The sections of the armature coil included between the points where connection is made to the commutator, all have the same number of turns. In the diagram only one turn is shown for each section, but any number may be used.

If the ends of the external circuit are connected to the two brushes A and B there will be a current from A to B as indicated. For the brush A rests upon the upper segment in the commutator which is connected with the top of the wire coil, and is in this case a point of high potential, while similarly the brush B is in connection with the bottom of the coil where the potential is low. The flow of current within the armature coil is around on each side as shown by the arrows, the two currents coming

A

together at the top and flowing out through the commutator at A, around through the external circuit, and in at the bottom of the armature coil where the current divides, half flowing around on one side and half on the other. The case resembles an external circuit connected to two batteries joined in parallel (Fig. 436). The electroFIG. 436.-Two batteries in motive force of each battery corresponds parallel. to that of one side of the armature.

B

740. Drum Armature.-Of every turn of wire on a ring armature part lies on the inside of the ring, and this does not contribute to the electromotive force. Whatever slight effect it may have, due to the weak magnetic field inside of the ring, is in opposition to the outside part. It is desirable to have as little inactive wire as possible in an armature since it adds to its resistance.

The drum armature is like a ring armature where the opening in the ring is filled up with iron and the turns of copper wire pass clear across the ring from one side to the other, so that the only inactive wire is that across the ends.

The core is a cylinder of iron made of a pile of thin sheet-iron plates bolted together, around which the coils of wire pass longitudinally lying in grooves made for them. In winding, the wire starts at one of the commutator segments, is passed around the core lengthwise in one of the grooves the desired number of times, suppose twice, and then is connected to the next com

mutator segment. It is then carried right on around the core in the next groove in the same direction as before, making two more turns, and then connected to the third segment of the commutator. This process is continued until the segment is reached where the winding began and there the end is made. fast. In this way an endless coil is constructed just as in the Gramme ring, and between each commutator segment and the one opposite there are two paths by which the current may flow within the armature, so that the current divides in the armature just as in the ring armature.

741. Foucault Currents.-In each of these armatures the inductive action which causes electromotive force in the copper coils also causes a similar electromotive force in the iron core tending to set up currents within the core itself. Such currents would spend energy in heat, and the double disadvantage would result that more work would have to be spent in turning the armature, and this useless expenditure of energy would go to unduly heat the machine.

In order to prevent these Foucault currents, or eddy currents as they are often called, the iron core is laminated or made up of thin plates insulated from each other by varnish, or paper, and lying across the direction in which the currents would flow. The thinner the sheets of iron the more perfectly is this waste. of energy prevented.

742. Electromotive Force of Armature.-The electromotive force of a ring armature is easily reckoned. The electromotive force of the ring is the same as that of one side, since the two sides of the ring act in parallel. Let N be the number of lines of force passing through the armature, n the number of revolutions per second, and C the number of turns of wire on the ring, then since each turn cuts down on one side across all N lines of force once

in every half revolution, that is in

1

2n

second, the

average electromotive force induced in each coil as it moves across the field

But all the coils on one side of the ring act together or in series,

hence if there are C coils of wire on the ring the total electromotive force must be

The electromotive force depends on three factors: the number of lines of force through the armature, the number of revolutions which it makes per second, and the number of coils of wire upon it.

The electromotive force of a drum armature is calculated from the same formula, C representing the whole number of wires on the armature which cut across lines of force.

743. Field Magnets. In most dynamo machines and motors the armature rotates between the poles of an electromagnet which receives its exciting current from the armature.

Three

FIG. 437.-Series and shunt field magnets.

modes of winding are in use, series, shunt, and compound. In the first diagram in the figure is shown a series-wound dynamo. The whole armature current passes around the field magnets and through the external circuit. Any resistance introduced into the external circuit, causing the current to diminish, weakens the magnetic field and therefore makes the electromotive force of the machine less. When there is no current flowing its electromotive force is zero except for the residual magnetism.

In the shunt arrangement the current in the armature divides, part flowing around the magnet and part to the external

circuit. In order that but a small current may be taken for the magnet, it is wound with many turns of rather fine wire.

The current through the shunt coil depends only on its resistance and on the difference of potential of the brushes; hence it is constant and the strength of the magnet is constant so long as the difference in potential of the brushes is unchanged. The electromotive force of such a dynamo is very nearly constant, but is slightly greater when no external current is flowing, for with increasing current in the external circuit there is more current and a greater fall of potential in the armature itself.

Compound winding is a combination of the shunt and series arrangements, in which there is a shunt coil and also a few turns carrying the whole current around the magnets. In this way a dynamo may be made to maintain a nearly constant potential at the terminals, though the external current may vary greatly, or it may be over-compounded so that its terminal electromotive force may be greater with large currents than with small.

Part II.-Direct-current Motors.

744. Motors.- An electric motor is an appliance in which an electric current gives motion to an armature, thus producing

mechanical work. Small direct-current motors usually have ring or drum armatures and are in most respects like dynamos.

The action of the ring armature in a motor may be understood from the diagram (Fig. 438). The current from a battery or other source is shown as flowing in at the upper brush and out at the lower one. Within the armature the current divides,

half flowing around and down through the coils on one side and half through those on the other side as shown by the arrows, and the effect of these currents in the armature is to make each half of the ring a magnet with its north pole at the top and south pole at the bottom. The attractions and repulsions between these poles and those of the field magnet cause the armature to rotate in the direction of the large arrows.

Another aspect of the action is worth considering. The gaps between the pole pieces and the armature are regions of intense magnetic force, and the wires on the outside of the armature carry currents directly across these lines of force, up (perpendicular to the paper) on the left and down on the right; there is, therefore, a force (§687) urging these wires to move across the lines of force toward the top of the diagram on the left and toward the bottom on the right.

745. Energy Spent in Motor.-While the motor is running mechanical work is being done in addition to the energy which is spent as heat in the armature in consequence of its resistance. But the total energy spent per second in the motor is equal to the product of the current strength by the difference of potential between the brushes. Therefore if the current is kept constant the difference of potential between the brushes must be greater when the motor is running and doing work than when the armature is at rest.

This increase in the difference of potential between the brushes due to the motion of the armature is the back electromotive force of the motor. There must be such a back electromotive force in every kind of device in which motion results from the flow of an electric current.

Let V1- V2 = difference of potential between brushes of motor.

1

2

IR = drop in potential due to the resistance of the armature.

V1 − V2 =E+IR where E is the back electromotive force.

2

746. Back Electromotive Force.-Connect an electric motor to a battery by which it may be driven and introduce into the circuit an incandescent lamp which will glow with full brilliancy when the armature of the motor is held stationary. On letting the armature run the lamp grows dim, and an ammeter in circuit