Electric Circuit Theory and the Operational Calculus Chapter VI, Propagation of Current and Voltage Along the Non-Inductive Cable

PROPAGATION OF C U R R E N T AND VOLTAGE A L O N G THE NON-INDUCTIVE CABLE T HE principal practical applications of the operational calculus in electrotechnics are to the theory of the propagation of current and voltage along transmission systems. Of such transmission systems the simplest is the non-inductive cable. The theory of the non-inductive cable is not only of great historic interest, relating as it does to Kelvin's early work on the possibility of transatlantic telegraphy, but is also of very considerable practical importance today, and serves as a basis for the theory of submarine telegraphy over long distances. We shall therefore consider the propagation phenomena in the non-inductive cable in some detail. The propagation phenomena in any type of transmission system are isolated and exhibited in the clearest possible manner when we confine attention to the infinitely long line, with voltage applied directly to the line terminals. Furthermore, as we shall see later, the solution for the infinitely long line is fundamental and can be extended to the more practical case of the finite line with terminal impedances. We therefore, in this chapter, shall confine our attention to the case of the infinitely long cable with voltage applied directly to the cable terminals. Consider a cable of distributed resistance R and capacity C per unit length, extending from ,r = 0 along the positive x axis. From a previous chapter (see equations (64) and (65) ), we are in possession of the operational equations of voltage and current; they are, for the infinitely long line, V=e-YLAP VC Ol (162) (163)