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the student on the upper side and toward him on the lower side, the direction of the magnetic field will be as shown. This coil has the same sort of magnetic field and produces the same forces as would be produced by a short thick magnet (shown, in section, by the dotted lines). The northseeking pole is on the left face, and the southseeking pole on the other face, as shown.

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The advantage of regarding the coil as equivalent to a magnet is that one can often more quickly determine the character of the forces when the coil is placed in a magnetic field. For example, consider the case illustrated in Fig. 284. In this figure the current is flowing in at A and out at B; hence the coil may be regarded as equivalent to a short magnet, with poles which are marked N' and S' in the figure. From the known action of poles on one another the rotational forces will be in the direction indicated by the arrows. Compare this case with Fig. 281, where the current and the field have relatively the same direction. In both cases it should be clear that the coils tend to rotate through a quarter-turn, or until the magnetic fields of the coil and the magnet are in the same direction.

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FIG. 283

It can be stated as a general rule that a coil tends to turn into the position where the number of magnetic lines passing through the coil will be a maximum.

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commonly used in the laboratory to measure or to detect small currents. In many cases it is desirable that they be made very sensitive. It is not difficult to understand some essential points which affect the sensibility.

When the suspended coil (Fig. 285) rotates on account of the torque due to the current-magnetic-field forces, it turns against the torque of the fine wire by which the coil is suspended. The smaller the wire used, the farther will the coil turn. To make the opposing torque of this wire very small, the wire is rolled out into

a thin, flat, narrow ribbon. In this form it has approximately the same tensile strength, which it needs to support the coil, but it exerts a smaller torque. The lower connecting wire is usually coiled into a spiral, thus increasing its length and diminishing its torque.

The stronger the magnetic field in which the coil is placed, the greater the torque tending to turn the coil when a current flows through it. The magnets are hence made of special steel which will produce strong fields. The field is often made stronger and more uniform by supporting from the frame of the instrument a soft-iron core in the center of the field (C in the figure).

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The greater the number of turns of wire on the coil, the greater the resultant torque; for there is a torque acting on each turn. But winding on a large number of turns requires the use of small wire. Decreasing the size of the wire and increasing its length increases the resistance of the coil. An increased resistance is for some kinds of work almost prohibitive. Consequently galvanometers of both kinds are made: some with coils with many turns of fine wire, having a high resistance; others with a smaller number of turns, of a larger wire, having a low resistance.

FIG. 285

468. Direct-current ammeters. The more common type of directcurrent ammeters has a coil mounted between the poles of a strong permanent magnet, as in the case of a moving-coil galvanometer. These coils, instead of being suspended with long thin wires, are mounted in jewel bearings, and held in place by two flat spiral springs similar to the hairspring of the balance wheel of a watch. Since the moving coil of an ammeter is entirely too delicate and sensitive to permit large currents to flow through it, most of the current flows through a shunt across the terminals. This arrangement is shown in Fig. 286. C represents the moving coil, and S the shunt. If 0.01 ampere flowing through the coil will give the maximum deflection, and if it is desired to have an instrument that will read a maximum of 10 am

peres, the resistance of the shunt must be of such value that when the total current is 10 amperes, 9.99 amperes will flow through the shunt and 0.01 ampere through the coil. For other values of the current, the part flowing through the coil will always be proportional to the total current (see equation 54, sect. 440). It is customary to number the scale so that it indicates the total current, and not the current through the coil.

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C

S

FIG. 286. An ammeter

469. Direct-current voltmeters. Although the electrostatic voltmeter is commonly used for certain types of work, especially for high voltages, the moving-coil types are frequently used in laboratories when the voltage is that of cells or power circuits which give direct or continuous currents. The moving coil of

a voltmeter is similar to that of an ammeter. There is no shunt, but a high resistance is inserted in series with the moving coil. A voltmeter is connected to the circuit in a

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FIG. 287

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To load

V

different manner from an ammeter. The ammeter is always in series, so that all the current flows through it; the voltmeter is connected across the circuit to the two lines the difference in potential of which is to be measured. Fig. 287 shows symbolically how an ammeter and a voltmeter are connected to the two wires of a battery circuit. The shunt of the ammeter and the series resistance of the voltmeter are shown in the figure. Usually these are on the inside of the instruments and not visible.

It is always a matter of some interest and curiosity to know why two such similar instruments as an ammeter and a voltmeter measure two different things. To aid the student an outline of the theory of the voltmeter will be given here.

The deflection of a voltmeter is proportional to the current which flows through its moving coil. This can be stated by

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where I is the current through the voltmeter coil, k is a constant, and d is the deflection. By Ohm's law the potential difference which is to be measured by the voltmeter is equal to the product of the current through the voltmeter, I, and the resistance of the voltmeter, r, or

V = Ir.

If the value of I from equation (78) is substituted in this equation, we obtain

V = kdr.

(79)

Both k and rare constants; hence equation (79) shows that the deflection, d, is proportional to the potential difference, V, of the points to which the voltmeter is connected. Since the scale may be marked in any desired manner, it can be graduated to indicate volts.

470. Electric motors. The tendency of coils placed in magnetic fields to rotate when the current flows through them is used in

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terminals of the coil, and a current sent through the coil, it would rotate only part way round. But if the terminals of the coil slide over the fixed ends of the connecting circuit in such a way that, as the coil turns around, each terminal of the coil slides off one of the fixed terminals and, a little farther on, slides onto the other fixed terminal, a continuous rotation can be produced. In Fig. 288 the terminals of the coil are shown as curved strips (see also Fig. 289), which, as the coil rotates, slide past the fixed terminals, or "brushes." With this arrangement the current in the side of the coil which happens to be next to the north-seeking pole will always flow away from the student, with the result that the current-magnetic-field force on that side of the coil is always acting downward (the student should verify this). The rotating part of the arrangement by which the current is changed

FIG. 289. A simple commutator

from one wire to another is called the commutator, and the strips to which the ends of the revolving coil are fastened are called the segments.

When the coil has turned through an angle of 90 degrees from the position shown in the figure, there will be in that position no torque tending to rotate the coil. Hence the torque will be neither

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FIG. 290. The armature of an automobile starting motor

continuous nor very effective. To overcome this a large number of coils are placed on the rotating part, with their planes inclined to each other, and instead of there being two segments in the commutator, a large number-thirty or forty-are used.

In Fig. 289 is shown a simple commutator. Fig. 290 shows a commutator (at the right end) and the coils of one type of commercial armature.

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