Direct current regimes in the linear electric circuits according to the relativistic circuit theory

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.