Arts. 377 and 399 must be applied (see exercise 21 on Chap. V.). 465. Excitation of Field-Magnets. There are several modes of exciting the magnetism of the field-magnets, giving rise to the following classification: 1. Magneto Machine, with permanent steel magnets. 2. Separately-excited Dynamo; one in which the currents used to excite the field-magnets are furnished by a separate machine called an "exciter." 3. Separate-coil Dynamo, with a separate coil wound on the armature to generate the exciting current. 4. Series-Dynamo, wherein the coils of the field-magnet are in series with those of the armature and the 000 Fig. 246. SHUNT MAIN Fig. 247. Fig. 248. external circuit (Fig. 246), and consist of a few turns of thick wire. 5. Shunt-Dynamo, in which the coils of the fieldmagnet form a shunt to the main circuit; and, being made of many turns of thin wire, draw off only a small fraction of the whole current (Fig. 247). 6. Compound-Dynamo, partly excited by shunt coils, partly by series coils (Fig. 248). The last three modes are illustrated in the accompanying diagrams. Each variety of winding has certain advantages depending on conditions of use. P E 466. Characteristic Curves. To study the behaviour of various types of dynamo, Hopkinson devised the method of characteristic curves, wherein the two elements of output - the volts and the amperes - are plotted out. If a series-dynamo is examined with amperemeter and voltmeter, while run at constant speed on various loads, its performance will be found to give a curve like OQV in Fig. 249, where the external volts are plotted vertically, the amperes horizontally. This curve is the external characteristic. The volts rise as the current is increased, because of the increase of magnetization, but when this is near saturation they fall again because of internal resistance and Xsundry reactions. At any point such as Q the resistance of the external circuit Fig. 249. M = N is represented by the slope of the line QO (i.e. by the trigonometrical tangent of the angle QOX), since tan QOX is equal to QM/OM (= the volts divided by the amperes). If line OJ be drawn so that tan JOX is equal to the internal resistance, then MN will represent the lost volts when the current OM. Adding to QM a piece PQ = MN, we obtain PM as the corresponding value of the total electromotive-force. In this way, from the curve OV we can construct the total characteristic OE. It will be evident that if the total resistance (i.e. the slope of the line OP) be increased P will come down the curve toward O, and there will be a certain point at which any further increase in the slope will produce a sudden drop of volts and amperes to almost zero. This is a peculiarity of seriesmachines; when running at a given speed they cease to yield any current if the resistance exceeds a certain critical value, depending in each machine on its construction. YI E For a shunt-dynamo the characteristic has a different form. When the machine is on open circuit, giving no current externally, the shunt circuit is fully at work exciting the magnet. The curve YV of volts at terminals begins at a high value, and as the current is increased by diminishing the resistance, the voltage gently falls. Part of this drop is due to internal resistance; part is due to armature reactions and magnetic distortion; and part to the reduction of the shunt current. If, as before, we draw OJ to represent by its N M X Fig. 250. slope the internal resistance, we can find the lost volts MN and add these on above Q, so obtaining P, a point on the total electromotive-force curve. This also drops slightly. If a shunt-dynamo be short-circuited, its magnetism is at once reduced to almost zero. To regulate the voltage of a shunt-dynamo a suitable rheostat (Fig. 206) may be introduced into its shunt circuit, to vary the exciting current. 467. Constant Voltage Machines. For glow-lamp lighting, machines are needed that will maintain the voltage constant, whether the current going to the mains be small or large. The current that flows out of the machine will regulate itself exactly in proportion to the demand; more flowing when more lamps are turned on, provided the potential difference between the mains is kept constant. For this purpose neither a series-dynamo nor a shunt-dynamo (driven at a constant speed) will suffice; though by hand-regulation, as above, a shuntdynamo may be used. It will be noted that, while in shunt-machines the characteristic drops as the current is increased, in series-machines the curve rises. Conse quently, by using a compound-winding, consisting of a shunt-winding (to give the proper voltage an open circuit) and a few coils of thick wire, in series with the main circuit (to raise the excitation in proportion to the output), the voltage may be kept remarkably constant. By over-compounding with more series windings the dynamo may be made to maintain a constant voltage at some distant point in the circuit. 468. Constant Current Machines — Series Lighting. - To maintain an unvarying current in a series of lamps, as is frequently wanted for lighting with arc lamps (Art. 448), special dynamos are used known as arc-lighting machines. The best known of these are the Brush and the Thomson-Houston dynamos. Both have open-coil armatures (in which the coils are not grouped in a closed circuit), with special commutators, and automatic devices to regulate the output, the one by shunting the exciting current, the other by shifting the brushes. The current may thus be kept at 10 amperes, while the volts change (according to the number of lamps in circuit) from 50 to 2000 or more. 469. Unipolar Machines. There is another class of dynamo-electric machines, differing entirely from any of the preceding, in which a coil or other movable conductor slides round one pole of a magnet and cuts the magnetic lines in a continuous manner without any reversals in the direction of the induced currents. Such machines, sometimes called "uni-polar " machines, have, however, very low electromotive-force, and are not practical. Faraday's disk-machine (Fig. 132) belonged to this class. 470. Periodic Currents. We have seen that the revolving of a simple coil in a magnetic field sets up electromotive-forces, which change in direction at every half-turn, giving rise to alternate currents. In each whole revolution there will be an electromotive-force which rises to a maximum and then dies away, followed immediately by a reversed electromotive-force, which also grows to a maximum and then dies away. Each such complete set of operations is called a period, and the number of periods accomplished in a second is called the frequency or periodicity of the alternations, and is symbolized by the letter n. In 2-pole machines n is the same as the number of revolutions per second; but in multipolar machines n is greater, in proportion to the number of pairs of poles. By revolving in a uniform field the electromotive-forces set up are proportional to the sine of the angle through which the coil has turned from the position in which it lay across the field. If in this position the flux of magnetic lines through it were N, and the number of spirals in the coil that enclose the N lines be called S, then the value of the induced electromotiveforce at any time t when the coil has turned through angle (= 2nt) will be E. = 2πnSN sin 0 ÷ 108, or, writing D for 2nSN/108, we have Ee In actual machines the magnetic fields are not uniform, nor the coils simple loops, so the periodic rise and fall of the electromotive-forces will not necessarily follow a simple sine law. The form of the impressed waves will depend on the shape of the polar faces, and on the form and breadth of the coils. But in most cases we are sufficiently justified in assuming that the impressed electromotive-force follows a sine law, so that the value at any instant may be expressed in the above form, where D is the maximum value or amplitude attained by E, and an angle of phase upon an imaginary circle of |