in 1860. The instruments which he devised for these investigations were

simple and convenient, but could not have been thought of for the purpose except by a manwhose knowledge was co-extensive with his ingenuity. One of his greatest investigationsbore on the "Kinetic Theory of Gases." Originating with D. Bernoulli, this theory wasadvanced by the successive labors of John Herapath, James Prescott Joule, and particularlyR. Clausius, to such an extent as to put its general accuracy beyond a doubt; but it receivedenormous developments from Maxwell, who in this field appeared as an experimenter (onthe laws of gaseous friction) as well as a mathematician. He wrote an admirable textbook oftheTheory of Heat (1871), and a very excellent elementary treatise on Matter andMotion (1876).

But the great work of his life was devoted to electricity. He began by reading, with the most

profound admiration and attention, the whole of Michael Faradays extraordinary self-revelations, and proceeded to translate the ideas of that master into the succinct andexpressive notation of the mathematicians. A considerable part of this translation wasaccomplished during his career as an undergraduate in Cambridge. The writer had theopportunity of perusing the manuscript of "On Faraday's Lines of Force", in a form littledifferent from the final one, a year before Maxwell took his degree. His great object, as itwas also the great object of Faraday, was to overturn the idea of action at a distance. Thesplendid researches of S. D. Poisson and Carl Friedrich Gauss had shown how to reduce allthe phenomena of statical electricity to mere attractions and repulsions exerted at adistance by particles of an imponderable on one another. Lord Kelvin had, in 1846, shown

that a totally different assumption, based upon other analogies, led (by its own specialmathematical methods) to precisely the same results. He treated the resultant electric forceat any point as analogous to the flux of heat from sources distributed in the same manner asthe supposed, electric particles. This paper of Thomson's, whose ideas Maxwell afterwardsdeveloped in an extraordinary manner, seems to have given the first hint that there are atleast two perfectly distinct methods of arriving at the known formulae of statical electricity.The step to magnetic phenomena was comparatively simple; but it was otherwise as regardselectromagnetic phenomena, where current electricity is essentially involved. An


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exceedingly ingenious, but highly artificial, theory had been devised by W. E. Weber, whichwas found capable of explaining all the phenomena investigated by Andr-Marie Ampre aswell as the induction currents of Faraday. But this was based upon the assumption of adistance-action between electric particles, the intensity of which depended on their relativemotion as well as on their position. This was, of course, even more repugnant to Maxwell's

mind than the statical distance-action developed by Poisson.

The first paper of Maxwell's in which an attempt at an admissible physical theory ofelectromagnetism was made was communicated to the Royal Society in 1867. But thetheory, in a fully developed form, first appeared in 1873 in his great treatise on Electricity andMagnetism. This work was one of the most splendid monuments ever raised by the geniusof a single individual. Availing himself of the admirable generalized co-ordinate systemofJoseph-Louis Lagrange, Maxwell showed how to reduce all electric and magneticphenomena to stresses and motions of a material medium, and, as one preliminary, butexcessively severe, test of the truth of his theory, he pointed out that (if theelectromagnetic medium be that which is required for the explanation of the phenomena oflight) the velocity of light in a vacuum should be numerically the same as the ratio of theelectromagnetic and electrostatic units. In fact, the means of the best determinations ofeach of these quantities separately agree with one another more closely than do the variousvalues of either.

One of Maxwell's last great contributions to science was the editing (with copious originalnotes) of the Electrical Researches of the Hon. Henry Cavendish, from which it appearedthat Henry Cavendish, already famous by many other researches (such as the mean densityof the earth, the composition of water, etc.), must be looked on as, in his day, a man ofMaxwell's own stamp as a theorist and an experimenter of the very first rank.

In private life Clerk Maxwell was one of the most lovable of men, a sincere andunostentatious Christian. Though perfectly free from any trace of envy or ill-will, he yetshowed on fit occasion his contempt for that pseudoscience which seeks for the applause ofthe ignorant by professing to reduce the whole system of the universe to a fortuitoussequence of uncaused events.

His collected works, including the series of articles on the properties of matter, such as"Atom", "Attraction", "Capillary Action", "Diffusion", "Ether", etc., which he contributed tothe 9th edition of Encyclopedia Britannica, were issued in two volumes by the Cambridge

University Press in 1890; and an extended biography, by his former schoolfellow and lifelongfriend Professor Lewis Campbell, was published in 1882.

Father: John Clerk (lawyer)Wife: Katherine Mary Dewar (m. 1858, no children)


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Thevenin's Theorem :. . This theorem was first discovered by German scientist Hermann von Helmholtz in 1853,

but was then rediscovered in 1883 by French telegraph engineer Lon Charles

Thvenin (1857-1926

Hermannvon HelmholtzAKA Hermann Ludwig Ferdinand von Helmholtz

Born: 31-Aug-1821Birthplace: Potsdam,GermanyDied: 8-Sep-1894Location of death: Charlottenburg, Berlin,GermanyCause of death: unspecified

Gender: MaleRaceorEthnicity: WhiteSexualorientation: StraightOccupation: Physicist

Nationality: GermanyExecutive summary: Law of Conservation of Energy

German philosopher and man of science, born on the31st of August 1821 at Potsdam, near Berlin. His father, Ferdinand, was a teacher of philologyand philosophy in the gymnasium, while his mother was a Hanoverian lady, a linealdescendant of the great Quaker William Penn. Delicate in early life, Helmholtz became byhabit a student, and his father at the same time directed his thoughts to natural phenomena.He soon showed mathematical powers, but these were not fostered by the careful trainingmathematicians usually receive, and it may be said that in after years his attention was

directed to the higher mathematics mainly by force of circumstances.

As his parents were poor, and could not afford to allow him to follow a purely scientificcareer, he became a surgeon of the Prussian army. In 1842 he wrote a thesis in which heannounced the discovery of nerve-cells in ganglia. This was his first work, and from 1842 to1894, the year of his death, scarcely a year passed without several important, and in somecases epoch-making, papers on scientific subjects coming from his pen. He lived in Berlin
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from 1842 to 1849, when he became professor of physiology in Knigsberg. There heremained from 1849 to 1855, when he removed to the chair of physiology in Bonn. In 1858 hebecame professor of physiology in Heidelberg, and in 1871 he was called to occupy the chairof physics in Berlin. To this professorship was added in 1887 the post of director of thephysico-technical institute at Charlottenburg, near Berlin, and he held the two positions

together until his death on the 8th of September 1894.

His investigations occupied almost the whole field of science, including physiology,physiological optics, physiological acoustics, chemistry, mathematics, electricity andmagnetism, meteorology and theoretical mechanics. At an early age he contributed to ourknowledge of the causes of putrefaction and fermentation. In physiological science heinvestigated quantitatively the phenomena of animal heat, and he was one of the earliest inthe field of animal electricity. He studied the nature of muscular contraction, causing amuscle to record its movements on a smoked glass plate, and he worked out the problem ofthe velocity of the nervous impulse both in the motor nerves of the frog and in the sensorynerves of man.

In 1847 Helmholtz read to the Physical Society of Berlin a famous paper, ber die Erhaltungder Kraft (on the conservation of force), which became one of the epoch-making papers ofthe century; indeed, along with Julius Robert Mayer, James Prescott Joule and Lord Kelvin,he may be regarded as one of the founders of the now universally received law of theconservation of energy. The year 1851, while he was lecturing on physiology at Knigsberg,saw the brilliant invention of the ophthalmoscope, an instrument which has been ofinestimable value to medicine. It arose from an attempt to demonstrate to his class thenature of the glow of reflected light sometimes seen in the eyes of animals such as the cat.When the great ophthalmologist, A. von Grfe, first saw the fundus of the living human eye,

with its optic disc and blood-vessels, his face flushed with excitement, and he cried,"Helmholtz has unfolded to us a new world!"

Helmholtz's contributions to physiological optics are of great importance. He investigatedthe optical constants of the eye, measured by his invention, the ophthalmometer, the radiiof curvature of the crystalline lens for near and far vision, explained the mechanism ofaccommodation by which the eye can focus within certain limits, discussed the phenomenaof color vision, and gave a luminous account of the movements of the eyeballs so as tosecure single vision with two eyes. In particular he revived and gave new force to the theoryof color vision associated with the name of Thomas Young, showing the three primary colors

to be red, green and violet, and he applied the theory to the explanation of color blindness.His great work on Physiological Optics (1856-66) is by far the most important book that hasappeared on the physiology and physics of vision.

Equally distinguished were his labors in physiological acoustics. He explained accurately themechanism of the bones of the ear, and he discussed the physiological action of the cochleaon the principles of sympathetic vibration. Perhaps his greatest contribution, however, washis attempt to account for our perception of quality of tone. He showed, both by analysis
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and by synthesis, that quality depends on the order, number and intensity of the overtonesor harmonics that may, and usually do, enter into the structure of a musical tone. He alsodeveloped the theory of differential and of summational tones. His work on Sensations ofTone (1862) may well be termed theprincipia of physiological acoustics. He may also be saidto be the founder of the fixed-pitch theory of vowel tones, according to which it is asserted

that the pitch of a vowel depends on the resonance of the mouth, according to the form ofthe cavity while singing it, and this independently of the pitch of the note on which thevowel is sung.

For the later years of his life his labors may be summed up under the following heads: (1) onthe conservation of energy; (2) on hydrodynamics; (3) on electrodynamics and theories ofelectricity; (4) on meteorological physics; (5) on optics; and (6) on the abstract principles ofdynamics. In all these fields of labor he made important contributions to science, andshowed himself to be equally great as a mathematician and a physicist. He studied thephenomena of electrical oscillations from 1869 to 1871, and in the latter year he announcedthat the velocity of the propagation of electromagnetic induction was about 314,000 metersper second. Michael Faraday had shown that the passage of electrical action involved time,and he also asserted that electrical phenomena are brought about by changes in interveningnon-conductors or dielectric substances. This led James Clerk Maxwell to frame his theory ofelectrodynamics, in which electrical impulses were assumed to be transmitted through theether by waves.

G. F. Fitzgerald was the first to attempt to measure the length of electric waves; Helmholtzput the problem into the hands of his favorite pupil, Heinrich Hertz, and the latter finallygave an experimental demonstration of electromagnetic waves, the "Hertzian waves", onwhich wireless telegraphy depends, and the velocity of which is the same as that of light.

The last investigations of Helmholtz related to problems in theoretical mechanics, moreespecially as to the relations of matter to the ether, and as to the distribution of energy inmechanical systems. In particular he explained the principle of least action, first advancedby Pierre-Louis Moreau de Maupertuis, and developed by Sir W. R. Hamilton, of quaternionfame. Helmholtz also wrote on philosophical and aesthetic problems. His position was thatof an empiricist, denying the doctrine of innate ideas and holding that all knowledge isfounded on experience, hereditarily transmitted or acquired.

The life of Helmholtz was uneventful in the usual sense. He was twice married,, first, in 1849,to Olga von Velten (by whom he had two children, a son and daughter), and secondly, in

1861, to Anna von Mohl, of a Wrtemberg family of high social position. Two children wereborn of this marriage, a son, Robert, who died in 1889, after showing in experimental physicsindications of his father's genius, and a daughter, who married a son of Werner von Siemens.Helmholtz was a man of simple but refined tastes, of noble carriage and somewhat austeremanner. His life from first to last was one of devotion to science, and he must be accounted,on intellectual grounds, one of the foremost men of the 19th century.
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Father: August Ferdinand Julius Helmholtz (headmaster, Potsdam Gymnasium, d. 1858)

Mother: Caroline Penn

Wife: Olga von Velten (m. 26-Aug-1849, d. 1859, two children)

Wife: Anna von Mohl (m. 16-May-1861)


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Lon Charles Thvenin

(30 March 1857, Meaux, Seine-et-Marne - 21September 1926, Paris) was a

French telegraph engineer who extended Ohm's

law to the analysis of complex electrical circuits.

Born in Meaux, France, Thvenin graduated fromthe cole Polytechnique in Paris in 1876. In 1878,he joined the corps of telegraph Engineers(which subsequently became the French PTT).There, he initially worked on the development of

long distance underground telegraph lines.Appointed as a teaching inspector at the cole

Suprieure de Tlgraphie in 1882, he became increasingly interested in the problems ofmeasurement in electrical circuits. As a result of studyingKirchhoff's circuit laws and Ohm'slaw, he developed his famous theorem, Thvenin's theorem,[1]which made it possible tocalculate currents in more complex electrical circuits and allowing people to reduce complexcircuits into simpler circuits called Thvenin's equivalent circuits.

Also, after becoming head of the Bureau des Lignes, he found time for teaching othersubjects outside the cole Suprieure, including a course in mechanics at the InstitutNational Agronomique, Paris. In 1896, he was appointed Director of the Telegraph

Engineering School, and then in 1901, Engineer in chief of the telegraph workshops. He diedin Paris.

He was a talented violin player. Another favorite pastime of his was angling. He remainedsingle but shared his home with a widowed cousin of his mother's and her two childrenwhom he later adopted. Thvenin consulted several scholars well known at that time, andcontroversy arose as to whether his law was consistent with the facts or not. Shortly beforehis death he was visited by a friend of his, J. B. Pomey, and was surprised to hear that histheorem had been accepted all over the world. In 1926, he was taken to Paris for treatment.He left a formal request that no one should accompany him to the cemetery except hisfamily and that nothing be placed on his coffin but a rose from his garden. This is how he

was buried at Meaux. Thvenin is remembered as a model engineer and employee, hard-working, of scrupulous morality, strict in his principles but kind at heart.
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Edward LawryNorton

Born: 28-July-1821Birthplace:Rockland, MaineDied: 28-january -1894Location of death: Chatham, New JerseyCause of death: unspecified

Gender: MaleRaceorEthnicity: WhiteSexualorientation: Straight

Occupation: Physicist

Nationality: New yorkExecutive summary: Law of Conservation ofEnergy

Norton's theorem is an extension ofThevenin's theorem and was introduced in 1926 separately by two people: Hause-Siemens researcherHans Ferdinand Mayer (1895-1980) andBell LabsengineerEdwardLawry Norton (1898-1983). Mayer was the only one of the two who actually published onthis topic, but Norton made known his finding through an internal technical report at BellLabs.

. .This theorem states that any linear bilateral circuit with combination of voltage sources ,current sources and resistors with two terminals is electrically equivalent to an ideal currentsoure, INo, in parallel with a single resistor, RNo.This equivalent is called Norton Equivalent.

Edward Lawry Norton was born in Rockland, Maine on July 28, 1898. He served as a radiooperator in the U.S Navy between 1917 and 1919. He attended the University of Maine forone year before and for one year after his wartime service, then transferred to M.I.T. in 1920,receiving his S.B. degree (electrical engineering) in 1922. He started work in 1922 at the

Western Electric Corporation in New York City, which eventually became Bell Laboratories in1925. While working for Western Electric, he earned a M.A. degree in electrical engineeringfrom Columbia University in 1925. He retired in 1961 and died on January 28, 1983 at the KingJames Nursing Home in Chatham, New Jersey.

Norton was something of a legendary figure in network theory work who turned out aprodigious number of designs armed only with a slide rule and his intuition. Many anecdotes
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survive. On one occasion T.C. Fry called in his network theory group, which included at thattime Bode, Darlington and R.L. Dietzold among others, and told them: "You fellows hadbetter not sign up for any graduate courses or other outside work this coming year becauseyou are going to take over the network design that Ed Norton has been doing single-handed."


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Nodal

Analysis

In electric circuits analysis, nodalanalysis, node-voltage analysis, orthe branch current method is amethod of determining the voltage(potential difference) between"nodes" (points where elements orbranches connect) in an electrical

circuit in terms of the branch currents.

In analyzing a circuit using Kirchhoff's circuit laws, one caneither do nodal analysis using Kirchhoff's current law (KCL)or mesh analysis using Kirchhoff's voltage law (KVL). Nodalanalysis writes an equation at each electrical node, requiringthat the branch currents incident at a node must sum to zero.The branch currents are written in terms of the circuit nodevoltages. As a consequence, each branch constitutive relationmust give current as a function of voltage;an admittance representation. For instance, for a resistor,Ibranch = Vbranch * G, where G (=1/R) is the admittance(conductance) of the resistor.

Nodal analysis is possible when all the circuit elements'branch constitutive relations have an admittancerepresentation. Nodal analysis produces a compact set ofequations for the network, which can be solved by hand ifsmall, or can be quickly solved using linear algebra by computer. Because of the compactsystem of equations, many circuit simulation programs (e.g. SPICE) use nodal analysis as abasis. When elements do not have admittance representations, a more general extension ofnodal analysis, modified nodal analysis, can be used.

While simple examples of nodal analysis focus on linear elements, more complex nonlinear

networks can also be solved with nodal analysis by using Newton's method to turn thenonlinear problem into a sequence of linear problems.
http://en.wikipedia.org/wiki/Potential_differencehttp://en.wikipedia.org/wiki/Node_(circuits)http://en.wikipedia.org/wiki/Electrical_circuithttp://en.wikipedia.org/wiki/Electrical_circuithttp://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_lawshttp://en.wikipedia.org/wiki/Mesh_analysishttp://en.wikipedia.org/wiki/Node_(circuits)http://en.wikipedia.org/wiki/Admittancehttp://en.wikipedia.org/wiki/Circuit_simulationhttp://en.wikipedia.org/wiki/SPICEhttp://en.wikipedia.org/wiki/Modified_nodal_analysishttp://en.wikipedia.org/wiki/Newton%27s_methodhttp://en.wikipedia.org/wiki/Newton%27s_methodhttp://en.wikipedia.org/wiki/Modified_nodal_analysishttp://en.wikipedia.org/wiki/SPICEhttp://en.wikipedia.org/wiki/Circuit_simulationhttp://en.wikipedia.org/wiki/Admittancehttp://en.wikipedia.org/wiki/Node_(circuits)http://en.wikipedia.org/wiki/Mesh_analysishttp://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_lawshttp://en.wikipedia.org/wiki/Electrical_circuithttp://en.wikipedia.org/wiki/Electrical_circuithttp://en.wikipedia.org/wiki/Node_(circuits)http://en.wikipedia.org/wiki/Potential_difference


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SUPER POSITION THEOREM

The superposition theorem is a method which allows to determine the current through or

the voltage across any resistor or branch in a network. The advantage of using this approach

instead of mesh analysis or nodal analysis is that it is not necessary to use

several equations to get

required voltage or current. The

theorem states the following:

The total current

through or voltage across a

resistor or branch may

be determined by summing the

effects due to each independent

source.

In order to apply the

superposition theorem it is

necessary to remove all sources

other than the one being examined. In order to 'zero' a voltage source, replace it with a

short circuit, since the voltage across a short circuit is zero volts. A current source is zeroed

by replacing it with an open circuit, since the current through an open circuit is zero amps. If

the purpose to determine the power dissipated by any resistor, first it must find either

the voltage across the resistor or the current through the resistor:


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e.engineering 6 equations

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