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The study of these phenomena has been undertaken and four additional chapters devoted to the change of circuit constants with the frequency, the increase of attenuation constant resulting therefrom, and the degeneration, that is rounding off of complex waves, the flattening of wave fronts with the time and distance of travel, etc., added. It comprises the investigation of phenomena which heretofore have rarely been dealt with in teict-books but have now become of such importance that a knowledge of them is essential for every electrical engineer, as they include some of the most important problems which electrical engineering will have to solve in the near future to nudntain its thus far unbroken progress. However, even in large transformers and at moderately high voltages, capacity effects occur in transformers, if the frequency is sufficiently high, as is the case with the currents produced in overhead lines by lightning discharges, or by arcing grounds resulting from spark discharges between conductor and ground, or in starting or disconnecting the transformer.The method of symbolic representation has been changed from the time diagram to the crank diagram, in accordance with the international convention, and in conformity with the other books; numerous errors of the previous edition corrected, etc. A few of these transient phenomena were observed and experi- mentally investigated in the early days of electrical engineering, for instance, the building up of the voltage of direct-current generators from the remanent magnetism. With such frequencies, of many thousand cycles, the internal capacity of the transformer becomes very marked in its effect on the dis- tribution of voltage and current, and may produce dangerous high-voltage points in the transformer. The high-potential coil of the transformer also contiuns shunted capacity, or capadty from the conductor to ground, and so each coil element consumes a charging current proportional to its potential difference against ground.Whether a book is still in copyright varies from country to country, and we can't offer guidance on whether any specific use of any specific book is allowed. Independence of oscillating current frequency on size of condenser and inductance. The oscillating current generator, discussion of its design. The equations of the oscillating current generator. Discussion of equations: frequency, current, power, ra*io of transformation. Calculation of numerical example of a generator having a frequency of himdreds of thousands of cycles per second. Substituting (7) and (11) in (18), and writing d = 2 Tzf^t and T = ;^ (19) ^ves t = cos (2n — 1) r = c cos (2 n — 1) (^ — /-) cos (2 n — 1)t and - v^^l'. (26) A simple harmonic oscillation as a line discharge would require a sinoidal distribution of potential on the transmission line at th?Please do not assume that a book's appearance in Google Book Search means it can be used in any manner anywhere in the world. Limitations of frequency by mechanical size and power. ^Jc,cos(2n-l)(9-c,sin(2n-l)tf|sin(2n-l)T^ ^^^^ = - \^c sin (2 n - 1) ( fig. instant of discharge, which is not probable, so that probably all lightning discharges of transmission lines or oscillations produced by sudden changes of circuit conditions are complex waves of many harmonics, which in their relative magnitude depend upo D the initial charge and its distribution — that is, in the case of the lightning discharge, upon the atmospheric electrostatic field of force.Nevertheless, this work is expensive, so in order to keep providing tliis resource, we liave taken steps to prevent abuse by commercial parties, including placing technical restrictions on automated querying. The lowest frequency or fundamental frequency of oscillation is, for n = 1, and besides this fundamental frequency, all its odd midtiples or higher harmonics may exist in the oscillation /=(2n-l)/,. that is, the frequency of oscillation of a line discharging to ground is independent of the size of line wire and its distance from the ground, and merely depends upon the length, l^ of the line, bring inversely proportional thereto.We also ask that you: Make non-commercial use of the files We designed Google Book Search for use by individuals, and we request that you use these files for personal, non-commercial purposes. (11) Writing L^ ^IJj = total inductance, and C^ = Ij J = total capacity of the circuit, equation (9) assumes the form /, = —^ . We thus get the numerical values, Length of line 10 20 30 40 50 60 80 100 miles 1.6 3.2 4.8 6.4 8 9.6 12.8 16X10* cm.Usage guidelines Google is proud to partner with libraries to digitize public domain materials and make them widely accessible. cos 31 and • • * ^ E^j\^C, Anfil, (4) and at Z = l^, Ci cos pi^ = 0, and since C^ cannot be zero without the oscillation disappearing altogether, cos/? Z, = (2n-l)^, (6) NATURAL PERIOD OF TRANSMISSION LINE 329 where n » 1, 2, 3 ...

Formerly high frequency currents were only a subject for brilliant lecture experiments ; now, however, in the wireless telegraphy they have found an important industrial use. The three cases of condenser charge and discharge : loga- rithmic, critical and oscillatory. The logarithmic case, and the effect of resistance in elimi- nating excessive voltages in condenser discharges. Starting from one point of the conductor, after a certain ^l--ih^F^nl-^h^l-^l-^l-^i l-^nnl-^ni-^l ^h "v [Wi Tiiiiniii Tiirii ^rjiimiimxixa Tig. Di Etrlbuled cupocit; at a high-po Lentia J transforni Br coil.Teleph- ony has advanced from the art of designing elaborate switch- boards to an engineering science, due to the work of M. length, the length of one turn, the conductor reapproaches the first point in the next adjacent turn.L ix X PREFACE and others, dealing with the fjurly high frequency of sound waves. Final equations of condenser charge and discharge, in exponential form. It ag^n approaches the first point at a different and greater distance in the next adjacent layer.Maintain attribution Tht Goog Xt "watermark" you see on each file is essential for in forming people about this project and helping them find additional materials through Google Book Search. Keep it legal Whatever your use, remember that you are responsible for ensuring that what you are doing is legal. Example of underground cable acting as oscillating cur- rent generator of low frequency. Resistance, Inductance and Capacitt in Series IN Alternating Current Circuit. In comparing with loca Uzed inductances and capacities, the distributed capacity and inductance, in free oscillation, thus are represented by their effective values (13) and (14). Substituting in equations (4), C, = c, ic„ (16) gives / = (Cj j Cj) cos pi *™* ^=V^(c,-/c.)8in^Z. 86, those with I =- 3, with two nodal pdnts, in Rg. The higher harmonics of the oscillation are the odd multiples of these frequencies.

Do not assume that just because we believe a book is in the public domain for users in the United States, that the work is also in the public domain for users in other countries. (17) NATURAL PERIOD OF TRANSMISSION LINE 331 By the definition of the complex quantity as vector represen- tation of an alternating wave the cosine component of the wave is represented by the real, the sine component by the imaginary term ; that is, a wave of the form c^ cos 2 nft c^ sin 2 nft is represented by c^ jc^, and inversely, the equations (17), in their analytic expression, are i = (Cj cos 2 Ttfi Cj sin 2 nft) cos fil 6 = y - (Cj cos 2 7:ft — Cj sm 2 zft) sm pi. Obviously all these waves of different frequencies represented in equation (20) can occur simultaneously in the oscillating dis- charge of a transmission line, and, in general, the oscillating discharge of a transmission line is thus of the form t = ^n Cn COS (2 n - 1) (0 — Yn) COS (2 n — 1) r, 1 = - V^ 2nc,,sin (2n - 1) (^ - r J sin (2n - 1) r.

Others, such as the investigation of the rapidity of the response of a compound generator or a booster to a change of load, have become of impor- tance with the stricter requirements now made on electric ssrstems. The distributed capacity of the transformer, however, is differ- ent from that of a transmission line. Assuming the circuit as insu- lated, and the middle of the transformer coil at ground potential, the charge consumed by unit length of the coil increases from zero at the center to a maximum at the ends.