ELECTRICITY

Let the coil consist of N turns of wire, then the flow of lines due to a current, I, is F=TOR 4π N2I Since there are N turns in the coil, the effect is the same as if it had but one turn and N times the above number of lines were passed through 4πN2I it; hence, NF= If the current turned on IOR or off is one C.G.S. unit, the number of lines 4TN1 which is called the inductance, or R' co-efficient of self-induction of the coil.

becomes

The value of the induced E. M. F. at a time, t, after the current has been made or broken depends upon the rate at which the current changes; but since the rate at which the current changes is not uniform, the induced E. M. F. is not uniform. If in a time, dt, which is small as compared with the time required for the current to reach its maximum value, the current changes by an amount, di, the rate at which the current is

di

changing at the time is and the value of the dt'

di dt

self-induced E. M. F. at the time, t, is-L. For the unit of self-induction, see ELECTROMAGNETIC UNITS (§ 110).

If R is

873. VALUE OF INDUCED CURRENT. If R is the resistance of a circuit having inductance, and i the value of the current at any time, t, after the circuit is closed, then from Ohm's law Ri is the value of the E. M. F. producing the current, and is equal to the impressed E. M. F., E, minus the di reverse E. M. F., L, due to the inductance; hence

di

dt

RiEL- ; for a given coil, L, is constant, and the equation solved gives the value of the current,

Rt

L

i=I(1-e). Therefore, after a time, 4, the t, current is less than its maximum value, I, by a quantity, Ie ̄ ̄ The quantity is called the

Rt

L

is

equal to unity; then 1 - s L
is the base of the Napierian system of logarithms,
and has for its value 2.7183, which, substituted,
gives 0.632 as the value of the current at the end
L

of a time,

Several of the more important applications of electromagnetic induction are described in the following sections.

874. INDUCTION-COILS. An induction-coil is an instrument for changing the energy of a current into that of another having a higher or lower E. M. F. It consists essentially of two coils having a common magnetic circuit. The coil into which the current is sent is called the primary, and that in which a current is induced, the secondary.

and both have the same iron core, consisting of a bundle of soft iron wires, as shown in Fig. 55, in order that a current made or broken in the primary may project the greatest possible number of lines through the secondary. Since the induced E. M. F. depends upon the change in the number of lines threading through the secondary, it is essential that the current in the primary be interrupted, or changed in value. Ordinarily, this is accomplished by means of an automatic circuit-breaker placed in circuit with the primary, as at B; when the primary circuit is closed, the core attracts the mass of iron, M, attached to the spring, E, thus breaking the circuit at B; the core, losing its magnetism, allows M to spring back, and the circuit is made again. Mechanical interrupters are also used.

The condenser, C, is connected with the points
T and T'; when the primary circuit is broken, the
inductance of the primary produces a direct
E. M. F., which prevents the current from dying
down immediately, and the current thus induced
flows into and charges the condenser, C; but the
condenser is free to discharge through the
primary, and sends a current through it in the

reverse direction, so that the flow of lines in the
core is not only reduced to zero, but reversed,
thus producing a more intense effect.

It has been shown that the condenser should
be of such capacity that it absorbs a charge at a
rate equal to the full delivery of the primary cir-
cuit during the time the circuit-breaker is opening
to the maximum sparking-distance; the condenser
then gives an equal reverse current through the
primary, thus doubling the change in the magnetic
flow, which doubles the induced E. M. F. The sec-
ondary is provided with two terminals, S and S',
between which the discharge of the secondary
takes place when the difference of potential
reaches such a value that the air no longer insu
lates.

in large coils the secondary is wound in flat spirals, well insulated from each other, as the difference of potential between adjacent wires is then not as large as when the coil is wound in layers from end to end. The primary is insulated from the secondary by a glass or rubber tube, and the turns of the secondary well insulated from each other, by boiling in melted paraffine or wax.

Spottiswood constructed a coil, the secondary of which consisted of 280 miles of wire wound in 340,000 turns, and gave a discharge through 421⁄2 inches of air.

A current which is rapidly alternating in direction may be used in the primary, but in that case the circuit-breaker is not used. (See § 76.)

875. TESLA'S INDUCTION COIL. Since the discharge of a condenser is oscillatory (see § 92), the rapidly alternating current thus produced, when sent through the primary of a properly constructed induction-coil, induces E. M. F. 's of enormous values; the discharge under these conditions is extremely beautiful and interesting. (See 894.)

While the above principle has long been known, we are indebted to Tesla for its successful application.

The electrical connections for securing the above conditions are shown in Fig. 56.

I is an ordinary Ruhmkorff induction-coil, the interrupter of which is not shown. The terminals

S

side the secondary, and the terminals of both are brought to the top of the case through hard rubber tubes. The whole is then immersed in oil in a zinc-covered wooden box. The action of the coil depends largely upon the proper adjustment of the capacity, self-induction and resistance in the circuit.

$76. TRANSFOrmer. A transformer is an induction-coil for the purpose of changing an alternating current, usually from a high to a low potential, though the reverse is sometimes the case.

of the secondary SS are connected with the condenser, C; the terminals of the condenser are connected to the primary, P, of the Tesla, or disruptive discharge coil as it is often called. G is a sparkgap consisting of two polished metal balls a small distance apart. S, is the secondary of the Tesla coil. When the current in the primary, P, is broken a high E. M. F. is induced in the secondary S; this charges the condenser until the potential is sufficient to overcome the resistance of the gap, G. The air then breaks down, and the oscillatory discharge of the condenser takes place through the primary, P1.

Fig. 57.

In the induction-coils previously described the object has been to transform a low to a high potential.

Faraday's ring (Fig. 54) is the earliest and the type of all transformers, and the electromotive force generated in the secondary circuit is to that employed in the primary very nearly as the rela tive number of turns in the two coils; if the primary has fewer turns than the secondary, it is called a "step-up" transformer, and a "stepdown" transformer when the primary has the greater number of turns.

Fig. 58 shows the coils. and magnetic circuit of one of the many comThe construction of the Tesla coil is shown in mercial types of transforFig. 57. PP is the primary, wound oppositely, in mers. It will be noticed two parts. In this particular coil each half of the that the magnetic circuit primary is composed of four layers of twenty- is entirely of iron, the four turns each, or ninety-six turns. The sec- iron being built up of ondary, SS, is also in two parts of twenty-thin sheets separated by four layers, ten turns each, or 260 turns for each varnish or simply the half. The two halves are wound oppositely and oxide on the plates, in Fig. 58. connected in series; the secondary is wound order that there may be no electric currents set on two spools of hard rubber, RR, held apart by the up by induction in the iron core. The direction hard rubber rods C. The primary is placed in- of the plate is arranged perpendicular to that in

ELECTRICITY

which the induced current would flow. The coils are placed inside of an iron box, which is then filled with oil, to further insulate the coils from each other.

M

M'

Fig. 59 shows the method of arranging transformers. M and M' are the high potential mains leading from an alternating-current dynamo, A. The primaries, P, are connected in parallel to the mains. The incandescent lamps, L, are placed in the secondaries, S.

The regulation of a transformer is an interesting case of self and mutual induction. The primary remains in connection with the mains, yet very little current flows through it unless the secondary is closed; furthermore, the current supplied by the secondary is the correct amount needed for the number of lamps turned on.

Consider one of the transformers represented in Fig. 59, and let the secondary circuit be open; the reverse E. M. F. in P due to its self-induction almost equals the E. M. F. supplied; hence but little current flows through P. If, now, the secondary be closed, with, say, one lamp in circuit, there will be mutual induction, and this acts in opposition to the self-induction in the primary; thus more of the E.M. F. impressed upon the primary from the mains is allowed to act; or in other words, the mutual induction due to a current in the secondary opposes the self-induction of the primary almost in proportion to the current flowing in the secondary.

If more lamps are turned on, the current in the primary regulates itself to suit the load.

The rate at which electrical energy is transformed into heat in a conductor is I'R (§ 43); therefore, if the current is doubled, the loss in the conductor is four times as great, or varies as to the square of the current. Since the energy of a current is also IV, or the strength of current times the fall of potential, the factors I and V may be varied, and the energy transmitted remain the same. For example, if I is five amperes, and V 1,000 volts, the rate at which energy is transmitted is 5,000 watts also, if I is ten amperes, and V 500 volts, the energy rate is 5,000. Now, if this energy is to be transmitted to a distance, through a conductor having a resistance of ohms, the loss in the conductor

529

would be, for the first case (5) X 2 = 50 watts; while in the second case it would be (10)2 x 2 = 200; therefore it would be more economical to use 5 amperes at 1,000 volts. There is a limit, however, to the extent this principle may be applied. It is not practical to use a voltage as high as 1,000 for incandescent lighting, on account of the danger to life, leakage, and difficulties attending the manufacture of the lamps; hence, when the elec trical energy is to be distributed over distances of as much as one or two miles, the current is generated as an alternating current at, say, 1,000 volts, and changed, by means of a transformer, to a potential of 100 volts before it enters the house or place where it is to be used. The loss in transformation is slight if the transformer is properly constructed.

When very great distances are to be overcome, the current is generated at as high a potential as is practical; it is then transformed to a still higher potential by means of a step-up transformer, transmitted at this potential, and changed back again by a step-down transformer at the other end of the line.

877. ROTARY TRANSFORMERS. A rotary trans former is not, strictly speaking, an inductioncoil, but a dynamo and motor combined. The armature has two sets of windings, one of which receives the current to be transformed, and drives the machine as a motor; the other set of windings on the armature generates a current at the potential desired. Both armatures have a common axis, and rotate in the same magnetic field.

$78. CHOKING-COIL. A choking-coil is one having large self-induction, but little resistance, and used as a resistance for alternating-currents. The primary of a transformer is a good example of such a coil, when the secondary circuit is open. They are usually constructed so that the selfinduction may be varied by varying the magnetic field, or the number of turns in the coil. Such a coil has the property of cutting down the current, but without the expenditure of energy which would take place were a simple resistance used.

879. DYNAMO ELECTRIC-MACHINES. Any treatment of the subject of electromagnetic induction would be incomplete without at least the elementary theory of the dynamo electric machine, which is by far the most important application of this principle. In the following articles no attempt is made to cover any but the most important and essential features of typical forms.

A dynamo electric-machine, or simply dynamo, may be defined as a machine for converting me. chanical energy into the energy of an electric current; it consists of a series of conducting circuits, so arranged that the magnetic flow through them is continually changing. Figure 60 is a diagram of a typical dynamo. A is the armature, made of soft iron, and carrying on its surface the conductors through which the magnetic flow is made to change, and in which the current is generated. S and N are the poles of an electromagnet, F, called the field-magnet; C is the col

1

magnetic flow through the circuit varies as the cosine of the angle revolved through.

The electromotive force generated in the circuit at any time does not depend on the flow, but the rate at which the flow is changing. At position 1, there is a large number of lines through the circuit, but if it be moved through a small angle, CO1, the number of lines is nearly as great as before, while at 3 the same small angle C'03 would produce a large change in the flow, hence the E. M. F. will be o at 1 and 5, and a positive maximum at 3, and a negative maximum at 7.

Let the circle (Fig. 63) be divided up into a great number of small angle parts do, and let dt be the time required for the d conductor to revolve through this angle do. The E.M. F.

a

b

Main Circuit
Fig. 60

A single closed circuit rotating in a uniform magnetic field, as shown in Fig. 61, constitutes

At position 1, the circuit incloses the maximum number of lines; at position 2, the number of lines is proportional to the line Oa, the exact number being Fcos 0, F being the maximum flow, and the angle moved through. At the position 3, the circuit does not inclose any lines; at position 4, the lines thread through from the opposite side of the loop, which is equivalent to a decrease in the flow from a maximum at 1 to a maximum at 5 in the other direction. At 7, the flow is again O, and increases to the maximum at 1; hence the

Fig. 64.

represent equal increments of time begun at 1
(Fig. 62); the vertical distances of the curve I are
the values of the cosine for the different positions
of the conductor, and represent the changes in the
magnetic flow. The corresponding values of the
sines are shown in curve II, the ordinates of which
represent the induced E. M. F. The maximum
values differ by 90°, or a quarter of a period.
The current in such a circuit changes direction to
correspond with the change in direction of the E. M.
F.; such a current is called an alternating current.
In case it is desired to send the current always
in the same direction, the coil terminates in two
parts of a split tube, a
and (Fig. 65) insu-
lated from each other,
and from the shaft; the
brushes, c and d, are
placed so that they ex-
change contacts the
same instant that the
circuit reverses, thus
sending the current in
the same direction, but
varied as before, all the curves lying above the axis,
as in Fig. 66.

с

d

Fig. 65.