(^ d. ^i. rz •FS3 QJarneU ItituerHtta Slibtarg ■ 3tliata, 2?Mu lork ALEXANDER GRAY MEMORIAL LIBRARY ELECTRICAL ENGINEERING THE GIFT OF THE McGraw-Hill Book Co.. Inc. 1921 Cornell University Library QC 523.F83E3 Elementary electricity and magnetism; a t 3 1924 004 457 978 Cornell University Library The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924004457978 ELEMENTARY ELECTRICITY AND MAGNETISM ip^y^ ELEMENTARY ELECTRICITY AND MAGNETISM A TEXT-BOOK FOR COLLEGES AND TECHNICAL SCHOOLS A<" >?^ f 1''. f'^ r; ... r '^ C^ BY C' ' r.X' nrt ^ ' '' ^ WM. S. FRANKLIN and 6aRRY MACNUTT / ^.r . ::.cm/ 7 'f,Tr f^P Neto ¥orfe THE MACMILLAN COMPANY LONDON : MACMILLAN & CO., Ltd. I914 All rights reserved W" ■' 1 ' / ' ■" ' '' ' ' \ '' ;.^ ] "^' }-l. .'<\ ! COPYBIGHT, 1914 ^£^, \ ' By (THE MACMILLAN COMPANY Set up and «iectrotyped. Published June, 1914 PRESS OF THE NEW ERA PRINTING COMPANt LANCASTER. PA. PREFACE AND INTRODUCTION "AUes Vergangliche ist nur ein Gleichniss." (Intelligibility is only likeness.) The study of electricity and magnetism as represented in the following chapters is independent of any consideration of the nature of the physical action which leads to the production of electromotive force in a voltaic cell or dynamo ; it is independent of any consideration of the nature of the physical action which constitutes an electric current in a wire ; it is independent of any consideration of the nature of the disturbance which constitutes a magnetic field; and it is independent of any consideration of the nature of the disturbance or stress which constitutes an electric field. This kind of study of electricity and magnetism may very properly be called electro-mechanics. Simple mechanics is the study of ordinary bodies at rest or in visible motion, and one of the most important ideas in me- chanics is the idea of force, but the science of mechanics is not concerned with, and indeed it sheds no light upon, the question as to the physical nature of force. Thus, the science of mechanics is not concerned with the question as to the nature of the action which takes place in a gas and causes the gas to exert a force on a piston; the science of mechanics is not concerned with the ques- tion as to the nature of the action which takes place in the material of a stretched wire causing the wire to exert a pull upon each of the two supports at its ends; the science of mechanics is not concerned with the nature of the action between the earth and a heavy weight which causes the earth to exert a force on the weight. It is sufificient for the science of mechanics that these things are what may be called states of permanency which involve certain invariant co-relations. Thus, in the case of a stretched wire there is a certain invariant relation between what we call the vi . PREFACE AND INTRODUCTION. value of the stretching force and the amount of elongation, In the case of a gas there is a certain invariant relation between the density of the gas and its pressure, and so on.* Similarly it is sufficient for the science of electro-mechanics that such things as electric current, electromotive force, magnetic field and electric field are states of permanency which involve in- variant co-relations. The character of the science of mechanics and of the science of electro-mechanics may be further exemplified as follows: A sample of steel under test is broken by a tension of 120,000 pounds, but the exact character of the action which takes place in the steel when it is placed under tension is not a matter for con- sideration. Neither does one need to consider the action which takes place in the furnace of the boiler which supplies steam to the engine which drives the dynamo which supplies current to the motor which drives the testing machine! A plate of glass under test is broken down and punctured by an electromotive force of 95,000 volts, but the exact character of the action which takes place in the glass when it is subjected to the electro- motive force is not a matter for consideration. Mechanics is concerned with the correlation of what may be called lump effects, such as the relationship between the size of 9. beam and the load it can carry, the size of a fly wheel and the work it can do when stopped, the thickness and diameter of a boiler shell and the pressure it can stand, the size of a submerged body and the buoyant force which acts upon it, the size and shape of the air column in an organ pipe and its number of vibrations per second, the thickness of a glass plate and the electromotive force it can stand, the size of a copper wire and the current it can carry with a given rise of temperature and so forth. Another important method in physics is the so-called atomistic * This statement does not distinguish between mechanics in a narrow sense and what is called thermodynamics, which is the study of changes of state; including the subject of heat and the whole of chemistry. See Franklin and MacNutt'a Mechanics and Heat, pages 273-279, for a full discussion of this matter. PREFACE AND INTRODUCTION. vii method.* This method is extensively used in the elementary study of heat and in elementary chemistry, and it is a tremen- dously powerful help to research in nearly every branch of physics and chemistry. We believe, however, that it is a mistake to set forth the hypotheses of the atomic theory in an elementary treatise on electricity and magnetism. Following the plan of our Mechanics and Heat, we wish to include an introduction to this text, but what needs to be said in introduction is very brief, assuming that the student has read the introduction to our Mechanics and Heat. If there is a widespread indifference towards rational physics study on the part of young men (and many of our teachers seem to think there is), it can be overcome, we believe, by leading young men to understand what KIND of interest they can be expected to have in such study. Gilbert Chesterton says, very wisely, that the only spiritual or philosophical objection to steam engines is not that men pay for them, or work at them or make them very ugly, or even that men are killed by them ; but merely that men do not play at them. This is precisely the objection to physical science; men do not play at it. The Authors. April 22, 1914. * The essential features of the atomistic method are set forth in a simple and intelligible way on pages 274-275 of Franklin and MacNutt's Mechanics and Heat. A third method in physics, one which is only beginning to be recognized, is the statistical method, which is described on pages 3SO-3S2 of Franklin and MacNutt's Mechanics and Heat. One must not think that the atomic theory of gases (the so-called kinetic theory), for example, is a branch of mechanics merely because the fundamental ideas are mechanical ideas. The classification of methods in physical science is properly based on a consideration of kinds of observation and the way in which accompany- ing theory is brought to bear upon the methods and results of observation. TABLE OF CONTENTS. Chapter I pages Effects of the Electric Current. Magnetism. . 1-26 Chapter II Chemical Effect of the Electric Current . . . 27-45 Chapter III The Heating Effect of the Electric Current . . 46-82 Chapter IV Induced Electromotive Force 83-124 Chapter V Electric Charge and the Condenser 125-171 ELECTRICITY AND MAGNETISM. CHAPTER I. EFFECTS OF THE ELECTRIC CURRENT. I. The electromagnet. Figure i shows an electric battery* connected to a winding of insulated wire on an iron rod. When so arranged the iron rod attracts other pieces of iron, and it is said to be magnetized. When the wire is disconnected from the cttibon M wire gjr-^inc terminal KTrPFffmr iron rod s dry battery Fig. 1. nail battery the iron rod loses its magnetism. The iron rod with its winding of insulated wire is called an electromagnet. A rod of hardened steel may be magnetized in the same way, but a rod of hardened steel retains, more or less permanently, a large part of its magnetism when the battery is disconnected. Such a magnetized rod of hardened steel is called a permanent magnet. The form of electromagnet which is used in electric bells and telegraph instruments is shown in Fig. 2. When the winding of * This word is here used in its familiar every-day sense. 2 I ELECTRICITY AND MAGNETISM. wire is connected to a battery the soft iron core becomes a magnet and attracts the loose bar of iron. The loose bar of iron is sometimes called the armature. ^-i JL. A m ViJ e _^ m iron parts side view Fig. 2. end view 2. The electric lamp. Figure 3 shows the essential parts of the familiar electric flash-lamp. It consists of a battery and an electric lamp connected as shown in the figure. The lamp is a piece of very fine tungsten wire mounted in an exhausted glass bulb with connecting lead-wires of platinum passing through the glass. £ 3 push button dry battery Fig. 3. When the push-button is pressed the fine wire in the lamp is heated to a high temperature and gives off light. 3. Electro-plating. Figure 4 shows a battery connected to two strips of copper C and A both of which dip into a solution of cop- per sulphate. Under these conditions a layer of metallic copper is deposited on the metal strip C. This action is called electro- plating. EFFECTS OF THE ELECTRIC CURRENT. 3 4. The electric current and the electric circuit. When the above described effects are produced an electric ci^nent is said to flow through the wire. The production of an electric current always requires an electric generator such as a battery or dynamo. The path of the emhon- ,j^ zinc terminal wire cathode- -anode battery copper sulphate solution Fig. 4. current is usually a wire, and this path is called the electric circuit. A steady electric current always* flows through a complete circuit, that is to say, through a circuit which goes out from one terminal of a battery (or dynamo) and returns to the other terminal of the battery (or dynamo) without a break. Such a circuit is called a closed circuit. When the circuit is not complete it is said to be an open circuit. The electric current ceases to flow through a circuit when the circuit is opened or broken. The electric current has three important effects, namely, the magnetic effect which is described in Art. i, the heating effect which is described in Art. 2, and the chemical effect which is described in Art. 3. These effects are by no means fully de- scribed in Arts, i, 2 and 3; indeed nearly the whole of the elementary study of electricity and magnetism is devoted to these three effects. * An electric current which lasts for a very short time, a thousandth of a second for example, can flow in an incomplete or open circuit. In such a case very im- portant effects are produced at the place where the circuit is broken. See Art, 76. ELECTRICITY AND MAGNETISM. 5. The electric bell. The familiar electric bell consists of an electromagnet which attracts a piece of iron attached to a small hammer, and this hammer is thus made to strike a bell. An interesting and important detail of the ordinary electric bell is push button dry battery Fig. S. the arrangement, called an interrupter, for repeatedly making and breaking the electrical circuit so as to cause the bell-hammer to vibrate continuously. The details of the interrupter are shown in Fig. 5. When the current flows, the armature of the electro- wire -^^ battery \ bell A beUB ,b Fig. 6. magnet is attracted and the circuit is broken at p. The electro- magnet then looses its magnetism and the armature is pulled back by a spring, thus again closing the circuit at p. This operation is repeated over and over again. EFFECTS OF THE ELECTRIC CURRENT. 5 Figure 6 shows how a single battery can be used to ring either of two bells. Bell A can be rung by pushing either button a or a', and bell B can be rung by pushing button b. The battery, buttons and bells can be located anywhere with reference to each other, provided only that the connections are as shown in the figure. 6. Conductors and insulators. The carbon plate of the battery forms a portion of the electrical circuit in Figs, i, 3 and 4, and the solution of copper sulphate forms a portion of the electrical circuit in Fig. 4. Any substance which can form a portion of an electrical circuit, that is, any substance through which the "electric current " can "flow" readily, is called an electri- cal conductor. Thus metals, carbon, and salt solutions are electrical conductors. Many substances, such as glass, rubber, dry wood and air, cannot* form a portion of an electrical circuit at ordinary temperatures, that is to say, the electric current cannot flow through such substances to any appreciable extent. Such substances are called insulators. An ordinary telegraph or telephone wire is insulated by being supported by glass or porcelain knobs which are called "insula- tors." The electric current cannot escape from the wire but it must flow along the wire to a distant city and back through another wire or through the ground. If one were to wind an electromagnet with bare wire the electric current would not follow the wire round and round the iron rod, and the iron rod would not be magnetized. Therefore the wire which is wound on an electromagnet is insulated 1^ a covering of silk or cotton or enamel. 7. The magnetic compass. The compass is a magnetized needle of hardened steel mounted on a pivot and playing over a horizontal divided circle. The direction in which the compass needle points at different places on the earth is shown in Fig. 7. * This statement is not strictly true; what is called an insulator is merely an extremely poor conductor. ELECTRICITY AND MAGNETISM. Everywhere on the heavy lines which are marked with a zero in Fig. 7, the compass needle points due north and south. In the extreme eastern portions of the United States, in western Europe, and over the whole of the North Atlantic Ocean the compass needle points to the west of north. Thus everywhere along the lines marked lo the compass needle points lo degrees west of north, everywhere along the lines marked 20 the compass needle points 20 degrees west of north, and so on. Throughout the western portions of the United States and over the greater portion of the North Pacific Ocean the compass needle points to the east of north. Fig. 7. Lines of equal magnetic declination. The deviation of the compass needle to the east or west of north is called the declination of the needle. The points of the compass as indicated by the magnetic needle are sometimes called magnetic north, magnetic east, magnetic south and magnetic west to distinguish them from the true or geographical points of the compass. The direction in which the compass needle points at a given place on the earth fluctuates during each day, and the average changes from year to year. Fig- ure 7 represents. ^he average declination for the year 1905. 8. Poles of a magnet. The familiar property of a magnet, namely, its attraction for iron, is possessed only by certain parts of the magnet. These parts of a magnet are calles the poles of the magnet. For example, the poles of a straight bar-magnet are usually at the ends of the bar. Thus Fig. 8 shows the appearance of a bar-magnet which has been dipped into iron filings. The filings cling chiefly to the ends of the magnet. When a bar-magnet is suspended in a horizontal position by a EFFECTS OF THE ELECTRIC CURRENT. fine thread, it places itself approximately north and south like a compass needle. The north pointing end of the magnet is called its north pole, and the south pointing end of the magnet is called its south pole. Fig. 8. The north poles of two magnets repel each other, the south poles of two magnets repel each other, and the north pole of one magnets attracts the south pole of another magnet; that is to say, like magnetic poles repel each other, and unlike magnetic poles attract each other. The north magnetic pole of the earth has the same polarity as the south pointing pole of a compass needle. 9. Magnetic figures. The magnetic field. When iron filings are dusted over a pane of glass which is placed over a magnet, the filings arrange themselves in regular filaments if the glass is jarred slightly. Figures 9 and 10 are photographic reproductions of magnetic figures obtained in this way; Fig. 9 shows the fila- ments of filings in the neighborhood of a single magnet; and Fig. Fig. 9. 8 ELECTRICITY AND MAGNETISM. 10 shows the filaments of iron filings between the unlike poles of two large magnets. Fig. 10. The magnetic figure shown in Fig. 9 conveys the idea that something "flows out of" one end of the magnet, traverses the surrounding region in smoothly-curved lines and "flows into" the other end of the magnet. In fact the entire region surround- Fig. 11. ing a magnet is in a peculiar physical condition as shown by the behavior of the iron filings, and the thing which "flows out EFFECTS OF THE ELECTRIC CURRENT. 9 of" one pole of the magnet and "flows into" the other pole is called magnetic flux. The region surrounding a magnet is called a magnetic field, and the filaments of iron filings in Figs. 9 and 10 show the trend of what are called the lines of force of the magnetic field. It is customary to think of the magnetic flux as "flowing out of" the north pole of a magnet and "flowing into" the south pole of a magnet as indicated by the arrows in Fig. 11. These arrows show what is called the direction of the magnetic field at each point. 10. Oersted's experiment. The magnetic effect of the electric current was discovered by the Danish physicist Oersted in 1819. Holding an electric wire above a compass needle as shown in Fig. 12, he found that the needle was deflected as indicated in the figure. A compass needle tends to set itself at right angles to a nearby electric wire. 11. The needle galvanometer. The galvanometer, or more correctly the galvanoscope, is an instrument for detecting the presence of an electric current in a circuit. Thus the movement carbon ati^ zinc terminal iBire dry battery S-pole pivot — ^ K N-pole magnetic needle Fig. 12. The north pointing pole of the needle is pushed towards the reader. of the compass needle in Fig. 12 shows the presence of an electric current in the wire, and therefore the arrangement shown in Fig. 12 might be called a galvanoscope. By placing a compass needle 10 ELECTRICITY AND MAGNETISM. coil of wire inside of a winding of wire (a coil) as shown in Fig. 13, a very weak current in the coil may produce a visible movement of the needle. Such an arrangement is called a needle galvanoscope or needle galvan- ometer. The magnetic needle of this galvanometer usually consists of a very short and light magnet suspended by a silk fibre, and the movement of the needle is usually indicated by a spot of light re- flected from a mirror which is at tached to the suspended magnet. 12. Direction of current. It is very convenient to think of an electric current as flowing in a definite direction along a wire, and it has been agreed to think of a current as flowing OUT of the carbon terminal of a battery, through the circuit and INTO the zinc terminal of the battery. Hi Fig. 13. north end of needle top view Fig. 14o. Fig. 146. In the discussion of Fig. 4 it was stated that copper was deposited upon the metal strip T which is connected to the carbon terminal of the battery. Therefore, according to the above EFFECTS OF THE ELECTRIC CURRENT. II agreement, we are to think of the copper as being carried through the solution in the direction of flow of the current. The direction of flow of a current through a wire (according to the above agreement) can be inferred from the direction of deflection of a compass needle, if we keep in mind the facts which are represented in Figs. 14a and 14b. The north pole of the compass needle starts to go around the wire in the direction indicated by the short arrow a in Fig. 14a, and the current in the wire flows in the direction, t, in which a nut would travel on a right-handed screw if the nut were turned in the direction in which the north pole of the compass needle starts to go around the wire as shown by the arrow a in Fig. 14b. When an iron rod is magnetized by the flow of current round it, the north pole of the rod is at the end towards which a nut would travel (on a right-handed screw) if the nut were turned in the direction in which the current flows round the rod as shown in Fig. 15. direction of flow of current S.pole I I — - ~Z-]r-^g^^:^=J N-pote Fig. IS. When it is desired to show an end-view of a wire through which current is flowing, the section of the wire is represented by a small circle, current jBowing towards the reader is represented by a dot in the circle, as if one were looking endwise at the point of an arrow ; and current flowing away from the reader is repre- sented by a cross in the circle, as if one were looking at the feathered end of an arrow, as shown in Fig. 16. © © Fig. 16. Current flowing away from reader. Current flowing towards reader. 13. Another aspect of the magnetic effect of the electric current. Side push of a magnetic field on an electric wire. 12 ELECTRICITY AND MAGNETISM. One aspect of the magnetic effect of the electric current is described in Art. i. Another aspect of this effect is shown in Fig. 17. A wire AB through which an electric current flows is stretched across the end of a magnet; the wire is pushed side- wise by the magnet (away from the reader in Fig. 17).* If the Fig. 17. The wire AB is puslied away from the reader. current is reversed or if the magnet is turned end for end the side push on the wire is reversed. Fig. 18. The wire AB is pushed away from the reader. The side force on the wire in Fig. 17 is exerted by the magnet, and this force is no doubt transmitted by something which connects the magnet and the wire together, namely, the magnetic * Let it be clearly understood that the wire in Fig. 1 7 is neither attracted nor repelled by the magnet. EFFECTS OF THE ELECTRIC CURRENT. 13 Unes of force which emanate from the magnet. These magnetic lines of force are indicated by the dotted lines in Fig. 17. Figure 18 shows a straight wire AB placed in a narrow air • gap between two opposite magnet poles. The fine lines across the gap represent the magnetic lines of force in the air gap, and these lines of force push the wire sidewise (away from the reader in Fig. 18). When an electric wire is placed in a magnetic field at right angles to the lines of force of the field, a force is exerted on the wire (a side push on the wire) at right angles to the lines of force and at right angles to the wire. 14. The magnetic field surrounding a straight electric wire. Figure 19 is a photograph of the filaments of iron filings on a horizontal glass plate, the black circle is a hole through the plate, and a straight electric wire passes vertically through this hole. The lines of force of the magnetic field which is produced by an electric wire encircle the wire, as shown by the filaments of iron filings in Fig. 19. 15. Explanation of the side push exerted upon an electric wire by a magnetic field. Figure 10 represents the magnetic lines of force between two opposite magnetic poles, and the attraction of 14 ELECTRICITY AND MAGNETISM. the two opposite poles for each other may be thought of as due to a state of tension in the lines of force. That is, the lines of force may be thought of as stretched rubber-like filaments leading from pole to pole in Fig. lo, and the attraction of the two opposite poles may be thought of as the tendency of these stretched fila- ments to shorten. Figure 20 shows how the magnetic field between the two oppo- site poles in Fig. 10 is modified by the presence of an electric wire. The glass plate upon which the filings were dusted in Fig. Fig. 20. 20 was horizontal, and the black circle represents a hole in the plate through which the vertical electric wire was placed. The lines of force from pole to pole pass mostly to one side of the wire in Fig. 20, and the wire is pushed sidewise by the tension of the lines for force (tendency of the lines of force to shorten). 16. The moving coil galvanometer and the ammeter. The side push of a magnetic field upon an electric wire, as shown in Figs. 17 and 18 and as explained in Art. 15, is made use of in the moving coil galvanometer and in the direct-current type of ammeter. Thus Fig. 21 shows the essential features of the moving coil galvanometer, usually called the D'Arsonval galvanometer from EFFECTS OF THE ELECTRIC CURRENT. 15 W -mirror ■ coil steel magnet its inventor. It consists of an elongated coil of fine insulated wire suspended between the poles NN and 55 of a strong magnet. The sus- pending wires W and W lead current into and out of the coil, the side push of the magnetic field upon the vertical portions, or limbs, of the coil turns the coil, and the motion of the coil is indicated by a spot of light which is thrown upon a fixed scale by the mir- ror. The most extensively used type of direct-current ammeter is essentially like the D'Arsonval galvanometer, ex- cept that the moving coil is supported by pivots, and the movement of the coil is indicated by a pointer which plays over a divided scale. The es- sential features of a direct-current am- meter are shown in Figs. 22 and 23. The vertical portions or limbs of the movable coil play in a narrow gap space between a fixed cylinder of soft iron and s f 1 N _-' '-- s N "- > w ^ ~-^-_ ~Z1. ~-^ _ \ L _y - / Fig. 21. Fig. 22. the soft iron pole-pieces N N and 55. Current is led into and out of the moving coil by means of two hair-springs, one at each end of the pivot-axis, and the side push of the magnetic field on the limbs of the coil in the gap spaces turns the coil and moves the pointer over the scale. 17. The magnetic blow-out. The side push of the magnetic field i6 ELECTRICITY AND MAGNETISM. upon the carrier of an electric current as shown in Figs. 17 and 18 and as explained in Art. 15, is made use of in the magnetic blow-out as follows : Fig. 23. When an electric switch is opened the current continues for a short time to flow across the opening, forming what is called an electric arc, as shown in Fig. 24. This arc melts the contact switch blade are switch socket Fig. 24. h magnet -switch blade -arc -switch socket Fig. 25. The arc is pushed towards or away from the reader. parts of the switch, and the switch is soon spoiled. This difficulty may be obviated to some extent by always opening the switch EFFECTS OF THE ELECTRIC CURRENT. 17 quickly and unhesitatingly, but where the switch is to be opened and closed hundreds of times per day, as in the control of a street car motor, it is necessary to blow out the arc so as to avoid the rapid wear of the switch contacts by fusion. This blowing out of the arc is accomplished by a magnet placed as shown in Fig. 25. This magnet pushes sidewise on the arc (towards or away from the reader in Fig. 25), and this sidewise push on the arc lengthens it very quickly and breaks the circuit. 18. The electric motor (direct-current type). The side push of a magnetic field upon an electric wire as shown in Figs. 17 and 18 and as explained in Art. 15 is made use of in the electric motor as follows: Fig. 26. Figure 26 shows an iron cylinder A A placed between the poles N and 5 of a powerful electromagnet. The air space between each magnet pole and the cylinder is called a gap space; and each gap space is an intense magnetic field, as indicated by the fine lines (lines of force). Figure 27 shows the cylinder with straight wires laid upon its surface, and the dots and crosses represent electric currents flowing towards the reader and away from the reader, respectively, as explained in Fig. 16. Under these conditions the magnetic field in the gap spaces (see fine 1 8 ELECTRICITY AND MAGNETISM. lines of force in Fig. 26) pushes sidewise on the wires, and turns the cylinder in the direction of the curved arrows in Fig. 27. Fig. 27. The arrangement in Fig. 27 is called an electric motor. The electromagnet NS is called the ^eW wagwei, and the magnetizing coils MM are called the field coils or field windings. The rotating cylinder A A with its winding of wire is called the armature. The arrangement of the wires on the armature and the method of leading current into and out of them so that the current may flow as indicated by the dots and crosses in Fig. 27 can be most Fig. 28. easily understood by considering the simplest type of armature winding, namely, the so-called ring-winding, the essential features of which are shown in Fig. 28. An iron ring AA is wound EFFECTS OF THE ELECTRIC CURRENT. 19 uniformly with insulated wire as shown, the ends of the wire being spliced together and soldered so as to make the winding endless. Imagine the insulation to be removed from the out- ward faces of the wire windings on the ring so that two stationary metal or carbon blocks (brushes) a and b can make good electrical contact with the wires as the ring rotates. Then if current is led into the windings through brush a and out through brush b, the current will flow towards the reader in the wires which lie under the south pole S, and away from the reader in the wires which lie under the north pole N, as shown by the dots and crosses in Fig. 27.* In practice, short lengths of wire are attached to the various turns of wire on the ring and led to copper bars near the axis of Fig. 29. rotation, as shown in Fig. 29. These copper bars are insulated from each other, and sliding contact is made with these copper bars as indicated in Fig. 29, instead of being made as indicated in Fig. 28. The set of insulated copper bars is called the commutator. *Let the reader carefully trace the flow of current in Fig. 28. The current which enters at brush a divides, and half of the current flows through the windings on each side of the armature. 20 ELECTRICITY AND MAGNETISM. The iron body of the armature (the iron ring in Figs. 28 and 29) is called the armature core. This core is built up of ring- shaped stampings of soft sheet steel which are supported by the spider. slots side view end view Fig. 30. arms of a spider as shown in Fig. 30. The entire surface of the armature core is slotted (slots being parallel to the armature shaft as shown in the side view in Fig. 30), and the armature wires are laid in these slots. A few, only, of the slots are shown in the end view in Fig. 30. Figure 31 shows a side view of the completed armature. The machine which is here described as the direct-current motor is properly called the direct-current dynamo. It is a motor when it receives electric current from some outside source and is used to drive a pump, or a lathe, or a trolley car. Exactly pulley commutator ^^^^^^^ armature Fig. 31- the same machine, when driven by a steam engine or water wheel, can be used as an electric generator to supply current for driving motors or for operating electric lamps. When so used the machine is called a dynamo electric generator or simply a generator. EFFECTS OF THE ELECTRIC CURRENT. 21 Bipolar dynamos and multipolar dynamos. Figure 28 shows current led into a ring winding at one point (at the brush a) Fig. 32. Arrangement of ring armature for a 4-pole field magnet. Fig. 33. Arrangement of a 4-poIe motor. and out at another point (at the brush b) . In this case current flows towards the reader in all of the wires on one side of the armature, and away from the reader in all of the wires on the 22 ELECTRICITY AND MAGNETISM. Other side of the armature, as indicated by the dots and crosses in Fig. 27. Under these conditions the field magnet should have two poles, a north pole and a south pole, as shown in Figs. 26 to 29. Figure 32 shows current led into a ring winding at two points (at brushes a and a) , and out at two points (at brushes b and b). In this case current flows towards the reader in all of the wires on the portions PP of the armature, and away from the Fig. 34. reader in all of the wires on the portions QQ of the armature. Under these conditions the field magnet should have four poles, two north poles and two south poles, as shown in Fig. 33. Figure 33 shows a direct-current dynamo with a four-pole field magnet with its magnetizing coils MMMM; and Fig. 34 is a general view of a six-pole direct-current dynamo. The ring armature and the drum armature. The wire on a ring armature passes from one end of the armature to the other on the outside of the ring and returns through the inside of the ring. In the drum armature, however, the wire crosses over to the opposite* side of the armature and returns on the outside. * This is for a drum armature which is to be used with a two-pole field magnet. EFFECTS OF THE ELECTRIC CURRENT. 23 \brush\ Yiff itt\ The relation between the ring and drum windings may be understood with the help of Fig. 35. Each wire u. on the interior of the ring may be thought of as shifted over to the opposite side of the ring at b, as shown. In this case it is evident that the conductor at 6 must not make contact with the lower brush because if it did the cross wires c and d would be short-circuiting connections from brush to brush. Every wire on the outside of a ring armature may be a commutator bar, or may be connected to a commuttor bar; whereas every second con- ductor on a drum armature may be a commuta- tor bar, or may be connected to a commutator bar. The ring armature is seldom used in modern Fig. 35. practice. Showing relation between ring and drum armature windings. PROBLEMS. I. The accompanying diagram Fig. pi shows a lamp L with connections arranged so that the lamp can be turned on or off at switch A (or B) regardless of how switch B (or .4) stands. Make four diagrams like Fig. pi showing the four possible combinations of switch-positions, and indicate the flow of current, if any, by arrows. supply mains ^.=-0- Fig. pi. 2. The six small circles in Fig. p2 represent the contact posts on a double-pole double-throw switch, and the dotted lines represent the switch blades. The diagram shows the lamp L taking current from the direct-current mains. Make a diagram showing the lamp taking current from the alternating current mains. 24 ELECTRICITY AND MAGNETISM. 3. The six small circles in Fig. ^3 represent the contact posts on a double-pole double-throw switch with crossed connections adapting it for use as a reversing switch, and the dotted lines represent the switch blades. Make a diagram showing a re- versed flow of current through the receiving circuit R. AC supply mains 1- 3- — O DC supply mains Fig. p2. Fig. p3. M^B(_m\< M-ff AO- ^^^mi AO- .6 B b B 4. Figure p/\. shows the diagram of connections of an ordinary telegraph relay, a "local" circuit connected to the binding posts BB is opened and closed as the lever L of the relay is moved back and forth by pulses of current coming over the telegraph line which is connected through the binding posts A A to ground; M is a screw with a metal tip, and H IS a screw with a hard- rubber insulating tip. Make a dia- gram showing M and H inter- changed, and showing AA and BB connected to each other and to a battery so that the relay will buzz like an ordinary interrupter bell. 5. In what direction did the compass needle point in igos at a place 30° west of Greenwich and 40° north latitude? At a place 150° west of Greenwich and 70° north latitude? 6. Figure p6 shows a magnet NS placed near a long straight electric wire. The wire exerts forces on the magnet poles N and 5 as indicated by the arrows F' and F". Draw a diagram showing the total, or resultant, force exerted on the magnet by the wire. Fig. pi. EFFECTS OF THE ELECTRIC CURRENT. 25 Note. A north pole near a long straight electric wire is acted on by a force (see arrow F' in Fig. ^6) which is in a plane at right angles to the wire (the plane of the paper in Fig. p6), the force is at right angles to a line drawn from the wire to the pole (the line r in Fig. ^6), and the direction of the force is such that the pole tends to travel around the wire in the direction in which a right-handed screw would have to be turned to make it travel in the direction of flow of current through the wire. The force exerted on a south pole is opposite in direction to the force which would be exerted on a north pole at the same place. The magnitude of the force exerted on a magnet pole by a long straight electric wire is inversely proportional to the distance of the pole from the wire. Q wire Fig. p6. Qwire N US Fig. ^8. 7. The current in Fig. p6 is reversed so as to flow towards the reader. Make a diagram showing the forces exerted on the poles N and 5 by the wire, and make a diagram showing the total, or resultant, force exerted on the magnet. 8. The small circle with a dot in Fig. p8 represents a straight wire at right angles to the paper with current flowing towards the reader. Draw arrows showing the forces exerted by the electric wire on the poles N and S of the magnet. 0ioire Fig. p9a. B Fig. p9b. Fig. p9c. g. Specify the direction of the side push exerted on the wire by the magnet pole in Fig. pga. Note. The force exerted on a wire by a magnetic field is at right angles to the wire and at right angles to the lines of force of the field, as stated in Art. 13. The direction of a magnetic field at a point (the direction of the lines of force at the 26 ELECTRICITY AND MAGNETISM. point) is the direction in which a compass needle would point if placed at that point, the north -pole of the needle being thought of as the pointing end of the needle. Now a magnetic needle put in place of the wire in Fig. p9a would point towards .S, as shown by the short arrows ff in Fig. p9b. Therefore, according to Art. 13, the wire will be pushed towards A or towards B; to determine which, the following considerations are sufficient: The lines of force of the magnetic field due to the current in the wire encircle the wire as explained in Art. 14 and as indi- cated by the curled arrows c in Fig. p9b, and the heads of the curled arrows are in the direction in which a right-handed screw would have to be turned to travel in the direction of flow of the current in the wire. Now the lines of force ff bend to one side of the wire so as to go with the curled arrows c, as shown in Fig. p9c\ and the tension of these bent lines of force pushes sidewise on the wire in the direction of the arrow F as explained in Art. 15. )wire Fig. plO. 10. Specify the direction of tlie side push exerted on the wire by the magnet pole in Fig. ^lo. CHAPTER II CHEMICAL EFFECT OF THE ELECTRIC CURRENT. 19. The chemical effect of the electric current again con- sidered. A very beautiful experiment showing the deposition of a metal -by the electric current is as follows: Two strips of lead are connected to seven or eight dry cells ( in series) and dipped into a solution of lead nitrate,* as shown in Fig. 36. The flow of current decomposes the lead nitrate and deposits beautiful feather-like crystals of metallic lead on the lead strip which is connected to the zinc terminal of the battery. cathode-- -i ■wire —\^.zme\ terminal -=- battery .J^'^carhon fermihal I -anode — lead nitrate solution Fig. 36. This decomposition of a solution by an electric current is called electrolysis, and the solution which is decomposed is called an electrolyte. Electrolysis is usually carried out in a vessel provided with two plates of metal or carbon as shown in Fig. 4. Such an arrangement is called an electrolytic cell, and the plates of metal or carbon are called the electrodes. Thus Fig. 37 repre- * Ordinary sugar of lead (lead acetate), which can be obtained at any drug store may be used instead of lead nitrate. 27 28 ELECTRICITY AND MAGNETISM. sents an electrolytic cell connected to direct-current supply mains. The electrode A at which the current enters the solu- tion is called the anode, and the electrode C at which the current leaves the solution is called the cathode. The chemical action which is pro- duced by the electric current in the electrolytic cell of Fig. 36 is as fol- lows: The lead nitrate (PbNOs) is separated into two parts, namely, Pb (lead) and NO3 (nitric acid radical). The lead (Pb) is deposited on the cathode, and the nitric acid radical (NO3) is set free at the anode where it combines with the lead of the an- ode, forming a fresh supply of lead nitrate which is immediately dis- solved in the electrolyte. That is to say, lead is deposited on the cath- ode and dissolved off the anode. The dissolving of lead off the anode may be made visible as follows: Allow the current to flow for a few minutes until a deposit of lead crystals is obtained on one electrode, then reverse the battery connections, and the previ- ously deposited lead crystals are quickly re-dissolved, a new deposit of lead crystals being formed on the other electrode. The chemical action produced by the electric current in an electrolytic cell takes place only in the immediate neighborhood of the electrodes. Fig. 37. 20. The measurement of current. Legal definition of the ampere. To measure a thing means fundamentally to divide it into equal unit parts and to count these parts. Thus, oil or wine is counted out by means of a gallon measure, and cloth is counted out by means of a yard stick. Many quantities, how- ever, cannot be divided into equal unit parts, and therefore such CHEMICAL EFFECT OF THE ELECTRIC CURRENT. 29 quantities must be measured indirectly. Thus, one of the effects of the rise of temperature is increase of volume, and the apparent increase of volume of mercury in a glass tube is used as a measure of increase of temperature. One of the effects of the electric current is the deposition of copper, as explained in Art. 3, and the amount of copper deposited per second by an electric current may be taken as a measure of the strength of the current. That is, we may consider one current to be twice as strong as another when it will deposit twice as much copper in a given time on the cathode in Fig. 4. Another effect of the electric current is the side force exerted on an electric wire by a magnet as shown in Figs. 17 and 18, and the value of this side force may be taken as a measure of the strength of the current in the wire. Indeed this magnetic effect is the accepted basis for the measurement of current, as fully explained in Part II of this treatise; and the' practical unit of current, as defined in the magnetic system, is the ampere. Very careful measurements have shown that one ampere will deposit about 0.000328 gram of copper per second from a solution of copper sulphate in water, or about 0.001118 gram of silver per second from a solution of pure silver nitrate in water. The international standard ampere. It is very difficult to measure a current accurately in terms of its magnetic effect so as to get the value of the current directly in amperes ; therefore, in accordance with the recommendation of the International Electrical Congress which met in Chicago in 1893, the ampere has been legally defined as the current which will deposit exactly 0.001118 gram of silver per second from a solution of pure silver nitrate in water. 21. Test of an ammeter by means of the copper coulombmeter. An electrolytic cell arranged for measuring an electric current by its chemical effect is called a coulombmeter. Thus, the copper coulombmeter consists of a heavy copper plate and a thin copper plate dipping into a solution of copper sulphate. The current 30 ELECTRICITY AND MAGNETISM. to be measured is passed through the coulombmeter so as to deposit copper on the thin electrode; this electrode is therefore called the gain plate. The amount of copper deposited in a given time is determined by weighing the gain plate before and after. Example. An ammeter to be tested was connected in circuit with a battery, a rheostat,* and a copper coulombmeter as shown in Fig. 38. The gain plate weighed 25.42 grams at the start. The circuit was closed at a certain instant, and after i hour and -WAAAA/ rheostat gain plate — battery -anode —jj..^ copper sufyhate solution Fig. 38. 20 minutes the circuit was opened. The gain plate was then washed and dried and found to weigh 29.66 grams. The average reading of the ammeter during the i hour and 20 minutes was observed to be 2.75 "amperes." To find the true value of the current corresponding to this ammeter reading the following calculation was made: The in- crease of weight of the gain plate was 4.24 grams, or, in other words, 4.24 grams of copper were deposited in 4800 seconds, which is at the rate of 0.0008833 gram per second; and the true *See Art. 40. CHEMICAL EFFECT OF THE ELECTRIC CURRENT. 31 cathode'— — anode —dilute sulphuric acid value of current flowing during the test was found by dividing 0.000883 by 0.000328, which gave 2.69 amperes. 22. Another aspect of the chemical effect of the electric current. The voltaic cell or electric battery. When electric current flows through an electrolytic cell chemical action is produced. For example, Fig. 39 shows a battery forcing current through dilute sulphuric acid, the electrodes being plates of carbon or lead or platinum. The sulphuric acid (H2SO4) is decomposed by the current, being sep- arated into H2 (hydrogen) and SO4 (sulphuric acid radical). The hydrogen appears at the cathode as bubbles of gas and escapes from the cell. The acid radical (SO4) appears at the anode where it breaks up into SO3 and O (oxygen). The oxygen appears in the form of bubbles and escapes from the cell, and the SO3 combines with the water (H2O) in the cell, forming H2SO4. The net result of the chemical action in the cell is therefore to decompose water (H2O) inasmuch as hydrogen gas and oxygen gas are given off by the cell. Now by burning the hydrogen and oxygen heat energy can be ob- tained, and therefore it is evident that work must be done {by the battery in Fig. jg) to decompose the H2O in the elec- trolytic cell. Usually the chemical action which is produced by the current in an electrolytic cell requires the doing of work as above ex- plained, that is to say, an electric generator (battery or dynamo) must be used to force the electric current through the electrolytic cell. In some cases, however, the chemical action which is produced by the flow of current through the electrolytic cell is a Fig. 39. 32 ELECTRICITY AND MAGNETISM. wire source of energy. In such a case it is not necessary to use a separate electric generator (battery or dynamo) to force electric current through the electrolytic cell, for such an electrolytic cell can maintain its own current through the electrolyte from elec- trode to electrode and through an outside circuit of wire which connects the electrodes. Such an electrolytic cell is called a voltaic cell or an electric battery. That is to say, a voltaic cell is an electroljrtic cell in which the chemical action produced by the the flow of current is a source of energy. 23. The simple voltaic cell. The simplest example of an electrolytic cell in which the chemical action produced by the current is a source of energy, is the so-called simple voltaic cell which is shown in Fig. 40. It consists of a carbon or copper electrode C and a clean zinc electrode Z in dilute sulphuric acid. The flow of current through this cell breaks up the H:S04 into two parts, namely, H2 (hydrogen) and SO4 (sulphuric acid radical). The hydrogen appears at the carbon electrode and escapes as a gas, and the SO4 appears at the zinc electrode where it combines with the zinc to form zinc sulphate (ZnS04). The combination of the zinc and the SO4 supplies more en- ergy than is required to separate the H2 and SO4. Therefore the chemical action which is produced by the flow of current through the cell is a source of energy, and the cell itself main- tains a flow of current. 24. Primary and secondary chemical reactions in the electro- Ijrtic cell. The decomposition of the electrolyte is the direct or immediate effect of the flow of current, therefore, the decomposi- tion of the electrolyte may be spoken of as the primary chemical action in an electrolytic cell. When the decomposed parts of the electrolyte appear at the Fig. 40. CHEMICAL EFFECT OF THE ELECTRIC CURRENT. 33 electrodes, chemical action usually takes place between these parts and the electrodes or between these parts and the water in the solution, and these chemical actions are called the secondary chemical reactions in the electrolytic cell. For example, the primary chemical reaction in the simple voltaic cell which is shown in Fig. 40 is the decomposition of the sulphuric acid into hydrogen (H2) and sulphuric acid radical (SO4); and the com- bination of the acid radical (SO4) with the zinc of the electrode is a secondary reaction. The primary chemical action in an electrolytic cell usually represents the doing of work on the cell, and the secondary chemical reactions in an electrolytic cell usually represent the doing of work by the cell ; therefore secondary reactions are very important in the voltaic cell or electric battery. 23. The use of oxidizing agents in the voltaic cell. The com- bination of the SO4 with the zinc of the anode is the secondary chemical action in the simple voltaic cell which is shown in Fig. 40. The available energy of the total chemical action which takes place in this cell may be greatly increased, however, by providing an oxidizing agent in the neighborhood of the carbon electrode so that the hydrogen may be oxidized and form water (H2O) at the moment of its liberation by the current. The energy of this oxidation increases the available energy of the chemical action as a whole, and greatly strengthens the cell as a generator of electric current. 26. Voltaic action and local action. Two distinct kinds* of chemical action take place in a voltaic cell, namely, (a) the chemical action which depends upon the flow of current and which does not exist when there is no flow of current, and (b) the chemical action which is independent of the flow of current and which takes place whether the current is flowing or not. The chemical action which depends on the flow of current is * The distinction between primary and secondary reactions has nothing to do with the distinction between voltaic action and local action, 34 ELECTRICITY AND MAGNETISM. proportional to the current, that is to say, this chemical action takes place twice as fast if the current which is delivered by the voltaic cell is doubled. This chemical action is essential to the operation of the voltaic cell as a generator of current, its energy is available for the maintenance of the current which is produced by the cell, and it is called voltaic action. The chemical action which is independent of the flow of current does not help in any way to maintain the current, it represents a waste of materials, and it is called local action. Local action takes place more or less in every type of voltaic cell. It may be greatly reduced in amount, however, by using pure zinc, and especially by coating the zinc with a thin layer of metallic mercury (amalgamation) . Example of local action. The zinc plate in the simple voltaic cell which is shown in Fig. 40 dissolves in the sulphuric acid even when no current is flowing through the cell, zinc sulphate and hydrogen are formed, and all of the energy of this reaction goes to heat the cell. If the zinc is very pure and if its surface is clean this chemical action takes place very slowly, but if the zinc is impure the action is usually very rapid. The hydrogen which is liberated during this local action appears at the zinc plate. Example of voltaic action. When the circuit in Fig. 40 is closed, hydrogen bubbles begin to come off the carbon electrode, and zinc sulphate is formed at the zinc electrode. This is voltaic action, and it ceases when the circuit is broken. The essential and important feature of voltaic action is that it is reversed if a current from an outside source is forced back- wards through the voltaic cell, provided no material which has played a part in the previous voltaic action has been allowed to escape from the cell. Thus in the simple voltaic cell, which is described in Art. 23, the sulphuric acid (HvSOi) is decomposed, zinc sulphate (ZnS04) is formed at the zinc electrode, and hydro- gen is liberated at the carbon electrode. If a reversed current is CHEMICAL EFFECT OF THE ELECTRIC CURRENT. 35 forced through this simple cell, the zinc sulphate previously formed will be decomposed, metallic zinc will l?e deposited upon the zinc plate, and the sulphuric acid radical (SO4) will be liber- ated at the carbon plate, where it will combine with the trace of hydrogen which is clinging to the carbon plate and form sulphuric acid (H2SO4). In this simple cell, however, the greater part of the liberated hydrogen has, of course, escaped, and the reversed chemical action due to a reversed current cannot long continue. Local action, being independent of the current, is not affected by a reversal of the current. 27. The chromic acid cell. The Grenet cell is similar to the simple voltaic cell, as shown in Fig. 40, except that the electrode C is of carbon and chromic acid is added to the electrolyte to fur- nish oxygen for the oxidation of the hydrogen as it is set free at the carbon electrode. There is, how- ever, a very rapid waste of zinc in this cell by local action even when the zinc is amalgamated, and the cell is now seldom used. A modi- fied form of the Grenet cell, known as the Fuller cell, is shown in Fig. 41. In this cell the electrolyte e is dilute sulphuric acid, the zinc anode Z is contained in a porous earthenware cup, and the chromic acid is dissolved only in that portion of the electrolyte which surrounds the carbon cathode C. In this cell there is not a rapid waste of zinc by local action, and the cell is extensively used. 28. Open-circuit cells and closed-circuit cells. A voltaic cell which can be left standing unused, but in readiness at any time for the delivery of current when its circuit is closed, is called an .open-circuit cell. A cell to be suitable for use as an open-circuit Fig. 41. The Fuller cell. 36 ELECTRICITY AND MAGNETISM. cell should above all things be nearly free from local action. The cell most extensively used for open-circuit service is the ordinary dry cell. A voltaic cell which is suitable for delivering a current steadily is called a closed-circuit cell The cell which is most extensively used for closed-circuit service is the gravity Daniell cell. 29. The ordinary dry cell. A sectional view of this cell is shown in Fig. 42. The containing vessel is a can made of sheet zinc. This can serves as one electrode of the cell, and a binding post is soldered to it. The zinc can is lined with several thicknesses of blotting paper P, and the space between the blotting paper and the carbon rod C is packed with bits of coke and manganese di- oxide. The porous contents of the cell are then saturated with a solution of ammonium chloride (sal ammoniac) , and the cell is sealed with asphaltum cement A. The zinc can is usually protected by a covering of paste board B. The dry cell has been humorously de- fined as a voltaic cell which, being hermetic- ally sealed, is always wet; whereas the old- style wet cell was open to the air and frequently became dry. Reputable manufacturers always stamp the date of manu- facture on their dry cells, and a purchaser should not accept a cell which is much more than one or two months old. The condition of a dry cell is most satisfactorily indicated by observing the current delivered when the cell is momentarily short circuited* through an ammeter. When the cell has been exhausted by use or when it has dried out by being kept too long, the short- circuit current is greatly reduced in value. An ordinary dry cell, when fresh, should give about 25 or 30 amperes on a momen- tary short circuit when the cell is at ordinary room temperature. * That is to say, the very low resistance ammeter is connected directly to the terminals of the cell. Fig. 42. The dry cell. CHEMICAL EFFECT OF THE ELECTRIC CURRENT. 37 30. The gravity Daniell cell. This cell consists of a copper cathode at the bottom of a glass jar and a zinc anode at the top as shown in Fig. 43. The electrolyte is mainly a solution of zinc sulphate. Crys- tals of copper sulphate are dropped to the bottom of the cell and a dense solu- tion of copper sulphate surrounds the copper cathode. This cell has a considerable amount of local action when it is allowed to stand unused, because of the upward diffusion of the copper sulphate. The cell is very extensively used in telegraphy and for op- erating the "track circuit" relays in automatic railway signalling. 31. The copper-oxide cell. The cathode of this cell is a com- pressed block of copper oxide (CuO) , the anode is a plate of zinc, and the electrolyte is a solution of caustic potash (KOH).* A sectional view of the cell is shown in Fig. 44. The zinc anode consists of two zinc plates (connected together), and the anode "-oil -zme -copper oxide Fig. 43. The gravity cell. -. KOB solution Fig. 44. The copper-oxide cell. (The zinc plates are connected together and to binding post B ) of copper oxide is held between the zinc plates in a frame of me- tallic copper. The copper-oxide cell is sold under a variety of trade names and it is used extensively as a closed circuit cell. * Or a solution of caustic soda NaOH. 38 ELECTRICITY AND MAGNETISM. 32. The storage cell. A voltaic cell may be completely re- paired after use by forcing a current backwards through the cell, if there is no local action in the cell, and if all of the materials which take part in the voltaic action remain in the cell. A voltaic cell which meets these two conditions is called a storage cell. The process of repairing the cell by forcing a current through it backwards is called charging, and the use of the cell for the delivery of current is called discharging. 33. The lead storage cell. The voltaic cell which is most extensively used as a storage cell is one in which one electrode is lead peroxide (PbOi), the other electrode is spongy metallic lead (Pb) and the electrolyte is dilute sulphuric acid (H2SO4). This cell is called the lead storage cell. The lead peroxide and the spongy metallic lead are called the active materials of the cell. These active materials are porous and brittle, and they are usually supported in small grooves or pockets in heavy plates or grids of metallic lead. These lead grids serve not only as mechanical supports for the active materials, but they serve also to deliver current to or receive current from the active materials which constitute the real electrodes of the cell. -JT Fig. 46. Fig. 45. Fig. 47. As a lead storage cell is discharged, the active material on both electrodes is reduced to lead sulphate PbS04; and when the cell is charged, the lead sulphate on one grid is converted back into CHEMICAL EFFECT OF THE ELECTRIC CURRENT. 39 spongy metallic lead, and the lead sulphate on the other grid is converted back into lead peroxide. Figure 45 is a general view of a lead storage cell. One of the battery grids is shown in Fig. 46, and a sectional view of the grid is shown in Fig. 47. The grid consists of a thick lead plate with fine grooves cut into its surface, and the active material is packed into these grooves.* 34. Definition of electrochemical equivalent. Chemical cal- culations in electrolysis. The amount of silver deposited per second in the operation of silver plating is proportional to the strength of the current in amperes, and the amount of silver deposited in one second by one ampere is called the electro- chemical equivalent of silver; it is equal to 0.001118 gram per ampere per second, or 4.025 grams per ampere per hour. In the great majority of cases no material is actually deposited at either electrode in the electrolytic cell, but chemical action is always produced in the immediate neighborhood of the elec- trodes, and the amount of chemical action which takes place in a given time due to the flow of a given current through the cell can be calculated from very simple data. A statement of the method employed in this calculation involves a number of chemical terms, and these terms are exhibited in the following schedules. The valencies of various chemical elements, acid radicals and so forth are shown by the numbers in the following exhibit. Thus one atom of hydrogen combines with one atom of chlorine and each has a valency of i, whereas one atom of copper combines with two atoms of chlorine in the formation of cupric chloride * A further discussion of this subject of batteries is given in Franklin's Electric Lighting, The Macmillan Co., New York, 1912. The Edison nickel-iron storage cell is discussed on pages 205-209; a discussion of battery costs is given on pages 208-211; directions for the management and care of the lead storage battery are given on pages 211-214; and the uses of the storage battery are discussed on pages 214-255- The most extensive treatise on the lead storage battery is Lamar Lyndon's Storage Battery Engineering, McGraw-Hill Book Co., New York, 1911. 40 ELECTRICITY AND MAGNETISM. SO that the valency of cupric copper is 2. The valency of cuprous copper, however, is i . The valency of the sulphuric acid radical (SO4) is 2. No attempt is made here to give a general definition of valency but merely to recall to the student's mind the knowl- edge of valency which he has obtained from his study of chem- istry. Exhibit of Valencies. Name Hydrochloric acid Sodium chloride Cupric chloride Cuprous chloride Chemical symbol Valency H I CI I Na I CI I Cu 2 Ch 2X1 Cu I CI I Name Sulphuric acid Sodium sulphate Cupric sulphate Cuprous sulphate Chemical symbol Valency Hz 2X1 2 Nao 2X1 SO4 2 Cu 2 SO, 2 CU2 2X1 SO4 2 Let m be the atomic weight of an element, or the molecular weight of an atomic aggregate or group such as the acid radical SO4 or such as the base radical NH4 (which occurs in ammonium chloride, NH4CI), and let v be the valency of the element or aggregate. Then mfv grams of the element or aggregate is called a chemical equivalent thereof. The chemical equivalents of a few elements and aggregates are shown in the following exhibit. Exhibit of chemical equivalents in grams. Symbol of substance Atomic or molecular weight . . Valency Chemical equivalent in grams Na 23 I 23 Ag 108 I 108 CI 35 S I 35-S NO3 62 I 62 SO, 96 2 48 Cu* 63.6 2 31.8 Cut 63.6 I 63.6 Zn 65.4 2 32.7 Al 27 I 3 903 Note. Atomic weights are given only approximately in round numbers for the sake of simplicity. THE LAWS OF ELECTROLYSIS. I. The amount of chemical action which takes place in an electrolytic cell is proportional to the current and to the time that the current continues to flow, that is to say, the amount of chemical action is proportional to the product of the current * Cupric copper, that is copper as it exists in ordinary cupric sulphate, CuSOj t Cuprous copper. CHEMICAL EFFECT OF THE ELECTRIC CURRENT. 41 and the time. This product may be expressed in ampere-seconds or in ampere-hours. Thus ten amperes flowing for five hours constitutes what is called 50 ampere-hours. II. To deposit one electrochemical equivalent of silver, that is 108 grams of silver, requires 26.82 ampere-hours, and 26.82 ampere- hours will liberate one chemical equivalent of any element or radical at an electrode in an electrolytic cell. For example : 26.82 AMPERE-HOURS WILL LIBERATE at the anode at the cathode 62 grams of NOa from nitric acid or 23 grams of Na from a solution of any nitrate solution. NaOH, or from a solution of any sodium salt. 48 grams of SO4 from sulphuric acid 31.8 grams of Cu from a solution of or any sulphate solution. any cupric salt. 3S-S grams of CI from hydrochloric 63.6 grams of Cu from a solution of acid or any chloride solution. any cuprous salt. 17.01 grams of OH from a solution of 9.03 grams of Al from a solution of caustic soda or potash. any aluminum salt. etc. etc. EXAMPLES OF ELECTROCHEMICAL CALCULATIONS. Note. When one of the elements or radicals which take part in a chemical reaction is di-valent the electro-chemical calcula- tions are simplified by considering the amount of chemical action which is produced by two times 26.82 ampere-hours. When one of the elements or radicals is trivalent the calculations are sim- plified by considering the amount of chemical action which is pro- duced by three times 26.82 ampere-hours. Thus in the follow- ing examples di-valent elements and radicals are involved, and the chemical action produced by 53.64 ampere-hours is taken as the basis of the calculations; 53.64 ampere-hours liberates too chemical equivalents of material at each electrode. Example (a). Let it be required to find how much zinc, how much caustic soda, and how much copper oxide are used up in the copper-oxide cell by the delivery of 0.5 ampere for 300 hours, local action being ignored. The following schedule shows the 42 ELECTRICITY AND MAGNETISM. reactions at anode and at cathode. The character of these re- actions is determined by purely chemical studies, and the reactions are supposed to be known ; we are here concerned only with the question as to how much of each material corresponds to 34 grams of hydroxy! (OH) and to 46 grams of Na, and the schedule shows these amounts at a glance. That is to say, 79.6 grams of copper oxide is reduced to metallic copper at the cathode, 65.4 grams copper oxide cathode grams NaOB aolution zinc anode 80 63.6 18 79.6 46 53.64 34 65.4 grams 80 143.4 36 2NaOH+Cu=B»0+CuO+2Na^ 22:^ — M'20H+Zn+2NaOB=NaiZnOt+2BtO ampere-hours of zinc is dissolved off the anode, and 80 grams of NaOH (from the solution) combines with the dissolved zinc to form sodium zincate (NajZnO..) as a result of the flow of 53.64 ampere-hours through the cell. The NaOH which is decomposed by the cur- rent, namely, (46 -f- 34) grams, is made up for or compensated by the 80 grams of NaOH which is formed by the reaction at the cathode. Therefore 53.64 ampere-hours gives a total consump- tion of 79.6 grams of CuO, 65.4 grams of Zn, and 80 grams of NaOH ; and to get the consumption corresponding to 150 ampere- hours the above amounts must be multiplied by 150/53.64. Example (b). One result of the discharge of a lead storage cell is that H2SO4 from the solution combines with the active material of the electrodes thus reducing the strength of the solu- tion. Let it be required to find how much H£S04 is taken from the solution by 53.64 ampere-hours of discharge. The following CHEMICAL EFFECT OF THE ELECTRIC CURRENT. 43 schedule shows the reactions at both electrodes. From this schedule we see that (96 + 2) grams of H2SO-1 is taken from the solution by the electrolytic action, and that another 98 grams of f A Uad peroxide cathode grams A B-iSOt solution spongy lead anode 36 303 98 239 2 2Ha0+PbS0i=HsS0t+Pb0i+2H' < ) a -4 e Q~ ,8 0- IC Q 1 !0 I^ \o it >Q j£ ~ 2< >a desreea centigrade Fig. 52. sulphuric acid, each of which has a resistance of 100 ohms at 0° C. Then the values of the resistances of (a), (&), (c), {d), (e) and (/) at other temperatures, as determined by experiment, are shown by the ordinates of the curves in Fig. 52. As shown in this figure, iron and copper increase greatly in resistance with rise of temperature, and German silver increases only slightly in resistance with rise of temperature. But carbon and sulphuric acid decrease in resistance with rise of temperature, carbon to a very slight extent and dilute sulphuric acid to a very great extent. HEATING EFFECT OF THE ELECTRIC CURRENT. 55 For most practical purposes the curves in Fig. 52 may be thought of as straight Hues so that: Rt = i?o(i + iSO (i) where i?o is the resistance of a wire at 0° C, Rt is the resistance of the wire at t° C. and ;8 is a constant for the material of which the wire is made. This constant /3 is called the tempera- ture coefficient of resistance of the material. The values of j3 for various materials are given in the table in Art. 41. 43 . Power required to maintain a current in a circuit in which all of the energy reappears in the circuit in the form of heat in accord- ance with Joule's law. Work must of course be done in forcing an electric current through 'an electric motor, but all of the work so done does not reappear in the motor wires as heat, a large portion reappears at the motor pulley and is delivered as mechanical energy to the machine which is driven by the motor. Work also must be done in forcing an electric current back- wards through an exhausted storage battery (to charge the battery), but all of the work so done does not reappear as heat in the circuit, a large portion of the work is expended in bringing about the chemical action which takes place as the battery is charged. When a current is maintained in a simple circuit of wire, or in a circuit containing glow lamps, all of the work done in main- taining the current does reappear in the circuit as heat, and the rate at which work is done in maintaining the current is equal to the rate at which heat energy appears in the wire. Now heat energy is generated by a current of I amperes at the rate of RI^ joules per second in a circuit of which the resistance is R ohms. Therefore to maintain a current of I amperes in a circuit having a resistance of R ohms work must be done at the rate of RI^ joules per second. That is: P = RI^ (i) where P is the power in watts (or joules per second) required to 56 ELECTRICITY AND MAGNETISM. maintain a current of I amperes in a circuit of which the re- sistance is R ohms. Equation (i) is true only when all of the work expended in maintaining the current reappears in the cir- cuit as heat in accordance with Joule's law. Example. A certain electric glow lamp has a resistance when hot* of 192.2 ohms. To calculate the power required to maintain a current of 0.51 ampere through the lamp, we multiply 192.2 ohms by (0.51 ampere)^ which gives 50 watts. 44. Electricity or energy; which? When water is pumped through a pipe it is usually the-amount-of-water-delivered-in-a- given-time that is important. The amount of power represented by the stream of water is of no great importance. It is the water itself that is useful, and the power expended in driving the pump is merely enough to carry the water where it is needed. But one might conceivably use a pump to drive water through a circuit of pipe for the sake of the heating effect of the moving water in the pipe or to drive a water motor placed anywhere in the circuit of pipe. In such a case one would be interested primarily in the amount of power represented by the stream of water because the desired effect (heating or motor driving) would depend upon the amount of power. So it is in the case of the electric current. It is not "elec- tricity" (whatever that is) that one uses, it is work or energy; and the important thing about belt , . , . an electric generator (a bat- tery or dynamo) is the amount B Jdrwen q£ pQ^g,- represented by the electric current delivered by . the machine. This may be illustrated most pointedly as follows: A wheel A drives another wheel 5 by a belt, as shown in Fig. 53. A person knowing nothing at all about ma- * The resistance of a glow lamp changes greatly with the temperature of the filament. HEATING EFFECT OF THE ELECTRIC CURRENT. 57 chinery and especially a person having no available words to use in describing such an arrangement, might look at the continuous stream of leather given off by wheel A at the point p and decide to call wheel A a leather generator! Everyone knows, however, that a driving wheel does not generate leather; it gives off energy or work, and the work is transmitted to the driven wheel by the belt. It seems very ridiculous to speak of a belt- wheel as a generator of leather, and indeed it is equally absurd to, speak of a battery or dynamo as a generator of electricity. One must be careful not to take electrical terms and phrases too literally. To speak of a dynamo as an electric generator is, however, not seriously objectionable, but to speak of "electricity" as a motive power indicates a very serious misunderstanding. When it is proposed to drive a machine by a leather belt it is always under- stood that something must drive the belt, but when it is proposed to drive a machine by "electricity" it is not always understood that something must drive the "electricity." Electricity as applied in the arts is merely a go-between like a leather belt, and no one ever thinks of leather as a motive power ! Electricity! What is electricity? It is what we think of as flowing through a wire which is connected to a battery. It, is what we think of in devising words to describe the effects whiqh are represented in Figs, i, 3 and 4 of Chapter I! What is elec- tricity? It is the quintessence of the vocabulary of the telephone engineer, the wireless telegrapher and the dynamo tender. Electricity belongs to etymology, the Great Science of Words! Let us turn back to the dynamo and consider what it is and what it does ! * 45. Electromotive force. We think of an electric generator (battery or dynamo) as a kind of "pump" forcing a "current of electricity" through a circuit, the "flow" of electric current * The question " What is electricity? " becomes to some extent legitimate in the application of the atomic theory as explained in Appendix B. 58 ELECTRICITY AND MAGNETISM. being opposed by a kind of "resistance." The centrifugal pump, or fan blower, is more nearly like the electric generator (battery or dynamo) than the ordinary piston pump, and therefore the centrifugal pump is used as the basis of the following discussion. Figure 51 shows a battery forcing a current of electricity through a circuit of wire. The battery in Fig. 51 exerts a kind of propelling force which causes a current of electricity to flow round the circuit of wire in spite of an opposing re- sistance, the resistance of the wire. The propelling force of the battery in Fig. 51 is the "elec- trical pressure difference" (cxt pressed in volts, as we shall see) between the terminals of the battery. That is to say, the electric current enters the bat- tery at low electrical pressure, the action of the battery is to raise the pressure, and the cur- rent flows out of the carbon terminal of the battery at increased pressure. Throughout this treatise the "propelling force" or "electrical pressure-difference" developed by a battery or dynamo is called electromotive force or voltage. In order to get a better idea as to the electromotive force of a battery or dynamo let us consider the familiar gravity cell which is described in Art. 30. The chemical action in the cell develops Figure 50 shows a centrifugal pump forcing a current of air or water through a circuit of pipe. The pump in Fig. 50 exerts a propelling force on the air or water, thus causing the air or water to flow round the circuit of pipe in spite of the friction which opposes the flow. The propelling force of the pump in Fig. 50 is the pressure- difference (in pounds per square inch) between the inlet and the outlet of the pump. That is to say, the water or air enters the pump at low pressure, the ac- tion of the pump is to raise the pressure, and the water leaves the pump at increased pressure. HEATING EFFECT OF THE ELECTRIC CURRENT. 59 energy twice as fast if the value of the electric current which flows through the cell (and through the circuit to which the cell is connected) is doubled. This is true because the chemical action in the cell (the voltaic action) depends upon the current as explained in Art. 26, and this chemical action takes place twice as fast when the current through the cell is doubled. A definite amount of zinc is consumed (by voltaic action) when one ampere flows through the cell for one second. Let E be the energy in joules developed by the consumption of this amount of zinc. That is, E joules per second is the rate at which energy is developed by the chemical action produced by one ampere, and EI joules per second is the rate at which energy is developed hy the chemical action produced by I amperes. Let us assume that all of this energy is available for pushing the current through the circuit, then the power developed by the battery cell in pushing electric current through the circuit will be EI joules per second, or EI watts. That is : P = EI (i) in which P is the power in watts delivered by the gravity cell, / is the current in amperes flowing through the gravity cell and through the circuit to which the cell is connected, and £ is a factor which has a definite value for the given type of cell as above explained. This factor E is called the electromotive force of the cell. The electromotive force of any generator (battery or dynamo) is the factor by which the current I must be multiplied to give the power output P of the generator. Note. It may seem from equation (i) of Art. 43 (namely, P = KP) that the power P delivered to a circuit should be proportional to the square of the current. But to increase the current delivered by a given battery the resistance of the circuit must be decreased as explained in Art. 40. In fact, as we shall see, it is necessary to halve the resistance of the circuit in order to double the current. 6o ELECTRICITY AND MAGNETISM. 46. Ohm's law. The rate at which energy is delivered by a battery is EI watts, as explained above, and the rate at which heat is produced in the circuit is RP watts according to Art. 38. Therefore, if all the energy supplied by the battery is converted into heat in the circuit in accordance with Joule's law, then the power developed by the battery must be equal to the rate at which heat is generated in the circuit, that is, EI must be equal to RP, or, cancelling 7, we must have: E = RI (i) or, solving for 7, we have : /=! w According to equation (i) the electromotive force of a generator (battery or dynamo) is equal to the resistance of the circuit multiplied by the current. According to equation (2) the current delivered by a generator (battery or dynamo) is equal to the electromotive force of the generator divided by the resistance of the circuit. These two relations were discovered by G. S. Ohm in 1827, and they con- stitute what is known as Ohm's law. Ohm's law is true when all of the energy delivered by an electric generator is used to heat the circuit, that is when EI = RP. Ohm's law is not true when a portion of the energy delivered by the generator is used to drive a motor or to produce chemical action as in the charging of a storage battery. 47. Polarization of a battery. If the electromotive force of a battery were invariable, then the current delivered by the battery would be doubled by reducing che resistance of the entire circuit* to one half, according to Ohm's law. The current delivered by a battery is not doubled, however, when the resistance of the circuit (the entire circuit) is halved, because the electromotive force of a battery falls off more or less with continued flow of * Including the circuit of wire and the electrodes and electrolyte in the battery itself. HEATING EFFECT OF THE ELECTRIC CURRENT. 6l current, or when the flow of current is greatly increased. When a battery delivers current the chemical action quickly exhausts the electrolyte (the acid or salt solution) in the immediate neigh- borhood of the electrodes (carbon and zinc plates), the energy of the chemical action is reduced, and the battery is weakened. This weakening shows itself as a decrease of electromotive force, and it is called polarization. The gravity Daniell cell does not polarize to any considerable extent. The ordinary dry cell polarizes greatly. 48. Ohm's law and Joule's law are nearly always applied to a portion of an electric circuit, not to an entire electric circuit. Consider the electric lamp in Fig. 54. Let R be the resist- current I ance of the lamp in ohms, and "j^ ^ let / be the current flowing in -=" batten/ \E (/^latnp the circuit in amperes. Then "=~ £ I Fig. 54. KP is the rate in watts at which heat is generated in the lamp. RI {= E) is the electromotive force between the terminals of the lamp. EI ( = RP) is the rate at which energy is delivered to the lamp. These statements all refer to the lamp in Fig. 54, not to the entire circuit. To avoid confusion one should always speak of the current IN a circuit, of the resistance OF a circuit (or the resistance of a portion of the circuit), and of the electromotive force BETWEEN THE TERMINALS OF any portion of a circuit. Example of the application of Ohm's law. A lamp or a circuit of wire is to be connected to iio-volt mains, and the question arises as to how much current will flow through the circuit. On the assumption that the voltage between the mains does not change, the current in the circuit can be found by dividing the voltage by the resistance of the circuit. Thus an ordinary 16- 62 ELECTRICITY AND MAGNETISM. candle-power carbon-filament glow lamp has a resistance of about 220 ohms when it is hot, therefore if it is connected between iio-volt mains, a current of 0.5 ampere will flow through it. When an excessive current is taken from supply mains the voltage falls off greatly, and the supply wires become very hot. The limit of current which it is allowable to take from a given set of supply mains is generally determined by the heating of the mains as explained in Art. 35. 49. Definition of the volt. Consider any portion of an electric circuit, for example consider the lamp in Fig. 54, and let / be the current flowing in the circuit. Then the electromotive force E between the terminals of the lamp is equal to RI as stated in the previous article, and if E is expressed in ohms and I in amperes, then E {= RT) is expressed in volts. That is, the product ohms X amperes gives volts. One volt is the electromotive force between the terminals of a one-ohm resistance when a current of one ampere is flowing through the resistance. The electromotive force of an ordinary gravity cell is about i.i volts. The electromotive force of an ordinary dry cell is about 1.5 volts. The voltages commonly used for electric lighting and motor service are 1 10 volts and 220 volts ; that is to say, the voltage between the supply wires in a building is usually either no volts or 220 volts. The usual voltage for electric railway service is 500 volts; that is to say, the voltage between the trolley wire and the rails is generally about 500 volts. 50. The voltmeter. Consider an ammeter (see Art. 16) of which the resistance is R ohms. When a current of I amperes flows through the ammeter the electromotive force across the terminals of the instrument is RI volts, and the scale of the instrument can be numbered so as to give the value of RI in volts instead of giving the value of Z in amperes. An ammeter arranged in this way is called a voltmeter. It would seem from the above that the only difference between HEATING EFFECT OF THE ELECTRIC CURRENT. 63 Mitmeter VjvoUmeter mam an ammeter and a voltmeter would be in the numbering of the scale ; but an instrument which is to be used as an ammeter must have a very low resistance in order that it may not obstruct the flow of current in the circuit IN which it is connected, and an instrument which is to be used as a voltmeter must have a very high resistance in order that it may not take too much current from the supply mains BETWEEN which it is connected. Thus a good ammeter for measuring up to 100 amperes has a resistance of about 0.00 1 ohm so that one-tenth of a volt would be sufficient to force the full current of 100 amperes through the instrument. A good voltmeter for measur- ing up to 150 volts has a re- sistance of about 15,000 ohms, so that about 0.0 1 ampere would flow through the instru- ment if it were connected across the terminals of a 150- volt generator. 51. Measurement of power by ammeter and voltmeter. The power delivered by a battery or dynamo is equal to EI watts, where E is the electromotive force between the terminals of the battery or dynamo in volts and I is the current in amperes delivered by the battery or dynamo. The power delivered to a lamp (or in general to any portion of a circuit) is equal to EI watts, where E is the electromotive force between the terminals of the lamp in volts, and / is the current in amperes flowing through the lamp. Figure 55 shows an ammeter Fig. 55. Ammeter and voltmeter connected for measuring power output of generator. direct current supply mains voltmeter Fig. 56. Ammeter and voltmeter connected for and a voltmeter connected SO as measuring power delivered to i. 1 »• 1 to measure the power delivered by a direct-current generator, and Fig. 56 shows an ammeter 64 ELECTRICITY AND MAGNETISM. and a voltmeter connected so as to measure the power deliv- ered to a lamp. The voltmeter should be momentarily discon- nected in Figs. 55 and 56 when the ammeter reading is being taken. Note. Power cannot be measured by an ammeter and a volt- meter arranged as in Figs. 55 and 56 in an alternating-current system. 52. Voltage drop in a generator. Let / be the current in amperes which is being delivered by a battery (or dynamo), and let R be the resistance of the battery in ohms. Then a portion of the total electromotive force of the battery is used to force the current through the battery itself. The portion so used is equal to RI according to Ohm's law. If the total electro- motive force of the battery is E volts, then the electromotive force between the terminals of the battery will be (E — RT) volts. A voltmeter connected to the battery terminals would indicate E volts when the battery is delivering no current*, but the voltmeter would indicate (E — RI) volts at the instant the battery beginsj to deliver a current of / amperes. The electro- motive force RI which is used to overcome the resistance of a battery (or dynamo) is called the voltage drop in the battery (or dynamo). Voltage drop along a transmission line. A current of I amperes is delivered to a distant motor or to a distant group of lamps over a pair of wires, the combined resistance of the pair of wires being R ohms. Let £0 be the voltage across the generator, and let £1 be the voltage across the motor or lamps as shown in Fig. 57. Then £1 is less than £0, the difference (£0 — £1) is the electromotive force which is used to overcome the resistance of both wires, and it is equal to RI volts. This loss of electromotive force along a transmission line is called the * Of course the battery delivers current to the voltmeter, but this is a negli- gible current because the resistance of the voltmeter is very large as compared with the resistance of the battery. t Continued flow of current causes a decrease of voltage by polarization as explained in Art. 47. HEATING EFFECT OF THE ELECTRIC CURRENT. 65 voltage drop along the line. For example, the electromotive force across the terminals of a generator is 115 volts. The generator supplies 100 amperes of current to a group of lamps at a distance of 1000 feet from the generator, and the wire (2000 feet of it) generatorl) JJ^ Ej CJ motor or lanvB Fig. 57. which is used for the transmission line has a total resistance of 0.05 ohm. Therefore the voltage drop along the line is 100 amperes X 0.05 ohm, or 5 volts; and the voltage across the terminals of the group of lamps is 1 15 volts — 5 volts =110 volts. 53. Measurement of resistance by ammeter and voltmeter. Figure 56 shows an ammeter and a voltmeter connected for measuring the current I flowing through a lamp and the voltage E across the terminals of the lamp. The resistance R of the lamp in Fig. 56 can be calculated from the ammeter and voltmeter readings, because, according to Ohm's law, we have RI = E so that R = Ejl. That ^ibaHery is, dividing the voltmeter reading E in :=: volts by the ammeter reading T in am- j oeres we get the resistance R of the lamp ^"^ : . r^, . , , r • Fig- 58. m ohms. This method of measurmg re- .^wo lamps in series. sistance is much used in shop testing. 54. Connections in series. When two or more portions of an electric circuit are so connected that the entire current passes through each portion, then the portions are said to be connected' in series. Thus Fig. 58 shows two lamps, L and L', connected in series. The ordinary arc lamps which are iised to light city streets are connected in series, and the entire current delivered by the generator flows through each lamp ; but the electromotive 6 66 ELECTRICITY AND MAGNETISM. force of the generator is subdivided. For example, a generator supplies 6.6 amperes at 2000 volts to a circuit containing 30 arc lamps connected in series. The entire current, 6.6 amperes flows through each lamp, but the electromotive force across the terminals of each lamp is 1/30 of 2000 volts or 67 volts. The electromotive force of a generator is subdivided among a number of lamps or other units which are connected in series. 55. The voltmeter multiplying coil. Given a voltmeter which, for example, reads up to 10 volts; one can use such a voltmeter for measuring a higher voltage by connecting an auxiliary resistance in series with it. Thus Fig. 59 shows a voltmeter V of which the resistance is R ohms, and it has an auxiliary re- supply mains H- — Bohms--n<^ 9R ohms H -i fAAAAAAAAAAf-J — -^i U-RI volts— ji>—. 9RI volts- it- lORI volts i Fig. 59. sistance of gR ohms connected in series with it. Under these conditions the voltage between the mains is found by multiplying the reading of the voltmeter by 10. This may. be explained as follows: Let I be the current flowing through the circuit in Fig. 59. Then RI is the electromotive force across the terminals of the voltmeter, and gRI is the electromotive force across the terminals of the auxiliary resistance. Therefore RI + gRI or Ioi?7 is the electromotive force between the mains; but the voltmeter reading gives the value of the electromotive force between its terminals, namely RI; therefore the electromotive force between the mains is ten times as great as the voltmeter reading. HEATING EFFECT OF THE ELECTRIC CURRENT. 67 36. Connections in parallel. When two or more portions of an electric circuit are so connected that the current divides, part of it flowing through each portion, then the portions are said to be connected in parallel. Thus Fig. 60 shows two lamps L and L', connected in parallel. The ordinary glow lamps which are used for house lighting are connected in parallel between copper mains which lead out from the terminals of the generator; and (if the resistance of the mains is negligible) the full voltage of the generator acts on each lamp, but the current delivered by the genera- I / tor is subdivided. For example, a -L 1 1 o-volt generator supplies 1000 am- 1=1 ^ peres to 2000 similar lamps con- ~T" nected in parallel with each other between the mains. The full volt- Two lalps in°paraliel. age of the generator acts on each lamp, but each lamp takes only 1/2000 of the total current. The current delivered by a generator is subdivided among a number of lamps or other units which are connected in parallel. Note. When a circuit divides into two branches, the branches are, of course, in parallel with each other, and either branch is called a shunt in its relation to the other branch. 57. The division of current in two branches of a circuit. Figure 61 shows a battery delivering a current to a circuit which branches at the points A and B. Let I be the current de- livered by the battery, I' the current in the upper branch, 7" the current in the lower branch, R' the resistance of the upper branch, and R" the resistance of the lower branch. The product R'l' is the electromotive force between the branch points A and B, also the product R"I" is the electromotive force between the branch points A and B. Therefore we have: RT = R"I" (i) The current in the main part of the circuit is equal to the sum of the currents in the various branches into which the circuit 68 ELECTRICITY AND MAGNETISM. divides. Therefore in the present case we have : 7 = 7' + I" (2) By using equations (i) and (2) the values of I' and I" can both be determined in terms of 7, R' and R". It is important to note that a definite fractional part of the total current flows through each branch; and equation (i) shows that the currents 7' and 7" are inversely proportional to the respective resistances R' and R". Thus if R' is nine times as large as R", then I" is nine times as large as I'. 58. The atometer multiplying shunt. A low-reading voltmeter can be used to measure a higher voltage by connecting an auxiliary resistance (a multiplying coil) in series with it as ex- plained in Art . 55 . A low-reading ammeter can be used to measure a larger current by connecting an auxiliary low resistance (a multiplying shunt) in parallel with it. It is not practicable, however, to use interchangeable shunts with a low resistance instru- ment (an ammeter). This may be illustrated by an. example as follows : The ammeter in Fig. 62 has, let us say, a resistance of o.oi ohm, and let us suppose that a o.oi-ohm shunt s is con- nected across its terminals. Un- der these conditions one half of the total current flows through the ammeter and one-half flows through j. Therefore the value of the total current is twice the ammeter reading. The diffi- Fig. 62. Impracticable arrangement of am- meter shunt. HEATING EFFECT OF THE ELECTRIC CURRENT. 69 culty, however, is that if s is detachable there is likely to be an appreciable* unknown resistance in the contacts of s with the two binding posts p and p' so that s may be in fact 10 or 20 per cent, greater than it is supposed to be. Any circuit IN which binding-post contacts are to be made must be of fairly high resistance if the uncertain resistance at the contacts is to be negligible. Figure 63 shows an ammeter provided with a permanent shunt, j and j being soldered joints. In this case the shunt J may be once for all adjusted by the maker of the instrument so that the full deflection of the instrument may correspond to any Fig. 63. Practicable arrangement of permanent ammeter shunt. desired number of amperes. In fact a manufacturer usually makes the working part, C, of all of his ammeters alike. The only difference between an ammeter for large current and an ammeter for small current is in the resistance of the shunt s. 59. The-millivoltmeter-with-interchangeable-shunts used as an ammeter. Figure 64 shows a low-resistance shunt j to which are permanently attached two heavy binding posts P and P' by means of which the shunt may be connected in the main circuit so that a current to be measured may flow through the shunt. Two small binding posts, p and p', are also permanently con- nected to the shunt (J and j being soldered joints), and a fairly high resistance ammeter can be connected to the two posts p and p' as shown in the figure. With this arrangement the contact resistances at p and p' are IN the high resistance circuit of the ammeter, and these contact resistances are therefore * Appreciable, that is, as compared with o.oi ohm. 70 ELECTRICITY AND MAGNETISM. negligible; and the shunt resistances between the permanently soldered joints j and j is invariable. O i -0- ■AAAAA- P J - -a - J p' Fig. 64. Practicable arrangement of detachable ammeter shunt, resistance of A being fairly large. The advantage of the arrangement shown in Fig. 64 is that one ammeter A can be used interchangeably with a number of shunts. When a high -resistance ammeter is used as indicated in Fig. 64 it is simpler to calibrate the instrument as a voltmeter so that the reading of the instrument may give the voltage between the terminals of the instrument. That is, the reading of the instru- ment gives the voltage E between the points j and j in Fig. 64, and the value of the current in the shunt may be found by divid- milliooHmeter ing E by the known resistance of the shunt, according to Ohm's law. Thus Fig. 65 shows the usual arrangement of a milli- voltmeter* and a shunt for the measurement of current. The shunt consists of one or more ribbons of manganin soldered and riveted to two massive blocks of metal A and B. * A low reading voltmeter, reading in thousandths of a volt, is called a milli- voUmeter. HEATING EFFECT OF THE ELECTRIC CURRENT. 7 1 If the shunt has a resistance of i/iooo of an ohm, the voltage E between the metal blocks must be divided by i/iooo (multi- plied by 1000) to give the current in the shunt in amperes. In this case the reading of the millivoltmeter (in thousandths of a volt) is the value of the current in amperes. If the shunt has a resistance of i/ioo of an ohm, the voltage E must be divided by i/ioo (multiplied by 100) to give the cur- rent in the shunt in amperes. In this case the reading of the millivoltmeter (in thousandths of a volt) must be multiplied by ID to give the current in amperes. If the shunt has a resistance of i/io of an ohm, the value of the current in amperes ig equal to 100 times the voltmeter reading. If the shunt has a resistance of i ohm, the value of the current in amperes is equal to 1000 times the millivoltmeter reading. 60. Combined resistance of a number of branches of a circuit. (a) The combined resistance of a number of lamps or other units connected in series is equal to the sum of the resistances of the individual lamps. (6) The combined resistance of a number of lamps or other units connected in parallel is equal to the reciprocal of the sum of the reciprocals of the resistances of individual lamps. Proposition (a) is almost self-evident. Pro- position (Jb) may be established as follows : Let E be the electro- motive force between the points A and B where the circuit divides into a number of branches (see Fig. 61). Then, according to Ohm's law, we have: E (I) (2) (3) where R', R" and R'" are the resistances of the respective r ^ R' I" = E R" I'" = E R'" 72 ELECTRICITY AND MAGNETISM. branches, and /', I" and /'" are the currents flowing in the respective branches. Let I be the total current flowing in the circuit ( = 7' + I" + /'"). The combined resistance of the branches is defined as the resistance through which the electromotive force E between the branch points would be able to force the total current I. That is, the combined resistance is defined by the equation : /-I (4) in which R is the combined resistance. Adding equations (i), (2), and (3), member by member, and substituting EjR for r + I" + I'", we have E BEE R~ R^'^ R"'^ R"' ^5) whence R = ~ ' (6) R'. ^ R" ^ K" PROBLEMS. 1. A current of 0.5 ampere flowing through a glow lamp generates 150 calories of heat in 10 seconds. What is the resistance of the lamp? Ans. 252 ohms. 2. A wire having a resistance of 250 ohms is coiled in a vessel containing 2000 grams of oil of which the specific heat is 0.60. The vessel itself (together with the coil) weighs 200 grams and the specific heat of the metal (of vessel and coil) is 0.095. A current of 1.5 amperes flows through the coil. How long will it take for the temperature of coil, oil, and vessel to rise one centigrade degree? Ans. 9. 11 seconds. 3. The field coil of a dynamo contains 25 pounds of copper (specific heat 0.094), weight of cotton insulation negligible. The resistance of the coil is 100 ohms. At what rate does the HEATING EFFECT OF THE ELECTRIC CURRENT. 73 temperature of the coil begin to rise when a current of 0.5 ampere is started in the coil? Ans. 0.0056 centigrade degree per second. 4. A given piece of copper wire has a resistance of 5 ohms, another piece of copper wire is 1.5 times as long but it has the same weight (and volume) as the first piece. What is its re- sistance? Ans. 11.25 ohms. 5. A given spool wound full of copper wire 60 mils in diameter has a resistance of 3.2 ohms. An exactly similar spool is wound full of copper wire 120 mils in diameter; what is its resistance? Ans. 0.2 ohm. Note. The spool will contain half as many layers and half as many turns in each layer of the larger wire, and the mean length of one turn of wire is the same in each case 6. What is the resistance at 20° C. of 2 miles of commercial copper wire 300 mils in diameter? Ans. 1.22 ohm. 7. What is the resistance at 20° C. of one mile of a conductor consisting of seven strands of copper wire, each 40 mils in dia- meter. Ans. 4.92 ohm. 8. A sample of commercial copper wire 3 feet long and 120 mils in diameter is found by test to have (at the same tempera- ture) the same resistance as 26.2 inches of pure copper wire 100 mils in diameter. Find the ratio: specific resistance of sample divided by specific resistance of the pure copper. Ans. 1.048. 9. Find the resistance at 20° C. of a copper conductor 100 feet long having a rectangular section 0.5 inch by 0.25 inch. Ans. 0.00653 ohm. ■JT / d \s Note. The area of a circle d mils in diameter is

X Z/2 is the total electromotive force between a and b. Therefore we have : -Eta abvolts = n^Z (i) or £ta volts = n^Z -H iqs (2) Equations (i) and (2) apply to a direct-current dynamo used as a generator or used as a motor. The equations express the induced electromotive force in the armature windings. When the current flowing through the armature is negligibly small then the electromotive force between the brushes, as measured by a voltmeter, is equal to the induced electromotive force in the armature windings. In a generator the electromotive force between the brushes is in general less than the induced electromotive force because a portion of the induced electromotive force is used to overcome the resistance of the armature windings as explained in Art. 52. In a motor the electromotive force between the brushes is in general greater than the induced electromotive force, as explained in the latter part of Art. 81. 81. Torque and speed equations of the direct-current shunt motor. A shunt motor is connected to constant-voltage supply mains as shown in Fig. 105, and it is desired to find an expression for the current la which flows through the armature and the speed n of the armature when the motor is loaded, the amount Il6 ELECTRICITY AND MAGNETISM. of load being expressed by the torque T with which the field magnet must act upon the armature to drive it. The field winding is connected directly to the supply mains, and therefore the shunt-field current is constant because the supply voltage E, is constant ; consequently the field excitation is constant, and the flux $ which passes through the armature supply main T EJconstant) "^^Z .** ' armature I J. supply main Fig. 105. core is nearly* constant. In the following discussion the vari- ations of $ are neglected, that is "I" is assumed to be constant. Torque equation. Let T be the torque in pound-inches exerted upon the armature by the field magnet, and let n be the speed of the armature. Then the mechanical power de- veloped in the turning of the armature by the field is 27r X 2.54 X 453-6 X 980 r ^^ „ T .. z • nl watts = 0.71 Mi watts. 10' Now the back electromotive force induced in the motor armature is «$Z/io' volts, and the power which is expended (from the supply mains) in forcing the armature current of /„ amperes against this back electromotive force is equal to their product, or n^Z/io^ X la watts. Furthermore all of the power expended in forcing the armature current against the back electromotive force reappears as the mechanical power developed in the turning of the armature by the field and is equal thereto (Lenz's law, see Arts. 77 and 62). Therefore we have: * The flux * Is not exactly constant because it depends to some extent upon the armature current h, which is variable. See Franklin and Esty's Elements of Electrical Engineering/ Vol. I, pages 151-161, The Macmillan Co., 1906. INDUCED ELECTROMOTIVE FORCE. ivj 0.71 nT watts = — - • /„ watts whence /„ = 0.71 X 108 X ^ (I) from which it is evident that the armature current is proportional to T. Thus when the motor is unloaded (for example, by throwing off the motor belt) the torque T required to turn the armature is very small (just enough to overcome the friction* losses). Therefore the armature current /„ is very small when the motor load is small, and it increases as the load increases. Speed equation. When the motor is unloaded the armature current is very small and the back electromotive force which is induced in the motor armature is sensibly equal to the supply voltage. But the back electromotive force is equal to n^^Z 4-10* where Wo is the zero-load speed of the motor. Therefore we have: E, = «o*Z -H iqs or E, «o = ^ X 108 (2) Let It be the unknown speed of the motor when it is loaded to such an extent as to take an armature current of /„ amperes. Then m$Z -^ 10* is the back electromotive force induced in the armature windings, and if we subtract this back electro- motive force from the supply voltage E, we get as a remainder the electromotive force which is used merely to overcome the resistance Ra of the armature windings, and this is equal to RaJa according to Ohm's law. Therefore we have: w$Z E, — „ = RJa ID* or E, — RJa ^, . , . n = ^ X io« (3) * Including what may be called "magnetic friction" losses in the armature core. See Elements of Electrical Engineering, Franklin and Esty, Vol. I, pages 127-132. Il8 ELECTRICITY AND MAGNETISM. From equations (2) and (3) we get : n Es — RJa f ,\ — = ^ \A) Wo -c-j It must not be forgotten that this entire discussion is based upon the assumed constancy of the armature flux $. PROBLEMS. 1. The armature of a direct-current motor has a resistance of 0.064 ohm, and when the motor is running under full load a current of 81 amperes is forced through the armature from no- volt supply mains. What is the back electromotive force in the armature? Ans. 104.8 volts. 2. The motor which is specified in the previous problem runs at a speed of 1200 revolutions per minute under full load when taking current from no- volt supply mains. At what speed, approximately, would the motor armature run if the load on the motor were to be thrown off, by throwing off the motor belt, for example? Ans. 1260 revolutions per minute. Note. If the "strength" of the field magnet of a motor does not change, then the back electromotive force in the motor armature is proportional to the speed of the armature Therefore the speed of the loaded motor is to the speed of the un- loaded motor as the back electromotive force of the loaded motor is to the back electromotive force of the unloaded motor; and v^hen the motor is unloaded the motor speeds up until the back electromotive force is very nearly equal to the supply voltage. 3. The electromotive force between the terminals of a shunt generator is 120 volts, and the resistance of the shunt field winding is 22 ohms. How much current flows through the shunt field winding? If the generator delivers 80 amperes to a group of lamps, how much current is delivered by the armature? Ans. (a) 5.45 amperes; (&) 85.45 amperes. 4. The resistance of the field winding of a series dynamo is 0.08 ohm, the dynamo, operating as a generator, delivers 80 amperes, and the electromotive force between the brushes is 125 volts. What is the electromotive force between the terminals of the machine, that is, between the points of attachment of the external circuit? Ans tt8.6 volts. INDUCED ELECTROMOTIVE FORCE. 1 19 Note. The series dynamo is seldom used as a generator in practice. The series dynamo is frequently used as a motor, in street cars, for example. 5. Find the power expended in field excitation in the two cases specified in problems 3 and 4. Ans. (a) 654 watts; (&) 512 watts. Note. All of the power delivered to the field winding of a dynamo reappears as heat in the winding in accordance with Joule's law. Therefore Ohm's law applies to the field winding. No power would be required to maintain the magnet- ism of the field magnet if a field winding of zero resistance could be obtained. When, however, the field magnet is being magnetized (during a small fraction of a second at the beginning) then some of the power deUvered to the field winding does not reappear as heat in accordance with Joule's law, but is used to establish the mag- netism. Thus if E is the voltage across the terminals of a magnet winding, / the current in the winding, and R the resistance of the winding, then EI is the rate at which work is delivered to the winding and RI^ is the rate at which heat is developed in the winding. Now the ultimate value of / is KjR, and when this ultimate value of I is reached we have EI — RP, but before / reaches this ultimate value EI is greater than RI^ and the excess is the power which at each instant is being used to establish the magnetism. 6. The winding of an electromagnet has a resistance of 22 ohms, and when the winding is connected across no-volt supply mains the current in the coil rises from zero at the beginning to 5 amperes ultimate value. The current must therefore have passed in succession the values i ampere, 2 amperes, 3 amperes and 4 amperes. Find the total rate at which work is being delivered to the coil, the rate at which heat is generated in the coil, and the rate at which work is being done in establishing the magnetism for each of the specified values of current. Ans. When the current is passing the value of one ampere work is deUvered to the winding at the rate of no watts, work is used to heat the winding at the rate of 22 watts, and work is used to establish magnetism at the rate of 88 watts. 7. Let it be assumed that the velocity, 7, of a boat is pro- portional to the propelling force E. One horse-power will propel the boat at a speed of one mile per hour. How much power would be required to propel the boat at a velocity of two miles per hour? I20 ELECTRICITY AND MAGNETISM. 8. The current I produced In a given circuit is proportional to the electromotive force E which acts upon the circuit. One watt of power will maintain a current of one ampere in the circuit. How much power would be required to maintain a current of two amperes? Note. It is most instructive to argue this problem as follows: To double / would require doubled E, and therefore EI would be quadrupled. 9. A force of no pounds will propel a boat steadily at a velocity of 5 feet per second. On the assumption that velocity is proportional to propelling force, find the factor by which steady velocity I must be multiplied to give propelling force E. In what units is this factor expressed. Ans. 22 pounds per unit velocity. 10. An electromotive force of no volts will maintain a current of 5 amperes in a circuit. On the assumption that current is proportional to electromotive force, find the factor by which current I must be multiplied to give the electromotive force E which is acting on the circuit. Ans. 22 volts per ampere. 11. The boat referred to in problem 9 is started from rest by a propelling force of no pounds, and after some time the boat reaches full speed of 5 feet per second. The speed must, there- fore, pass through the following values: i foot per second, 2 feet per second, 3 feet per second and 4 feet per second. Find, for each of these speeds, the total rate at which work is being done on the boat, the rate at which work is being spent in over- coming friction, and the rate at which work is being used to establish the motion of the boat (the work so used is stored in the boat as kinetic energy). Ans. When speed of the boat is I foot per second work is done on the boat at a total rate of no foot-pounds per second, work is spent in overcoming friction at the rate of 22 foot-pounds per second, and work is used at the rate of 88 foot-pounds per second to establish the motion or to increase the speed of the boat. 12. A two pole direct-current dynamo has 500 feet of copper wire wound upon it, and the diameter of the wire is 60 mils. INDUCED ELECTROMOTIVE FORCE. 121 What is the resistance of the armature from brush to brush? Ans. 0.36 ohm. Note. From Fig. 28 or 29 it will be seen that the wire on the armature of a two-pole direct-current dynamo presents two paths from brush to brush, and these two paths are of course in parallel. 13. The ring-wound armature of a 4-pole direct-current dynamo has 500 feet of 60 mil copper wire wound upon it. (See Figs. 32 and 33.) What is the resistance of the armature from brushes aa to brushes hbl Ans. 0.09 ohm. 14. The large water-wheel-driven alternators in the upper power house at Niagara Falls have a speed of 250 revolutions per minute and they give an alternating electromotive force having a frequency of 25 cycles per second. How many field poles are there in the field magnet of one of these machines? Ans. 12. 15. The first of the large steam-driven power plants in New York City were equipped with alternators which were mounted directly on the crank shafts of large reciprocating engines running at a speed of 75 revolutions per minute. The fre- quency of the alternating electromotive force which is generated is 25 cycles per second. How many field poles are there in one of the field magnets of one of these alternators. Ans. 40. 16. A fixed percentage of the power output, EI, of a generator is to be lost as RI^ loss in a transmission line. Show, on the basis of this assumption, that the amount of copper wire in pounds required to transmit a given amount of power over a given distance is quartered if the generator voltage E is doubled. Note. If E is doubled, then / will be halved inasmuch as the power output EI is a given amount. Also the line loss in watts is fixed in value, But the line loss is RI^ where R is the resistance of the line (including both wires). There- fore, since / is halved and RP is unchanged, it is evident that R is quadrupled. From this point the argument can be carried forward on the basis of equation (i) of Art. 41. 17. The earth's magnetic field at the equator is approximately horizontal, in a north-south direction, and its intensity is about 0.5 gauss. A copper wire 10 meters long and weighing 400 grams (400 X 978 dynes) is stretched horizontally east and west. 122 ELECTRICITY AND MAGNETISM. Find the current which would have to flow through the wire (from west to east) in order that the whole weight of the wire would be supported by the upward push of the earth's magnetic field on the wire. Ans. 7824 amperes. 18. A two-pole direct-current dynamo has an armature core 30 centimeters long, that is / in Fig. 102 is equal to 30 centi- meters and of course the pole pieces are 30 centimeters broad (in direction parallel to armature shaft). The diameter of the dynamo pulley is the same as the diameter of the armature, a force of 1000 pounds (1000 X 453.6 X 980 dynes) applied tan- gentially at the rim of the pulley is required to hold the armature stationary when a current of 100 amperes flows through each armature wire, and there are 250 armature wires under the pole faces that is in the gap spaces between the pole pieces and the armature core. What is the intensity of the magnetic field in the gap spaces? Ans. 5927 gausses. 19. At what sidewise velocity would the armature wires of the dynamo of problem 18 have to move in order that an electromotive force of 4 volts might be induced in each wire in the gap spaces? Ans. 2250 centimeters per second. 20. The diameter of the armature of the dynamo of problems 18 and 19 is 40 centimeters. What speed of the armature in revolutions per second would produce a sidewise velocity of the armature wires of 2250 centimeters per second? Ans. 17.9 revolutions per second. 21. The span of each pole face of the dynamo of problem 18 is 40 centimeters, that is the area of each pole face is 30 X 40 square centimeters. How many lines of flux pass from the N-pole of the field magnet through the armature cove to the S-pole of the field magnet? Ans. 7,112,400 lines. 22. Calculate the induced electromotive force between the brushes {E = ^Zn) of the dynamo of problems 18 to 21 at a speed of 17.9 revolutions per second. Ans. 499 volts. INDUCED ELECTROMOTIVE FORCE. I23 Note. There are 250 armature conductors under the 80 centimeters span of the two pole faces and the number of conductors Z on the entire circumference of the armature is — X 250 which gives 392. 80 23. The ring armature of a bipolar direct-current dynamo has 260 turns of wire upon it, it is driven at a speed of 1200 revolutions per minute and the electromotive force between the brushes (when the armature current is negligibly small) is no volts. What is the value of the armature flux $? Ans. 2,115,000 lines. 24. A shunt generator is driven at a speed of 1200 revolutions per minute, and it gives an electromotive force of 1 10 volts between its brushes (armature current negligibly small) with a total of 56 ohms in its shunt field circuit. If the generator is driven at a speed of 1500 revolutions per minute how much additional re- sistance will have to be connected in the shunt field circuit in order that the electromotive force may be increased in proportion to the increase of speed so as to be 137.5 volts? Ans. 14 ohms. Note. In order that the electromotive force may be increased in proportion to the increase of speed, the value of * must remain unchanged and therefore the current in the shunt field winding must remain unchanged. 25. The electromotive force of a shunt generator (armature current negligibly small) decreases from no volts to 93 volts when the speed of the generator is reduced from 1000 revolutions per minute to 900 revolutions per minute. The armature flux $ at the higher speed is 1,000,000 lines, (a) What would the elec- tromotive force of the generator be at the lower speed if the armature flux were unchanged? {b) What is the value of the armature flux at the lower speed? Ans. (a) 99 volts; (&) 939,390 lines. 26. The resistance of the armature of a direct-current gener- ator (including brushes and brush contacts) is 0.14 ohm. The electromotive force induced in the armature («$Z) is 120 volts and the armature current is 70 amperes. Find the value of the electromotive force between the brushes. Ans. 1 10.2 volts. Note. See Art. 52. 124 ELECTRICITY AND MAGNETISM. 27. A shunt motor connected as shown in Fig. 105 runs at a speed of 1200 revolutions per minute when the supply voltage, E„ is no volts, and it runs at a speed of 1350 revolutions per minute when £» is increased to 132 volts; motor load being zero, (a) What would the speed be at the increased voltage if the armature flux $ were unchanged? (6) What is the value of the armature flux at the higher voltage, its value at the lower voltage being 1,000,000 lines. Ans. (o) 1440 revolutions per minute; {b) 1,067,000 lines. 28. A shunt motor connected as shown in Fig. 105 has a zero load speed of 1200 revolutions per minute when the supply voltage E, is equal to no volts. The motor is loaded until its armature current /„ is 10 amperes, find the speed on the as- sumption that the armature flux $ remains unchanged. The resistance of the armature from brush to brush is 0.7 ohm. Ans. 1 1 22 revolutions per minute. CHAPTER V. ~mr ELECTRIC CHARGE AND THE CONDENSER. 82. The elimination of the water hammer effect by an air cushion. The eUmination of the spark at break by a condenser. The water hammer effect which is produced when a hydrant is suddenly closed is sometimes _ sufficiently intense to burst the - ""^ pipe or injure the valve of the hydrant. In some cases, there- fore, it is desirable to protect the hydrant by an air cushion, as shown in Fig. 106. When the hydrant in Fig. 106 is -i== — closed (however quickly) the ' ' moving water in the pipe is brought to rest gradually, and as it slowly comes to rest it com- presses the air in the chamber CC. pipe hydratii -water Fig. 106 centrifugal pump cheek valve pipe Fig. 107. Wire ■ -^ battery DdZ :2D Fig. 108. Figure 107 shows a centrifu- Figure 108 shows a battery gal pump maintaining a stream maintaining a " current of elec- ta 126 ELECTRICITY AND MAGNETISM. tricity" through a circuit. If the circuit is broken at p, the electric current will continue for a short time to flow throueh the circuit into the metal plate A and out of the metal plate B. This continued flow of the electric current into plate A and out of plate B causes what we may think of as an "electrical bending" (an elec- trical stress) of the layer of insulating material DD, and this "electrical bending" soon stops the flow of current; then the layer of insulating ma- terial "unbends" and produces a reversed surge of electric current through the circuit. The two metal plates A and B together with the layer of insulating material between them constitute what is called a condenser. A condenser is usually made of sheets of tin foil of water through a circuit of pipe. If the check valve is suddenly closed, the water will continue for a short time to flow through the circuit into the chamber A and out of the chamber B. This continued flow of the water into chamber A and out of chamber B causes a bending (a mechanical stress) of the elastic diaphragm DD, and this bending soon stops the flow of water; then the diaphragm unbends and produces a reversed surge of water through the circuit of pipe. Fig. 109. separated by sheets of waxed paper. Thus the heavy horizontal lines in Fig. 109 represent sheets of tin foil, and the fine dots represent insulating material. In order that the following effects may actually be observed the condenser in Fig. 108 must be made of a large number of sheets of tin foil and waxed paper. The actual flow of current into the metal plate A and out ELECTRIC CHARGE AND THE CONDENSER. 127 of the metal plate B when the circuit is broken at p in Fig. 108 is shown by the fact that no spark at break is produced when the condenser AB is connected, whereas a very perceptible spark at break is produced when the condenser AB is not connected. The reversed surge of current which takes place after the original current has been stopped in Fig. 108 may be shown as follows: Disconnect the condenser AB, make and break contact at p, hold a magnetic compass near one end of the core of the inductance coil, and the core will be found to have retained a large portion of its magnetism; in other words, the core will not have become by any means completely demagnetized when the circuit is broken and the current reduced to zero. Then connect the condenser AB, make and break the circuit at p as before, and again test the core of the inductance coil with a compass. The core will now be found to have lost nearly the whole of its magnetism because of the reversed surge of current. A reversed surge of current from the condenser in Figs. 84 and 85 is the cause of the very quick demagnetization of the core of an induction coil. 83. The momentary flow of current in an open circuit. Idea of electric charge. When the metallic contact at p in Fig. 108 is broken the electric circuit remains closed as long as the current continues to flow across the break in the form of a spark. The intensely heated air in the path of a spark is a conductor. When the condenser AB is connected as shown in Fig. 108, there is no spark at break, and the circuit is actually opened at the moment the contact at p is broken. Therefore the continued flow of current through the circuit after the contact at p in Fig. 108 is broken is an example of the momentary flow of current on an open circuit. The current continues momentarily to flow through the open circuit into plate A and out of plate B, and the two plates A and B are said to become electrically charged. The plate into which the momentary current flows is said to become positively charged, and the plate out of which the momentary current flows is said to become negatively charged. 128 ELECTRICITY AND MAGNETISM. The flow of current in an open circuit may be shown by con- necting a small incandescent lamp and a condenser in series to alternating-current supply mains as shown in Fig. III. With each reversal of the alternating supply voltage a momentary current flows through the lamp, and the repeated pulses of current heat the lamp filament to incandescence. When the lamp and condenser are connected to direct-current supply mains, as shown in Fig. 1 10, a single momentary current flows through the lamp when the connection is first made, but this single momentary pulse of current has no appreciable heating effect on the lamp filament. If a switch be connected so as to rapidly reverse the direct-current supply- mains alternating-current supply mains M2> lamp Lh(S> lamp condenser Fig. 110. condenser Fig. 111. connections to the supply mains in Fig. no, then a pulse of current will flow through the lamp at each reversal, and if the reversals are made rapidly enough the lamp filament will be heated to incandescence. 84. The function of choke coil and condenser in the lightning arrester. Figure 113 shows the essential features of the lightning arrester for protecting a dynamo G from a lightning stroke. When the lightning strikes the trolley wire, a very large electro- motive force acts for a very short time between the trolley wire and ground, the spark gap breaks down, and the lightning dis- charge flows across the spark gap to earth. Meanwhile the large electromotive force has started an appreciable current through the choke coil, but nearly the whole of this current flows into one plate of the condenser and out of the other plate of the condenser ELECTRIC CHARGE AND THE CONDENSER. 129 to earth; the current has been so small, however, and of such short duration that the voltage across the condenser terminals (and across the dynamo terminals) has not risen to any consider- able value. Thus the dynamo A is protected from the action of a high voltage across its terminals. If the condenser in Fig. 113 is omitted, as shown in Fig. 115, the small momentary current which is established in the choke coil must of necessity flow through the dynamo A , and in con- sequence the full voltage of the lightning stroke is brought into action across the dynamo terminals.* The detailed action in Figs. 113 and 115 may be understood by the following parallel statements: \v)aU, rubber cushion^ hammer/ tr olley wire ch oke coil spark gap , , condenser 777777777^7777777/^777^777777777777^/777777^7777 ground Fig. 112. Fig. 113. Wall well protected from shock. Dynamo well protected from lightning stroke. The ball in Fig. 112 can be set in motion for a moment because of the yielding quality of the rubber cushion. A very considerable momen- tary current can flow through the choke coil in Fig. 113 be- cause of the "yielding quality" of the condenser. That is, the momentary current need not flow through the dynamo G, but it can flow into one plate of the condenser and out of the other plate of the condenser, * The connecting wires and especially the end turns of wire on the dynamo act to some extent like the condenser in Fig. 113. 130 ELECTRICITY AND MAGNETISM. Therefore nearly the whole of the momentary force of the hammer blow is used to set the ball in motion. The ball in Fig. 112 thus suddenly set in motion is brought slowly to rest as it compresses the cushion, and the only force exerted on the wall is the small force arising from the compression of the cushion. thus charging one plate posi- tively and the other plate negatively. Therefore nearly the whole of the momentary electromo- tive force of a lightning stroke is used to set up a current in the choke coil. The current thus set up in the choke coil is slowly reduced to zero as it charges the con- denser, and the only electro- motive force exerted across the terminals of the dynamo G is the small electromotive force across the condenser terminals arising from the charging of the condenser. uhM troUey wire choke coil spark gap [ \ 000000 Fig. 114. Wall not protected from shock. ground Fig. lis. Dynamo not well protected from lightning stroke. The rigid wall in Fig. 114 is understood to have a very great mass, and it cannot be set in motion to an appreciable extent by a hammer blow. The winding of the dynamo G in Fig. 115 has a very great inductance, and an electric current of appreciable value cannot be established in it by ELECTRIC CHARGE AND THE CONDENSER. 131 Therefore the ball cannot move a very sudden lightning stroke, perceptibly, and no portion of Therefore no appreciable cur- the force of the hammer blow rent can flow through the choke can be used to set the ball in coil,* and ,no portion of the motion. electromotive force of the light- ning stroke can be used to establish a current in the choke coil. That is to say, all of the elec- tromotive force of the lightning stroke is transmitted to the dynamo G by the choke coil. Or, in other words, the choke coil does not protect the dy- namo from shock. 85. The telegraph-telephone composite. An arrangement, called the telegraph-telephone composite permits the use of a single telegraph line for telegraph service and for telephone service simultaneously, and it depends upon the combination of choke coils and condensers as shown in Fig. 116. The telephone telephone rj^^set That is to say, all the force exerted by the hammer blow is transmitted to the wall by the heavy ball. Or, in other words, the heavy ball does not protect the wall from shock. condenser ttation A choke coil relay C) key _c X condenser telephone ~~> set choke coil station B relay key way station i groaad X Fig. 116. Telegraph and telephone composite. * The end turns of wire on the dynamo act to some extent like the condensei' in Fig. 113. 132 ELECTRICITY AND MAGNETISM. current (which is a high-frequency alternating current) and the telegraph current (which rises and falls slowly in value) both flow together over the line and return through the ground. But only the telephone current flows through the condensers and telephones, and only the telegraph current flows through the choke coils, relays and keys (the keys are of course all closed but one). 86. Electric oscillations. When a hammer strikes an anvil it rebounds and falls again and again upon the anvil. When a hydrant is suddenly closed the moving column of water rebounds and is driven again and again against the closed valve of the hydrant. This is shown by the fact that a succession of sharp clicks is generally heard after the sudden closing of a hydrant. Also when the check valve in Fig. 107 is suddenly closed, the reversed surge of water current which is described in Art. 82 generally "over-shoots," as it were, and produces a reversed bending of the diaphragm; and this reversed bending of the diaphragm then produces a second reversed surge (in the direction of the original flow), and so on. Similarly, when the circuit in Fig. 108 is suddenly broken at p, the reversed surge of current which is described in Art. 82 gen- erally "over-shoots," as it were, producing a second reversed surge (in the direction of the original current), and so on. These repeated surges of current back and forth in a circuit are called electric oscillations. If the friction which opposes the flow of water through the pipe in Fig. 107 is great, the back and forth surges of the water soon cease; indeed the first reverse surge may be the only one that is perceptible. Similarly if the electrical resistance* of the circuit in Fig. 108 is great, the back and forth surges of electric * Loss of energy in the production of heat occurs to a very considerable extent in the iron core in Fig. io8 ; and in some cases an oscillating electrical circuit radiates energy in the form of electric waves. Both of these effects as well as the heating of the circuit because of its resistance cause the back and forth surging of current to die away. ELECTRIC CHARGE AND THE CONDENSER. 133 current soon cease; indeed the first reversed surge is the only one that is perceptible with an arrangement like that shown in Fig. 108 or with an arrangement like that shown in Fig. 85. unatretehed spring initial 1 position 1 1 L 1 in \ \ + i i guilibrium ;■«>«« X position i J_ P coil of wire f ■ ^H — htMei^ condenser extreme T poution wire Fig. 117. Figure 117 represents an un- stretched spring, the attached weight being supported, let us say, by the hand. If the hand is removed, the full pull of gravity E will be- gin at once to act upon the Fig. 118. Figure 118 represents an un- charged condenser, the battery circuit being broken at p. If the circuit is closed, the full electromotive force E of the battery will begin at once to 134 ELECTRICITY AMD MAGNETISM. weight L, and the velocity I of the weight will continue to increase so long as the down- ward pull of gravity is greater than the reacting pull due to the increasing stretch of the spring. The movement of the weight in Fig. 117 is assumed to be frictionless for the salte of simplicity of statement. When the spring is stretched by a certain amount Q, there- acting pull of the spring is equal to the pull of gravity, but at this instant the velocity I of the weight has reached a maximum value. Consequently the weight goes on moving downwards, but the reacting pull of the stretched spring now exceeds the downward pull of gravity. Therefore the velocity I of the weight begins to decrease. When the velocity of the weight has been thus reduced to zero, the stretch of the spring has reached a certain value 2Q (if there have been no friction losses of energy). act upon the circuit, and the current / in the circuit will continue to increase so long as the electromotive force of the battery is greater than the re- acting electromotive force due to the increasing charge on the condenser.* The resistance of the connecting wires in Fig. 118 is assumed to be zero for the sake of simplicity of statement. When the condenser is charged to a certain extent Q, the reacting electromotive force of the condenser is equal to the electromotive force of the bat- tery, but at this instant the current I in the circuit has reached a maximum value. Consequently the current continues to flow, but the re- acting electromotive force of the charged condenser now exceeds the electromotive force of the battery. Therefore the current I in the circuit begins to decrease. When the current has been thus reduced to zero, the charge of the condenser (posi- tive charge on one plate, nega- tive charge on the other) has reached a certain value zQ (if there have been no resistance losses of energy). ELECTRIC CHARGE AND THE CONDENSER. 135 Then the reacting pull of the Then the reacting electro- stretched spring starts the motive force of the charged weight moving upwards. condenser starts the current flowing in a reverse direction through the circuit. The weight therefore moves The current therefore surges repeatedly up and down until it repeatedly back and forth finally comes to rest with the through the circuit until it spring stretched so as to give a finally dies away with the con- reacting pull equal to the denser charged so as to give a downward pull of gravity. reacting electromotive force equal to the electromotive force of the battery. 87. Electrostatic attraction. The electrostatic voltmeter. When a momentary current flows into plate A and out of plate B in Fig. 108, the plates are said to become electrically charged, as stated in Art. 83, the plate into which the momentary current flows is said to become positively charged and the plate out of which the momentary current flows is said to become nega- tively charged. Two plates which have thus been oppositely charged attract each other when the intervening insulating ma- terial is a fluid like air or oil. This attraction between two oppositely charged metal plates is utilized in the electrostatic voltmeter which consists of a very delicately suspended metal plate and a stationary metal plate, both carefully insulated. The electromotive force to be meas- ured is connected to these plates, a momentary flow of current charges one plate positively and the other plate negatively, the suspended plate is moved by the electrostatic attraction between the plates, and a pointer attached to the movable plate plays over a divided scale. Figure 119 is a general view of an electro- static voltmeter. The moving element of the instrument con- sists of two very light metal vanes VV (seen edgewise in the figure) mounted on a pivot and carrying a pointer p, and 136 ELECTRICITY AND MAGNETISM. the Stationary element consists of two metal plates PP (also seen edgewise in the figure). The plates PP are connected together and to one terminal of the voltage to be measured, and the other terminal of the voltage is connected to the nioving element VV by means of the controlling hair spring. Electrostatic attraction is familiar to every one. A hard-rubber comb, for example, is charged with electricity when it is passed through dry hair, at the same time the hair is oppositely charged, and each hair is at- tracted by the comb. Fig. 119. Westinghouse type electrostatic voltme- ter. 88. Definition of the coulomb. A current of water through a pipe is a transfer of wa- ter along the pipe. Let Q be the amount of water which dur- ing t seconds flows past a given point in the pipe, then the quotient Qjt is the rate of flow of water through the pipe, and this rate of flow may be spoken of as the strength I of the wa- ter current. If the strength I of the water current in cubic feet per second is given, then the amount of water flowing past a given point of the pipe in t seconds is given by the equation : Q = It in which I is the strength of the water current in cubic feet per second, and Q is the number of cubic feet of water which flows past a given point of the pipe in t seconds. Similarly an electric current in a wire may be looked upon as the transfer of "electricity" along the wire, and the quantity Q of "electricity" which flows past a point on the wire during t seconds may be defined as the product of the strength of the current and the time, that is we may write : Q = It (I) in which / is the strength of the current in amperes, and Q is the quantity of electricity which flows past a point on the wire ELECTRIC CHARGE AND THE CONDENSER. 137 during t seconds. It is evident from equation (i) that the product of amperes and seconds gives quantity of electricity, and therefore the unit of quantity of electricity is most conve- niently taken as one ampere-second, meaning the amount of elec- tricity which during one second flows past a point on a wire in which a current of one ampere is flowing. The ampere-second is usually called the coulomb. One ampere-hour is the quantity of electricity carried in one hour by a current of one ampere. 89. Measurement of electric charge. The ballistic galvanom- eter. A very large quantity of electric charge may be determined by observing the time during which the charge will maintain a sensibly constant measured current. Thus, a given storage cell can maintain a current, say, of ten amperes for eight hours so that the discharge capacity of the storage battery is equal to eighty ampere-hours. The quantities of charge which are most frequently encountered in the momentary flow of electric current in open circuits are, however, exceedingly small. For example, the terminals of a given condenser are connected to iio-volt direct-current mains, and the momentary flow of current repre- sents the transfer of, say, o.oooi of a coulomb which corresponds to a flow of one ampere for a ten-thousandth of a second. It is evident that such a small amount of electric charge cannot be measured by the method above suggested. Such small quanti- ties of electric charge are measured by means of the ballistic galvanometer. This galvanometer is an ordinary D'Arsonval galvanometer such as described in Art. 16. When a momentary pulse of current is sent through such a galvanometer, the coil is set in motion, and a certain maximum deflection or throw of the coil is produced. Let d be the measure of this momentary maximum deflection or throw on the galvanometer scale. A certain amount of charge Q is represented by the momentary pulse of current and this amount of charge is proportional to the throw d. That is, we may write : Q = kd (i) 138 ELECTRICITY AND MAGNETISM. in which jfe is a constant for the given galvanometer, and it is called the reduction factor of the galvanometer. The value of the reduction factor k is generally determined in practice by sending through the galvanometer a known amount of charge Q and observing the throw d produced thereby. 90. The capacity of a condenser. A ballistic galvanometer BG, a condenser and a number of dry cells are connected as shown in Fig. 120. One terminal of the condenser is connected glass handle Fig. 120. to a flexible wire which is fixed to the end of a glass handle. By touching the wire W to the point h, the electromotive force E of one dry cell acts upon the condenser, and the momentary flow of current which charges the condenser produces a throw of the ballistic galvanometer. The condenser can then be discharged by touching the wire W to the point a. By touching the wire W to the point c, the electromotive force 2E of two dry cells acts upon the condenser, and the momentary flow of current which charges the condenser produces a throw of the ballistic galvanometer. The condenser may then be discharged as before. By touching the wire W to the point d, the electromotive force 3E of three dry cells acts upon the condenser, and the momentary flow of current which charges the condenser causes a throw of the ballistic galvanometer; and so on. In this way the throws of the ballistic galvanometer may be observed when the con- denser is charged by an increasing series of voltages E, 2E, 3E, ELECTRIC CHARGE AND THE CONDENSER. I39 4£, and so forth, and it is found that the throw of the ballistic galvanometer becomes larger and larger in proportion to the voltage. But the throw of the ballistic galvanometer is pro- portional to the charge which is drawn out of one plate and forced into the other plate of the condenser. Therefore the amount of charge which is drawn out of one plate and forced into the other plate of a condenser is proportional to the electromotive force which acts upon the condenser. Therefore we may write : e = C£ (I) where Q is the quantity of charge which is drawn out of one plate and forced into the other plate of a condenser when an electromotive force of E volts is connected so as to act upon the condenser, and C is a constant for a given condenser. The factor C is adopted as a measure of what is called the capacity of the condenser. Therefore a condenser would have unit capacity if an electromotive force of one volt would draw one coulomb of charge out of one plate and force one coulomb of charge into the other plate of the condenser. It is evident from the above equation that C, the capacity of a condenser, is expressed in coulombs-per-voU. One coulomb- per-volt is called a farad, that is to say a condenser has a capacity of one farad when an electromotive force of one volt will draw one coulomb out of one plate of the condenser and force one coulomb into the other plate of the condenser. Condenser capacities as usually encountered in practice are very small fractions of a farad. Thus the capacity of a condenser made by coating with tin foil the inside and outside of an ordi- nary one-gallon glass jar would be about one five-hundred- millionth of a farad, or 0.002 of a microfarad. A microfarad is a millionth of a farad, and in practice capacities of condensers are usually expressed in microfarads. The approximate dimensions of a one-microfarad condenser are as follows: 501 sheets of tin foil separated by sheets of paraffined 140 ELECTRICITY AND MAGNETISM. paper 0.02 inch in thickness, the overlapping portions of the sheets of tin foil being 10 inches by ID inches, as shown in Fig. 121. Two pieces of metal of any shape separated b; insulating material constitute a condenser; the only reason for using sheets of metal with thin layers of insulating material between is to obtain a large capacity. 91. Example showing the use of the ballistic galvanometer. A condenser of which the capacity is C farads is charged by an electromotive force of E volts, and discharged through a ballistic galvanometer ; and the observed throw of the galvanom- eter is d scale divisions. Then: CE = kd (I) This equation is evident when we consider that CE is the charge which has been drawn out of one plate of the condenser and forced into the other plate by the charging electromotive force E, and this amount of charge flows through the galvanometer when the condenser is discharged ; furthermore the charge which flows through the ballistic galvanometer is equal to kd according to Art. 89. Another condenser of which the capacity is C farads is charged by the same electromotive force E, and discharged through the ballistic galvanometer; and the observed throw of the galvanometer is d' scale divisions. Then: ELECTRIC CHARGE AND THE CONDENSER. 141 C'E = kd' (2) Dividing equation (i) by equation (2) member by member, we get C d ^ d „, a = d' °^ ^ = d>-^ ^3) from which C can be calculated if C is known. The standard condenser. A condenser of which the capacity has been carefully measured* is called a standard condenser. Thus, if C in equation (3) is the known capacity of a standard condenser, the value of C may be calculated. A standard condenser may be used to determine the reduction factor of a ballistic galvanometer. Thus, if C is the known capacity of a standard condenser, and if £ is a known voltage, then everything but k is known in equation (2), so that the value of k may be calculated. For example, a one microfarad condenser ( C = o.oooooi farad) is charged by an electromotive force of which the value is 14.21 volts and discharged through a ballistic galvanometer; and the galvanometer throw is observed to be 82.1 scale divisions. The value of k, as calculated by equation (2), is then found to be 1.73 X lo"' coulomb per scale division. 92. Inductivity of a dielectric. The insulating material be- tween the plates of a condenser is called a dielectric. Indeed, the insulating material between any two oppositely charged bodies is called a dielectric. The capacity of a condenser depends upon the size of the plates, upon the thickness of the dielectric and upon the nature of the dielectric. The dependence of the capacity of the condenser upon the nature of the dielectric is a matter which must be determined purely by experiment. Thus Fig. 122 represents two metal plates with air between them, and Fig. 123 represents the same plates immersed in oil. The dis- tance between the plates is understood to be the same in Figs. 122 * Methods of measuring capacity are described in Gray's Absolute Measure- ments in Electricity and Magnetism, Vo l. I, pages 418-450., 142 ELECTRICITY AND MAGNETISM. and 123. Let C be the capacity of the condenser in Fig. 122 with air as the dielectric, and let C be the capacity of the con- denser in Fig. 123 with a given kind of oil as the dielectric. The oil oil Fig. 122. Fig. 123. ratio C'jC is called the inductivity* of the oil. Thus the induc- tivity of kerosene is about 2.04, that is, the capacity of a given condenser is 2.04 times as great with kerosene between the plates as with air between the plates. The accompanying table gives the inductivities of a few dielectrics. TABLE. INDUCTIVITIES OF VARIOUS SUBSTANCES. Crown glass (according to composition) 3.2 to 6.9 Flint glass (according to composition) 6.6 to 9.9 Hard rubber 2.08 to 3.01 Sulphur (amorphous) 3.04 to 3.84 Paraffin 2.00 to 2.32 Shellac , 2.74 to 3.67 Ordinary rosin 2.48 to 3.67 Mica (according to composition) 5.66 to 10 Petroleum about 2.04 Water about 90. 93. Dependence of capacity of a condenser upon size and distance apart of plates. When the dielectric of a condenser is of uniform thickness and when the metal plates are large as compared with their distance apart (thickness of dielectric), * What is here called the inductivity of a dielectric is sometimes called dielectric constant, or specific capacity of a dielectric, or specific inductive capacity of a dielectric. ELECTRIC CHARGE AND THE CONDENSER. 143 then the capacity C of the condenser is proportional* to ajx for a given dielectric, where x is the thickness of the dielectric and a is the area of the sheet of dielectric between the plates. Therefore, if we choose a given dielectric, we may write C=B- (I) X in which 5 is a constant. When x is expressed in centimeters, and a in square centimeters; when air is chosen as the dielec- tric; and when C is expressed in farads; then the value of B as found by experiment is 884 X io~'^. Therefore we have : Cu.,aradB = 884XI0-1«X^ (2) When a dielectric whose inductivity is k is used instead of air, the capacity of the condenser is k times as great, or: ka Cta laraaa = 884 X lO"" X — (S) in which C is the capacity in farads of a condenser of which the plates are separated by a layer of dielectric x centimeters thick and a square centimeters in area (between the plates), and k is the inductivity of the dielectric. The meaning of a may be understood with the help of Fig. 121. If there are 501 sheets of tin foil there will be 500 sheets of dielectric, and a will be equal to 500 X 10 inches X 10 inches or 322500 square centimeters. 94. The work done by an electromotive force E in pushing a given amount of charge, Q, through a circuit. When Q coulombs of electric charge flows through a battery of which the electromotive force is E, the amount of work W done by the battery is EQ joules. That is: W= EQ (i) * It can be shown from almost purely geometrical considerations that C is proportional to ajx, but it is sufficient to accept this proportional relation as the result of experiment. The value of the proportionality factor B must be deter- mined by experiment directly or indirectly. 144 ELECTRICITY AND MAGNETISM. This is evident from the following considerations. Imagine a current / flowing through the battery; then EI watts is the rate at which the battery does work, and Elt joules is the amount of work done in t seconds. But the product It is the amount of charge Q (in coulombs) which has been pushed through the circuit. Therefore the work done, namely Elt joules, is expressible as EQ joules. Therefore we have equation (I). 95. The potential energy of a charged condenser, A charged condenser represents a store of potential energy in much the same way that a stretched spring or the distorted diaphragm DD in Fig. 107 represents a store of potential energy, and before con- sidering the amount of potential energy in a charged condenser it is helpful to consider the amount of potential energy in a stretched spring. Let g represent the elongation of a spring due to a stretching force e as shown in Fig. 124. As is well known g is proportional stretched spring Fig. 124. to e; therefore if we plot corresponding values of g and e as abscissas and ordinates respectively, we will get a straight line cc as shown in Fig. 125. Consider the total amount of work W which is done while the spring is being stretched from g = o to q = Q, and while the stretching force is increasing from e = o to e = £. The aver- age value of the stretching force is J^ E, as may be understood from Fig. 125, and the work done is equal to the product gf the ELECTRIC CHARGE AND THE CONDENSER. 145 total stretch Q and the average stretching force J^£. That is: W = ViEQ and this work W is stored in the stretched spring as potential energy. Thus a stretch of 3 feet ( = Q) is produced in a large spring, and the stretching force rises from zero to 60 pounds axitof e Fig. 12s. {= E). The average value of the stretching force is 30 pounds (= 3^£), and the work done is 90 foot-pounds (= }/^EQ); and this work is stored in the stretched spring as potential energy. Similarly, a condenser is charged by applying it to an electro- motive force which begins at zero and rises to E volts, and the amount of work W which is done in charging the condenser is equal to }/^EQ where 3^£ is the average value of the charging electromotive force, and Q is the total charge which is drawn out of one plate of the condenser and pushed into the other plate. This statement is in accordance with equation (i) of Art. 94. Therefore: W = y2EQ (I) where W is the potential energy of a charged condenser, E is the voltage acting on the charged condenser, and Q is the charge which has been drawn out of one plate of the condenser and pushed into the other plate ; W is expressed in joules when E is in volts and Q in coulombs. We may substitute CE for Q in equation (l), according to equation (i) of Art. 90, and we get: W=y^CE' (2) 146 ELECTRICITY AND MAGNETISM. or we may substitute Qj C for E in equation (i), according to equation (i) of Art. 90, and we get: w = y2f (3) Following is a rigorous derivation of equation (3) as applied to a stretched spring. Let q be the elongation of the spring when the stretching force is e. Then q and e are proportional, so that: q = Ce (4) where C is a constant for the given spring. Let Ag be the added elongation due to an increment Ae of the stretching force, and let AW be the work done on the spring to produce the added elongation. Then: AW is greater than e .Ag and AW is less than (e + Ae) .Ag or AW — — is greater than e and less than (e+A«). Ag Therefore AWjAq approaches « as a limit when Ae and Ag both approach zero or, using differential notation, we have dWjdq = e; or, using the value of e from equation (4), we have: ^=-^ (S) dq C ^^' Now the potential energy W of the spring when its elongationis Q, is the amount of work done in stretching the spring from g = o to q — Q, and this is found by integrating equation (s) from g = o to g = Q, which gives: W = -^ (6) 2C 96. Disruptive discharge. Dielectric strength. When the electromotive force which charges a condenser is increased more and more, the dielectric of the condenser is eventually broken down; this break down occurs in the form of an electric spark, it discharges the condenser, and it is called a disruptive discharge. By a condenser is here meant two metal bodies of any shape separated by insulating material. The e'ectromotive force re- quired to break down a dielectric depends upon three things, namely, (a) the shape of the metal bodies, (6) the minimum dis- tance* between the metal bodies, and (c) the nature of the dielec- * This is not true when the distance is very small or when the bodies are in a very good vacuum. ELECTRIC CHARGE AND THE CONDENSER. 147 trie. The dependence upon the shape of the metal bodies is illustrated by the fact that a given electromotive force will produce a much longer spark between points than between flat metal surfaces. In the whole of the following discussion the dielectric is assumed to be between flat metal plates. When the dielectric is perfectly homogeneous like air or oil, the voltage required to break it down is very nearly proportional to its thickness, and the voltage required to break down such a dielectric divided by the thickness of the dielectric is called the specific strength of the dielectric. Thus the specific dielectric strength of air is about 35,000 volts per centimeter. When the dielectric is non-homogeneous the voltage required to break it down is not even approximately proportional to its thickness. The most familiar example of a non-homogeneous dielectric is the material which is used for insulating the windings of dynamos and transformers. This material is made up of layers of cloth and varnish and mica with occasional layers of air. If a tank is made with one wall of porous material like unglazed earthenware, the pressure of the fluid in the tank has three important effects upon the wall, namely, {a) a certain amount of fluid soaks through the wall, (&) the wall is slightly elastic and it yields a little to the fluid pressure, and (c) the wall has a certain ultimate strength and it will burst if the pressure exceeds a certain amount. Similarly the electromotive force which acts on a condenser has three important effects upon the dielectric of the condenser, namely, (a) a certain amount of electric current "soaks" through the dielectric as it were, because the dielectric is an electrical conductor although a very poor one, {b) the dielectric has a certain amount of electrical "elasticity" (induc- tivity as it is properly called), and it "yields" a little to the electromotive force and allows a certain amount of charge to be drawn out of one plate and forced into the other plate of the con- denser, and (c) the dielectric has a certain ultimate strength and it will be ruptured if the electromotive force exceeds a certain amount. 148 ELECTRICITY AND MAGNETISM. to high voltage electric machine B W. Fig. 126. Spark guage diagram. 97. The spark-gauge. The electromotive force required to produce a spark between polished metal spheres in air depends upon the length of the air gap between the spheres and upon the diameter of the spheres; and the accompanying table gives the ob- served sparking voltages corres- ponding to different lengths of air gap and different diameters of spheres. The spark-gauge is an arrange- ment for measuring an electromo- tive force by observing the length of spark it will produce. As an example consider the following test of the break-down voltage of the rub- ber insulation on a wire. The ar- rangement is shown in Fig. 126. The two spheres BB of the spark gauge are connected to a high voltage electric machine,* one of the spheres is connected to the metal core of the wire to be tested, and a wire from the other sphere is wrapped around the outside of the insulation of the wire to be tested, as shown. The spheres BB are near together at the start, and they are slowly separated until the spark breaks through the insulation on the wire and ceases to jump between the spheres. For example the air gap between the spheres was increased to 0.6 centimeter before the insulation on the wire broke down, and the spheres were each 2 centimeters in diameter; therefore the break-down voltage, as taken from the table, was 20,400 volts. Break down tests are nearly always made in practice by using alternating voltage from a step-up transformer, and the spark gauge usually has needle points instead of polished metal spheres. *See Art. no. ELECTRIC CHARGE AND THE CONDENSER. 149 TABLE* SPARKING VOLTAGES IN AIR AT 18° C. AND 745 MM. PRESSURE. Spark gap in centimeters Between polished metal spheres 0.5 centimeter diameter. Volts Between polished metal spheres 1.0 centimeter diameter. Volts Between polished metal spheres 2 centimeters diameter. Volts Between polished metal spheres 5 centimeters diameter. Volts O.I 4.830 4,800 4,710 0.2 8,370 8.370 8,100 0.3 11.370 11,370 11.370 0.4 13,800 14,400 14,400 0.5 15,600 17,400 17,400 18,300 0.6 17,100 19,800 20,400 21,600 0.7 18,300 21,900 23,100 24,600 0.8 18,900 24,000 26,100 27,300 0.9 19,500 25,500 28,800 30,000 I.O 20,100 27,000 31,200 32,700 I.I 20,700 33,300 35,700 1.2 21,000 35,400 38,400 1-3 21,600 37,200 41,100 1.4 21,900 38,700 43,800 i-S 22,200 40,200 46,200 1.6 41,400 48,600 98. The disruptive-discharge as a means for exciting electric oscillations. The method described in connection with Fig. ii8 for producing electric oscillations is never used in practice; a more satisfactory method is as follows : A condenser C, Fig. 127 to high voltage supplfi Fig. 127. (usually consisting of a number of glass jars with coatings of tin foil inside and outside, called Leyden jars), is connected to the high-voltage terminals a and & of a step-up transformer. As the voltagef between a and b rises the condenser becomes * A table giving sparking voltages between needle points is given in Franklin and Esty's Elements of Electrical Engineering, Vol. II, page 44. b 150 ELECTRICITY AND MAGNETISM. charged, eventually the spark gap G breaks down, and then the charge on the condenser surges back and forth through the inductance coil L and across the gap G until the energy of the charge is dis- sipated. When the back and forth surges cease, the air gap G quickly cools* and regains its insulating power, the condenser is again charged until the gap G breaks down, and another series of surges takes place, and so on. The Hertz oscillator. Two brass rods A and B, Fig. 128, have a spark gap G between them. The rods are connected to the high-voltage terminals of an induction! coil, and at each interruption of the primary circuit of the induction coil the rods A and to terminah ot II 5 ^re charged sufficiently to produce a high voltage G , n tu- 1 • induction coil } spark across the air gap G. 1 his spark is a sudden break-down of the insulation of the gap, and this break-down is followed by Fig. 128 a back and forth surging of current across the gap and along the rods A and B. A condenser C and an inductance coil L arranged as shown in Fig. 127 constitute what is called an electric oscillator. Also the arrangement of the two rods A and B in Fig. 128 is an electric oscillator. The type of oscillator shown in Fig. 128 was devised by Heinrich Hertz in 1888, and this type of oscillator gives off a large portion of its energy in the form of electric waves. The use of the electric oscillator in wireless telegraphy. Figure 129 shows the essential features of a sending station for wireless telegraphy. A condenser discharges across an air gap G thus producing high-frequency surges or oscillations through the coil L. This coil L serves as the primary coil of a trans- former (without iron) the secondary coil of which is S, and the * The air in the path of an electric spark owes its electrical conductivity not only to high temperature, but also, and indeed chiefly, to the fact that the air molecules are broken up into charged atoms which are called ions. t The reader must distinguish between the two terms induction coil and induc- tance coil or inductance. antena ELECTRIC CHARGE AND THE CONDENSER. 151 high frequency alternating electromotive force thus induced in the coil 5 produces high-frequency surges of current up and down in a sending antenna, and electric waves pass out from the antenna because of these surges. These electric waves pro- duce up and down surges of current in a similar receiving antenna at the dis- tant station, and the surges of current thus produced in the receiving antenna actuate the receiving instrument. The - antenna as usually constructed consists of a wide band of wires stretched be- 6 tween two cross pieces and supported by two masts, the supporting cables be- ing insulated, and the band of wires be- ^'^' ^^^' , , ., „ , . , , Essential features of wire- nig connected to the coil 5 which is ^ss sending station. shown in Fig. 129. \ ground 99. The making of ozone. Ozone is a form of oxygen in which three atoms are joined together in a molecule, whereas the molecule of ordinary oxygen consists of two atoms. Ozone is a very active oxidizing agent. It is a powerful antiseptic, and it is extensively used in some European cities for the sterilization of water. When the disruptive discharge takes place in air small quanti- ties of nitrous oxide are formed and also a portion of the oxygen of the air is converted into ozone. The molecules of oxygen and nitrogen are torn to pieces (to atoms) by the disruptive discharge, and when recombination takes place some of the oxygen atoms unite in triplets (ozone) and some of the oxygen atoms combine with nitrogen atoms, forming nitrous oxide. In an intense electric spark a large amount of nitrous oxide and a small amount of ozone are formed, in the diffused discharge which is known as the corona discharge (see Art. iii) ozone alone is formed. The essential features of the ozone machine are shown in Fig. 152 ELECTRICITY AND MAGNETISM. 130. The two metal plates A and B are connected to the high- voltage coil of a step-up transformer. The glass plate between A and B serves as a barrier to prevent the formation of an intense spark from A to B; with this glass plate in position the metai plate A glass pUte S S 6_ metal plate B Fig. 130. Essential features of ozonizer (o and 6 connected to high voltage supply of alter- nating current). entire region 55 is filled with the corona discharge, and a blast of air is blown through the region 55, thus bringing a large quantity of air under the influence of the corona discharge. 100. The electric field. When a momentary electric current flows through an open circuit, certain important effects are pro- Fig. 131. duced in the gap which breaks the circuit. In order that these effects may be easily observed a very high voltage must be used. ELECTRIC CHARGE AND THE CONDENSER. 153 The most convenient device for generating a high voltage is the influence electric machine which is described in Art. 1 10. Figure 131 shows two brass balls A and B which have been charged by a momentary electric current drawn out of one ball and pushed into the other by an influence machine. When an ordinary wooden tooth-pick suspended by a fine thread is placed in the Fig. 132. region between A and B, the tooth pick points in a definite direction at each point very much as a magnetic needle points in a definite direction at each point when it is placed between magnet poles. The short black lines in Fig. 131 and 132 repre- sent the various positions of the tooth-pick. The behavior of the tooth-pick shows that the whole region sur- rounding the charged metal balls A and B in Fig. 131 is in a peculiar condition, and this region is called an electric field. The direction of the electric field at each point is indicated by the direction of the tooth-pick when it is placed at that point, and lines drawn through the electric field so as to be, at each point, in the direction of the field at that point are called the lines of force of the electric field. Figure 132 shows the lines of force of the electric field between two charged flat metal plates. The lines of force in the region between the plates are straight lines, and the electric field is said to be uniform. 154 ELECTRICITY AND MAGNETISM. loi. Intensity of electric field. It would be permissible to adopt arbitrarily the ratio Ejx as a measure of the intensity of the uniform electric field be- \silk thread tween the flat metal plates in Fig. 132, E being the elec- tromotive force between the plates and x being the dis- tance between the plates. Thus the intensity of the elec- tric field would be expressed in volts per centimeter or volts per inch. It is desirable, how- ever, to base the definition of electric field intensity upon some observable effect as in the following discussion. Fig. 133, are connected to an electromotive force E. The l|l|l|l|l|l|l|l|l hattery Fig. 133. The ball 6 oscillates to and fro. Two metal plates A and B, electric machine giving a high electric machine is represented in Fig. 133 as a battery for the sake of clearness. A small metal ball b is suspended between A and 5 by a silk thread. If this ball is started it continues to vibrate back and forth from plate to plate. Regarding the behavior of the vibrating ball the following statements may be made: (a) Work evidently is done to keep the ball b oscillating back and forth, and this work is evidently done by the battery. {b) The only way the battery can do work is by continuing to draw charge out of one plate and push it into the other plate. It is evident therefore that the ball carries charge back and forth between the plates. (c) The successive movements of the ball are similar, and there- fore if the ball carries charge at all it must carry a definite amount each time it moves across. Let this definite amount of charge be represented by q; this charge is positive when the ball moves from A to B, and negative when it moves from B to ELECTRIC CHARGE AND THE CONDENSER. 155 A. At each movement of the ball the battery supplies the amount of charge g, drawing it out of plate B and pushing it into plate A. Therefore at each movement of the ball the battery does an amount of work Eg according to equation (i) of Art. 94. (d) Let F be the average mechanical force acting on the ball b while it is being pulled across from plate to plate. Assuming the ball b to be very small in diameter, it moves the distance x in traveling from plate to plate. Then Fx is the amount of work done on the ball while it moves from plate to plate. (e) The work Eq done by the battery during one movement of the ball is equal to the mechanical work Fx done on the ball, therefore we have Fx = Eq, or F=f-5 (I) Any region in which a charged body is acted upon by a force* is called an electric field. Thus the region between A and B in Fig. 133 is an electric field because the charged ball b is acted upon by the force F. The force F with which an electric field pulls on a charged body placed at a given point in the field is proportional to the charge 2 on the body so that we may write : F = k (2) in which / is the proportionality factor, and it is called the intensity of the electric field at the point. From equations (i) and (2) it is evident that the intensity of the electric field between the plates A and B in Fig. 133 is: /=! (3) that is, the intensity of the electric field between the plates is equal to the electromotive force between the plates divided by * A force which depends upon the charge on the body and which does not exist when the body is not charged. 156- ELECTRICITY AND MAGNETISM. the distance between the plates. In the above discussion F is spoken of as the average force acting on the ball b in Fig. 133 while the ball is moving from plate A to plate B. As a matter of fact this force is constant if the ball b is very small. Direction of electric field at a point. The direction of an electric field at a point is the direction in which the field would pull on a positively charged body placed at that point. Tension of the lines of force in an electric field. Two op- positely charged metal plates attract each other as stated in Art. 87. Thus the oppositely charged plates in Fig. 132 attract each other. This attraction may be thought of as due to a tension of the lines of force; that is, the lines of force may be thought of as if they were filaments of rubber stretching from plate to plate and pulling the plates towards each other. If the lines of force in an electric field are like stretched fila- ments of rubber one would expect the lines of force to pull outwards on every part of the surface of a charged body. In fact each part of the surface of a charged body is pulled out- wards by the surrounding elec- tric field. This outward pull may be beautifully shown by pouring melted rosin in a thin stream from a metal ladle which is supported by an in- sulated handle and connected to one terminal of an electric machine. The lines of force which emanate from the lip of the metal ladle pull the melted rosin into extremely fine jets which shoot straight outwards from the lip. These jets congeal in the form of excessively fine fibers which float about in the air. 102. The idea of electric charge as the ending of electric lines of force. Figure 134 represents two metal bodies A and B to Fig. 134. ELECTRIC CHARGE AND THE CONDENSER. 157 which a battery is connected as shown. The battery draws a certain amount of charge out of one body B and forces it into the other body A , and the entire surrounding region becomes an electric field, the lines of force of which are shown in the figure. The positive charge on body A may be thought of as the beginning of the lines of force, and the negative charge on body B may be thought of as the ending of the lines of force, the direc- tions of the lines of force being indicated by the arrow heads in the figure. 103. The pith-ball electroscope. The presence of an electrical field may be shown by the behavior of a suspended wooden tooth- pick as described in Art. 100, and such a device may therefore be called an electroscope. A more sensitive electroscope is made pith balli Fig. 135. by suspending a small pith ball by a very fine slightly conducting thread. When a charged body is brought near to such a sus- pended pith ball the ball becomes charged as indicated in the figure, and the lines of force from the charged body to the ball pull the ball towards the body as shown. The suspending thread may be made slightly conducting by soaking it in dilute salt water and allowing it to dry. 104. Electric charge resides wholly on the surface of a metal body. Experiment shows that to whatever degree a hollow metal shell may be charged, no effect of the charge can be observed 158 ELECTRICITY AND MAGNETISM. inside of the shell, however thin the shell may be; that is to say, the lines of force of the outside electric field do not penetrate into the metal but terminate at its surface. Therefore the elec- tric charge on a metal body may be thought of as residing on the surface of the body. Figure 136 shows a hollow metal ball C placed between two charged bodies A and B. The presence of the ball C modifies the trend of the lines of force as may be seen by comparing Fig. 136 with Fig. 134, but the lines of force do not penetrate to the interior of the ball C. The interior of a metal shell is entirely screened from outside electric field* This is an experimental fact. An electric field may be detected by its action upon a very light body like a suspended tooth-pick or a suspended pith ball. No evidence of electrical field can be detected inside of the ball C by such a device. Fig. 136 Fig. 137. Mechanical analogue of electrical screening. Consider a mass of steel B, Fig. 137, which is entirely separated from a sur- rounding mass of steel by an empty space eee. Stress and dis- tortion of the surrounding steel cannot affect B in any way, and conversely stress and distortion of B cannot affect the sur- rounding steel, because the empty space is incapable of trans- mitting stress. This empty space, in its behavior towards * The screening is not complete while an electric field is changing rapidly. ELECTRIC CHARGE AND THE CONDENSER. 159 mechanical stress, is analogous to a metal (or any electrical conductor) in its behavior towards electrical stress (electrical field). 105. A charged conductor shares its charge with another con- ductor with which it is brought into contact. A brass ball with a glass handle may be charged by touching it to one terminal of an influence machine, and if the brass ball is brought near to a sus- pended pith ball, as shown in Fig. 135, the charge on the brass ball will be indicated by the behavior of the pith ball. A brass ball A is charged by touching it to a terminal of an influence machine, the ball A is then touched to another brass ball B {A Fig. 138. Charge on single ball. Fig. 139. Charge shared by two balls and B both have glass handles) , ifeew 6o