Abstract
The paper is dedicated to a missing chapter of the circuit theory, which is connected with the special theory of relativity. It is concerned with the direct current regimes in the linear electric circuits, which are moving with speeds smaller than the speed of light or close to it. In it a series of basic questions, connected with the relativistic forms of the fundamental laws for the electric circuits (Kirchhoff’s current law, Kirchhoff’s voltage law, Ohm’s law, Joule’s law, the energy conservation law), are observed. The relativistic forms of the basic quantities of the electric circuits (currents, voltages, powers) and the relativistic relations of the basic parameters of the circuits (resistances, conductances, capacitances, inductances) are presented, too. These formulas are extracted step by step by the help of Maxwell-Hertz-Einstein system of basic equations of the electromagnetic field, which is applied to fast moving objects (linear electric circuits) with arbitrary velocities less than the speed of light or even close to it. The final results are illustrated by the help of some simple examples about fast moving linear electric circuits. Their analyses are presented step by step in order to show the validity of the received relations.
Highlights
The creation of the Maxwell’s theory of the electromagnetic (EM) field had an enormous influence on the development of the modern physics (Maxwell, 1873)
As a result of the research the basic laws (Kirchhoff’s current law, Kirchhoff’s voltage law, Ohm’s law and Joule’s law) in relativistic form for fast moving electric circuits working in direct current (DC) regimes were extracted
Two numeric examples with fast moving linear electric circuits illustrate most of the extracted relations, too
Summary
The creation of the Maxwell’s theory of the electromagnetic (EM) field had an enormous influence on the development of the modern physics (Maxwell, 1873). The last equation presents Kirchhoff’s current law in relativistic form. If we apply the notations of Einstein and Laub (Einstein, 1908) for the transverse and the longitudinal components of the electric field intensities, the components of the electric field intensities in equations (25) – (27) and (70) – (74) can be notated as follows: E'x' = E'x'cond. ) in the coordinate systems S' and S , where the components of the electric field intensities act upon, we can extract the relations of the voltage drops there: u'IIcond . The correctness of equations (58) - (62) and (75) - (79) giving the relativistic relations of the current densities, the currents, the electric field intensities and the voltage drops in both coordinate systems can be proved by Joule’s law in point form for a small longitudinal or transverse element of a conductor with a current:. The relations among the powers are presented in (Pauli, 1958)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: ANNUAL JOURNAL OF TECHNICAL UNIVERSITY OF VARNA, BULGARIA
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
