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found. For exampie, between the + brush and the middle point M of the circuit, there is a difference of potential of 500 volts, and the same amount between the middle point and the — brush. Similarly any two points on the circuit will have a difference of potential equal to fifty volts, multiplied by the number of lamps included between them.
Personal Danger from Series Circuits. — If a man standing on the ground touches a very highly insulated circuit, only a very slight current will pass through his body; but if the insulation is low or any defect exists at any particular point, then a considerable current may flow through his body. In Fig. 2 the line is supposed to have a ground connection at the point P, due to a defect in the insulation. This will cause the potential of the circuit to be zero at that point; consequently a man may stand on the ground, and touch the line at that point with perfect impunity. If he touches the wire at point Q he will receive a barely perceptible shock, due to 100 volts, since there are two lamps between that point and the ground connection; but if the circuit be touched at the point R, the difference of potential between it and the ground connection being 18 x 50 = 900 volts, will produce a dangerous, or perhaps fatal, current. When the defect in the insulation does not amount to what is called " dead ground," but has a resistance, for example, of 1,000 ohms, then a man touching the wire at the point K will receive a shock due to 900 volts as before; but the resistance of the ground connection, which is 1,000 ohms, will be in series with his body. Consequently the current will be less; and, assuming the resistance of his body to be 1,000 ohms, the current will be one-half as great as in the first case. If the ground connection has a resistance of 8,000 ohms, the current through the body would
be = — of an ampere, which is not dangerous.
8,000 + 1,000 10 1
We may sum up these various cases as follows : —
1. A very highly insulated direct-current electrical circuit may be touched at any one point without danger by a man standing on or in connection with the ground.
2. If a ground connection exists on a series electrical circuit, the danger of touching the circuit increases directly with the resistance between the ground connection and the point of contact.
3. The resistance of the ground connection is in series with the body of any one connected with the ground and touching the wire at some other point.
4. It is never safe, however, to assume the insulation to be perfect, or that a ground connection exists at some particular point, or that it has a high resistance. The circuit should always be treated as if the most dangerous possible conditions existed.
Regulation of Series Systems. — The condition required on series circuits is usually the maintenance of a constant current. This is accomplished by designing the dynamo so that it will automatically generate a nearly constant current. The various dynamos used in series arc-lighting, such as the 'Brush, ThomsonHouston, and Wood machines, are well-known examples of this type of generator. They are provided with regulating devices, which either shift the brushes or vary the strength of the field, or both, in order to keep the current at a constant value. In addition to these special regulators, such machines are so designed that they have considerable self-induction, resistance, and armaturereaction, all of which tend to prevent the current from rising to a high value, even when the machine is short-circuited.*
Series Arc-Lighting System. — The general arrangement of the apparatus and circuit is represented in Fig. 1. The dynamo and lamps may be selected from the various well-known and thoroughly successful forms of constant-current arc-lighting apparatus. The determination of the proper size of wire is not very difficult. General custom and considerations of strength require that no wire smaller than No. 8, A. W. G., should be used. Similarly it would not usually be necessary to employ a conductor larger than No. 4, because the potential being high, and the current small, the loss of energy is not great, even in a wire several miles in length. To take a specific case, let us assume a circuit five miles long, supplying 80 arc lamps, the potential being 4,000 volts and the current 10 amperes. If No. 6 wire is used, the resistance would be 2.1 ohms per mile, or 10.5 ohms for the whole line. This involves a drop of 105 volts and a loss of energy of 1,050 watts, which is only 2.63 per cent; consequently it is evident that the use of a little larger or a little smaller wire would not seriously affect the economical working of such a line. The substitution of No. 3 for No. 6 wire would save one-half the loss of energy, the cross
,* For a description of such machines see Vol. I., p. 330.
section and weight being twice as great, and the cost of the insulated conductor would be nearly doubled. With No. 6 wire the total weight of copper would be 2,098 pounds, and the cost of the wire (insulated) would be about #500. It is doubtful if it would be wise to invest an additional $500 in order to use No. 3 wire and save one-half the energy or 525 watts.
The New Brush Arc-Lighting System is an interesting case of series distribution. In the original type of Brush dynamo the armature is provided with two or more separate open-coil windings, connected to a corresponding number of commutators. The circuit leads through these windings in series, so that the construction may be regarded as equivalent to several armatures in series.
Figs. 3 and 4. Original Arrangement of Brush Arc Lighting System.
This arrangement is represented diagrammatically in Fig. 3, in which A, B, and C are three commutators connected in series with each other and with the line that supplies a number of lamps, L, L, etc., in the usual manner. Assuming each armature winding to generate 2,000 volts, the total E.M.F. of the machine will be 6,000 volts. The distribution of potential in this case is shown in Fig. 4, the + brush of C being + 3,000 volts, and the — brush of A being — 3,000 volts, with respect to the potential of the earth, which is represented by the zero line OO. The fall of potential through the circuit is indicated by the inclined lines, P O and O N, the total amount being 6,000 volts, and the middle point being zero. This assumes an ideal case with a uniform distribution of conductor resistance and insulation resistance, but would be approximately true for a practical case in which the system was in good condition. If the insulation of some portion of the circuit became poor, it would tend to make the poten- FV+6000 tial at that point approach zero, producing a corresponding change in the rest of the circuit. For example, a ground connection at the negative terminal N would bring that point to zero, and the positive terminal P would then become + 6,000 volts, as represented in Fig. 5:
The new Brush system, illustrated in Fig. 6,.differs from the old in the fact that the lamps, L, L, are inserted in the circuit between the commutators A, B, and C, in which case the line consists of three loops. With this arrangement, the E.M.F. generated by each of the three armature windings is consumed by the lamps
between it and the next armature winding, so that the potential does not rise above + 1,000 volts, or fall below — 1,000 volts, in the ideal case represented in Fig. 7. Even if the circuit becomes grounded at any point, the potential will nowhere exceed 2,000 volts, and the maximum difference of potential existing between any portions of the circuit will not be greater than this amount. A voltmeter connected across from the — brush of B to the + brush of C would only indicate 2,000 volts, in spite of the fact that the E.M.F. generated between those points is 4,000 volts, the remaining 2,000 volts being used in the lamps between B and C. This reduction or subdivision of the total E.M.F. is the advantage of this system, and avoids the dangers involved in the use of the ordinary types of machine for supplying a large number (50 to 200) of arc lamps in series. On the other hand, it is necessary to arrange the line in several loops instead of having one long circuit. In Fig. 6, for example, there would be six wires running out from the station, while Fig. 3 would only require two. Nevertheless, the former plan may be preferable to the operation of three separate dynamos, which would be less efficient, occupy more space, and demand more attention than a single large machine.
If desired, the number of lamps on any loop may be increased or decreased, since the current is kept constant by a regulator on the dynamo; and it is quite immaterial where the resistance is introduced in a series circuit. In fact, any or all of the lamps may be cut out, or they may be put upon two loops and none on the third, or the full load may be placed on a single loop, in which case the arrangement reduces to the ordinary one shown in Fig. 3. When the number of lamps on any loop is augmented or diminished, the potential difference between its terminals varies in direct proportion, so that two-thirds of the lamps on one loop would require a P.D. of 4,000 volts between the brushes to which it is connected. This gives great flexibility to the system, and provided the lamps are not very unequally divided, the pressure is not excessive on any one loop. It should be noted that in either the old or the new system, the full E.M.F. of 6,000 volts would be found to exist if the circuit be opened at any point. Indeed, the P.D. would tend to rise momentarily considerably above the normal voltage.*
Series Incandescent Lamps on Arc Circuits. — Several forms of incandescent lamps have been designed and manufactured for use on the regular 10-ampere arc circuits. These consist of lamps similar in general principle and construction to those used for constant potential, parallel distribution, but containing a shorter filament of larger cross-section that is sufficiently heavy to carry the full current of 10 amperes.
The most important consideration is that of maintaining the continuity of the circuit when the filament of any lamp happens to break, which might occur at any time. This may be accomplished
♦ Vol. I., p. 331.