Development of the theory of electrical circuits from the end of the nineteenth century

Up to 80-ies of the nineteenth century there was a gradual accumulation of information about the features of the physical processes in AC circuits, which include mainly include possible differences in voltage and current phases, excitement, and the mutual self-induction EMF and current existence of the capacitor.

Quantitative relationships sometimes only discern the quality of the arguments, as was typical for all of Faraday's researches. And later studies were more qualitative in nature.

For example, BS Jacobi, analyzing the formation of the EMF generator, argued that it is proportional to the angular speed of rotation of the armature, the number of winding turns and the intensity of the magnetic field. The Helmholtz works Maxwell, William Thomson (Lord Kelvin), F. Neumann and other physicists there are rigorous mathematical relationship between the instantaneous values ​​of currents and voltages, there are the basic equations in differential form chains.

In the 80's attempts to compare the action of direct and alternating currents, the concept of an ideal sinusoidal current is introduced. It was found, for example, relatively easy to calculate that the power generated in the resistor sinusoidal current and compare it with the capacity allocated to the same DC resistor. In 1888, W. Thomson has shown the possibility of using Fourier harmonic analysis for each batch (non-sinusoidal) current (Fourier his famous method proposed in 1822, developing the theory of heat).

Development of the theory of electrical circuits from the end of the nineteenth century

In light of the non-sinusoidal currents harmonic analysis was found out most of the harmful role of higher harmonics and the output of the need to take special technical measures was made for generators EMF shape possibly close to a sine wave. In 90-ies took "controversy about the sinusoid" in the pages of electrical logs.

In 1887 Gisbert Kapp (1852-1922 gg.), Later professor of the University of Birmingham, led the exact formula transformer emf, now known to every electrician.

A great contribution to the development of alternating current theory, introduced the Italian physicist G. Ferraris, who in his book "On the phase difference in the currents of the delay vsledstvii induction and the losses in the transformer torus" (1886) considers the first phase difference between the currents in the primary and secondary windings transformer, and provides methods for calculating the hysteresis losses and eddy current. " Later, in 1893, he explored and processes in single-phase motors, using the method of rotating vectors.

Ferraris fundamental work entitled "Scientific electrical base" was published in 1898. It was the first guide on Theoretical Electrical Engineering, appeared in Russian translation in 1904

In 1889, Professor Thomas of Greenwich Naval College Blakeslee suggested to represent a sine value in the form of a vector. The method of vector diagrams opened great opportunities for visual representation of the processes in order harmonic current. In particular, this method made it possible to extend Ohm's law in the circuit containing resistors, inductance and capacitance, and under the influence of harmonic voltages.

An important role in the development of modern ideas in the field of AC theory played a study MO Dolivo-Dobrovolsky. In his report at the International Congress of electricians in Fraikfurte-to-Mann (1891) valley-Dobrovolcky showed that the magnetic flux in the magnetic coil included in an AC circuit, is entirely determined by voltage (if you count the frequency and the number of turns specified) and It depends on the magnetic resistance. With the change in the magnetic resistance changes only the magnetizing current.

This provision, which Dolnvo-Dobrovolsky calls the first major position AC theory, is indeed the source of all calculations of electromagnetic devices. He further noted that if the magnetic flux changes sinusoidally, the EMF (or, respectively, voltage) also varies as the sine, the EMF and magnetic flux are different in phase. They were introduced by the active and reactive current components of the concept, which he called respectively watt (workers) and wattless (excitatory) currents. The method of expanding any current into two components was recommended Dolivo-Dobrovolsky for practical calculations and analysis of processes in electrical machines and apparatus.

Dolivo-Dobrovolsky recommended to accept as the basic form of a sine wave current waveform. With regard to the current rate, he spoke in favor of 30-40 Hz. Later, as a result of the critical selection of received applications, only two current industrial frequency 60 Hz in the United States and 50 Hz in other countries. These frequencies were optimal, for increasing the frequency leads to an excessive increase in the electrical machinery rotational speed (with the same number of poles), and reducing the frequency adversely affects the uniformity of illumination.

Somewhat later, in 1892, Dolivo-Dobrovolsky has developed on the basis of the provisions set out the basic theory and designing transformers, denying the spreading erroneous assertion that the transformers are in principle may not be cost-effective devices. In the 90s the works of some scientists (S. Evershed, Ben-Eschenburg, G. Cappa et al.), The most important questions of the theory of transformers have been investigated.

Based on the method of vector diagrams of the opportunity to investigate the behavior of a circuit when one of the parameters. It became known line and pie charts, ie, method of loci. Especially productive he was for electrical machines theory (A. heulandite). In 1902, J. Lacour published a book, which describes the construction of a pie chart according to the experiments of idling and short circuit.

The logical conclusion of the general theory of alternating current circuits was extremely productive idea to put the vector diagram on the complex plane. This allowed trigonometric operations on vector images sinusoidal functions of time to replace the algebraic operations on complex numbers. It was found, moreover, that the integral-differential equations for the instantaneous topological values ​​in stationary processes could be replaced by algebraic equations for the complex images.

Although the idea of ​​using complex numbers for network analysis with harmonic influences literally was in the air, the undoubted merit in the broad introduction of the method of complex amplitudes ( "symbolic method") belongs to the well-known American electrical Charlsu Proteus Steinmetz (1865-1923 gg.). In 1901, Steinmetz made a fundamental course called "Theory of Electrical Engineering."

In 1899 in London, it was published and other symbolic method, which is proposed to replace any analytical expression impact his image of the operator. The English physicist Oliver Heaviside (1850-1925 gg.), Carried away by Maxwell's treatise, shut up as a lonely hermit in his home office, decided one after the other problems in the theory of electrical circuits and electromagnetic fields. When he lacked the mathematical knowledge he quickly developed the necessary mathematical apparatus. So to meet the challenges of the transition process, he came up with the operational calculus based on the Laplace transform.

By the end of the last century found a natural conclusion in its main parts of the theory of electrical circuits, the actual harmonic function of time was presented first vector on the plane, then the complex character and, finally, any time function - the image of the operator. The said effects have been mapped to the complex and operator substitution scheme, ie We were put into circulation the concept of integrated and operator resistances.

With the expansion of the practical applications of electrical energy began training of scientific and engineering personnel electricians. In some technical schools have developed special courses. For example, in Russia in 1840 was organized by the officer class for the study of electricity and magnetism in connection with the needs of the mine electrical engineering. In 1856, the Main Engineering School of the War Department began to prepare engineers in electrical engineering. In 1884, at the St. Petersburg Institute of Technology came eletrotekhnicheskikh specialty, and in 1891 the St. Petersburg eletrotekhnicheskikh Institute was opened on the basis of the Telegraph School.

At the St. Petersburg Polytechnic Institute, opened in 1902, the future academician Vladimir Fedorovich Mitkevich (1872-1951 gg.) In 1904 began to teach a course "The theory of electric and magnetic phenomena," and at the Moscow Higher Technical School since 1905 started to read courses "Theory of the current variables" and "Electrical measurements" future corr. USSR Academy of Sciences and a professor at Moscow Energy Institute Adol'fovich Karl Krug (1873-1952). With names VF Mitkevich and KA Circle associated base Petersburg and Moscow electrotechnical schools.

Veselovsky O. Shneiberg A. I "Essays on the History of Electrical Engineering"