Transient Current Density in a Pair of Long Parallel Conductors

Abstract

Two infinitely long parallel conductors of arbitrary cross section connected to a voltage source form a loop. If the source voltage depends on time, then due to induction there is no constant current density in the loop conductors. It is only recently that a method has been published for accurately calculating current density in a group of long parallel conductors. The method has thus far been applied to the calculation of steady-state current density in a loop connected to a sinusoidal voltage source. In the present article, the method is used for an accurate calculation of transient current using transient current density. The transient current is analysed when connecting and short-circuiting the sources of sinusoidal, constant and sawtooth voltages. For circular cross section conductors, the dependences of maximum current density, maximum current and the time of achieving steady state on the source frequency, the distance of the conductors and their resistivity when connecting the source of sinusoidal voltage are examined.

One Hundred and Fifty Years of Skin Effect

“…The values of Ĵrec were obtained by a method published in refs. [9][10][11][12], and in Figure 3 they are only given in one quarter of the conductor cross section because not only the amplitude but also the initial current density phase are symmetrical along the symmetry axes of the cross section x = 5 mm and y = 8 mm. Figure 4 gives the current density in a quarter of the rectangular cross section of a solitary conductor at the instant t = 0.39 T in Example 2.…”

“…All the phenomena given above can be analysed and quantitatively described based on the knowledge of current density in conductors, and therefore the method for calculating current density in a group of conductors is of fundamental significance. An accurate method for calculating current density in conductors forming a group has only recently been published [9][10][11][12]. The subject of investigation in [9][10][11][12] is a physical and mathematical model of a task referred to as the basic task.…”

“…An accurate method for calculating current density in conductors forming a group has only recently been published [9][10][11][12]. The subject of investigation in [9][10][11][12] is a physical and mathematical model of a task referred to as the basic task.…”

“…where d i is the length of the diagonal of rectangle A i . The mathematical model is a system of N ordinary differential equations of the first order [9][10][11][12]. A detailed description of the physical and mathematical models is given in [9][10][11][12], together with the solution to specific cases.…”

“…Part of the calculation of current density in conductors is the calculation of independent magnetic fluxes. The determination of independent fluxes is described in [9][10][11][12]. If in the calculation of current density in a solitary conductor or in a loop formed by two conductors the conductor cross sections are symmetrical and the values of conductor resistivity are also symmetrical, the determination of independent fluxes is simple if symmetry is used [13][14][15][16][17][18][19][20][21].…”