Gisbert Kapp.

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Generation, Measurement, Distribution,
and Application.












Reprinted from Professional Papers of the Corps of Royal
Engineers, by permission of the Committee of the R. E. Insti-
tute, and with the consent of the author.




THE writings of Mr. Kapp have always interested
American engineers. In fact, whenever a new
branch of our science develops into attractive im-
portance and requires "treatment," we expect that
Mr. Kapp will place the matter before us in simple
terms and illustrate the points of interest by exam-
ples possessing practical importance. The follow-
ing pages accord with the previous writings of Mr.
Kapp in this respect.

Starting with the assumption that the reader is
acquainted with the behavior of steady currents in
circuits whose constants are readily obtainable, he
proceeds to explain the growth of a periodic cur-
rent, and in so doing beguiles the student into



mastering a few simple mathematical methods, a
knowledge of which is fundamentally necessary.

As the volume advances its scope becomes appar-
ent, for it treats in a simple and yet effective man-
ner of periodic currents in general, of the phase
relations of impressed and induced E. M. F's pos-
sible in simple circuits, of Alternators (somewhat
in detail), of the requirements of Central Stations
(briefly), of Alternating Current Motors, and finally
of Multiphase Currents. One does not expect ex-
haustive treatment of any one of these subjects
within the compass of a small book.

From an educational standpoint Chapters I. and
II. are of especial importance. These forty
pages might well be increased fourfold, for al-
though they contain a summary of the elemental
knowledge necessary for a correct understanding of
the principles operating alternating currents in
simple circuits, possessing resistance and self-
induction, they do not treat of capacity effects and
the problems incident thereto. In Chapter IV. we
have some of the formulae for calculating induced


E. M. F.s (whether occurring in alternators or in
transformers) with constants for particular cases of
armature coils. Chapter V. is devoted to Machine
Construction, and points out the dependence of
efficiency on core wastes, giving a curve of the
relation of watts per ton of core metal lost by
hysteresis, to the induction density. Chapter VI.
is devoted to transformers and briefly points out
the necessity for careful design in this, the simplest
of alternate current apparatus. The chapters on
Central Stations are of interest, as they not only
describe a few English plants, but also give us the
author's criticisms on various distribution methods.
The chapters on Alternate Current Motors and Mul-
tiphase Currents complete the little volume.

There are one or two opinions expressed by the
author to which exceptions may be taken, notably
the statement on page 143 that the resultant field
produced by quarter-phase currents varies 40$, and
that the Dobrowolski-Tesla arrangement of three
phased currents produces a shifting field of more
constant value than the quarter-phased or two-


phased arrangement. For a discussion of these
points the reader may consult The Electrical World,
vol. xix., p. 249, Kelly; vol. xx., p. 4, Dolivo-
Dobrowolski; p. 36, Kelly, Steinmetz; p. 114, C.
E. L. Brown.

In general, however, Mr. Kapp's statements are
clear, true, and convincing, and are of interest and
value to every American engineer.






APPENDICES, . . ,. ' ~^ 44


APPENDIX, . * ^.." , . . 5&






CURRENTS, '. - ' I0 5






Alternating Currents of Electricity:





WHEN we think or speak of electric currents we
are accustomed to regard them in the light of ma-
terial currents, of something which flows along a
path formed by the conductor, and has, therefore,
a direction. We say that electricity flows along
the conductor or through the conductor from the
place of higher to that of lower potential; in the
same way that water will flow from , the higher to
the lower level through a pipe. Such a view is, of
course, purely conventional. As a matter of fact
we do not know whether it is the positive electric-



ity that flows ip. t a : given direction, or the negative
electricity that^febws in the opposite direction, or
, l <ynbth^r ^bot& electricities flow simultaneously in
opposite directions, or whether there is any trans-
fer of electricity through the wire at all. Indeed,
according to modern views, there is merely transfer
of energy,. but not through the wire, the transfer
taking place throughout the space surrounding the
wire. To talk about an electric current flowing
through a wire may therefore be an unscientific
way of expressing our meaning, but it is a very
convenient way, and, therefore, generally adopted.
Now in adopting this conception of the flow of a
certain thing called electricity along a predescribed
path, we have also adopted the idea that this flow
takes place in a direction which is perfectly well
defined in each given case. We have no sense by
which we can directly perceive an electric current
or note its direction. It is true that if we get a
shock we are made aware that a current has passed
through us, but no number of shocks will help a
man in the slightest degree to an understanding of
the real nature of electric currents, nor enable him
to determine their direction. We must be content


to study, not the currents themselves, but their
chemical, thermic, magnetic, and mechanical ef-
fects. Amongst other things we must also deter-
mine the direction of current by one or other of
these effects. For instance, we know that a wire
stretched north-south over a compass needle, and
carrying a current, will deflect the needle. If the
north-seeking end is deflected to the left or west-
ward, we know by Ampere's rule that the current
flows from south to north. Conversely, if the de-
flection is in the opposite sense, we conclude that
the current is from north to south. If the current
is obtained from a battery without the intervention
of any piece of moving apparatus, such as a revers-
ing key, we notice that the needle once deflected
remains in that position as long as the current
flows, and we naturally conclude that the current
flows continuously in the same direction, that it
is, in fact, a " continuous " current. Now suppose
you were to notice that the needle, after remaining
deflected to the left for a certain time, were to
swing over to the right and to remain deflected in
that position an equal time, then again swing to
the left, and so take alternately these two opposite


positions, you would immediately conclude that
someone had put a reversing key into your circuit,
and was amusing himself by working it at regular
intervals. The behaviour of the needle would, in
fact, have shown you that you have no longer to
do with a continuous current, but that your current
has become an alternating current, that is, a cur-
rent which changes its direction periodically. You
will notice that I have assumed that the needle has
time to follow each impulse of the current, in other
words, that the periodic time of the current is large
in comparison with the time of oscillation of the
needle. Suppose, however, that I were to work the
reversing key so fast that the needle cannot fol-
low the different impulses ; in this case it will, of
course, remain in its north-south position, and will
have become useless as an instrument for the de-
tection of an alternating current. We require an
apparatus which will respond far more readily than
a sluggish compass needle to the different current
impulses which follow each other with great rapid-
ity. To get such an apparatus, let us take an iron
diaphragm, and hold near the centre of it a coil of
insulated wire forming part of the circuit, or bet-


ter still, an electromagnet with a laminated core;
why the core should be laminated I shall explain
later on. For the present it interests us to note
that the poles must be in such a position that at
least one of them may act on the diaphragm.
Thus a ring-shaped magnet which has no free
poles would not serve our purpose ; a straight bar
magnet, however, will do well. Now observe what
happens if an alternating current is sent through
the coil of this magnet. At the moment of press-
ing down the key to complete the circuit the bat-
tery begins to send a continuous current through
the coil and the core begins to get magnetized.
The magnetization grows from zero to a maximum,
and retains that value until the key is lifted again,
when it falls to zero. Now reverse the current and
go through the same process. It is obvious that at
each reversal of the current the magnetization must
pass through zero, and the end of the core which
is presented to the diaphragm will alternately be-
come a north and south pole. The diaphragm will,
therefore, be alternately attracted and released, or,
in other words, it will vibrate, and if the period of
vibration is quick enough, that is, if I manipu-


late the reversing key very rapidly, a musical note
may be produced. Conversely, if I approach an
electromagnet to a diaphragm and find that the
latter is not permanently attracted, but is set in
vibration and emits a musical note, then I conclude
that the current which flows through the coil of the
electromagnet is an alternating current, and the
rapidity of the alternations, or, as it is called,
the "frequency" of the current, can be judged
from the pitch of the note. In explaining this
experiment I have, for the sake of simplicity, as-
sumed that the current is furnished by a battery,
and that its alternating character is produced by
means of a reversing key. This mechanism is,
however, not an essential part of the experiment or
of its explanation. The essential part is that the
current shall grow from zero to a maximum, and
diminish again to zero, then change its direction
and grow to a negative maximum, diminish to
zero, then become positive again, and so on. Such
a current is produced by a certain class of electric
machines called "alternators," which will occupy
us a good deal during this lecture. But before en-
tering into this subject I wish to show you experi-


mentally the fact that an alternating current can
produce these oscillating or wave-like magnetic
effects which I described a moment ago. The ap-
paratus I shall use in my illustrations is extremely
simple. I have here a small electromagnet of the
kind used in connecting arc lamps to alternating
current circuits, and which is technically termed a
" choking coil." For a diaphragm I use the bottom
of an ordinary biscuit tin, and you will observe that
when I approach one end of the choking coil to the
biscuit tin there is emitted a sound which can be
heard all over the room. The sound is not exactly
a clear musical note, because, as might have been
expected in a rough-and-ready apparatus of this
kind, the elasticity of the diaphragm is by no
means perfect. But such as the sound is, it serves
quite well to show that the diaphragm is set vibrat-
ing by the current, and, in fact, every telephone
receiver exemplifies the same action.

The study of alternating currents is greatly facil-
itated by a rational and simple manner of repre-
senting them graphically. There are various ways
in which we can so represent not only alternating
currents, but any quantity which varies periodi-


cally. The most obvious way of representing an
alternating current is by drawing a curve, the two
co-ordinates of which represent time and the in-
stantaneous current strength. In Fig. i the time

FIG. i.

is measured on the horizontal, and the current
strength on the vertical. We thus obtain a wavy
line which cuts at regular intervals through the
axis of abscissae. These are the points of reversal
when the current strength is maximum, positive
where the line lies above, and negative where it
lies below the axis. The exact shape of the curve
depends on the construction of the machine which
produces the alternating current; but I may at
once say that in nearly all the theoretical investi-
gations of alternating currents it is assumed that
the curve follows, or rather represents, a sine func-


tion, and that this assumption is sufficiently near
the truth for all practical purposes. All of you
know, of course, what a sinusoidal curve is, and I
need, therefore, not explain it at length. As, how-
ever, the way of plotting a sinusoidal curve brings
me to a second method of representing an alternat-
ing current graphically, I must say a few words
about it. Imagine yourself standing some distance
in front of a steam engine in a line with the axis of
the cylinder, and looking at the crank pin. The
latter will then appear to be moving up and down,
making equal excursions to both sides of the cen-
tre of the crank shaft. You will, in fact, see the
projection of the crank on a vertical, and the length
of this projection at any instant is equal to the
length of the crank multiplied with the sine of the
angle which the crank makes at that instant with
the horizontal. The angle is, of course, the pro-
duct of the angular velocity and the time; and
since the angular velocity is constant, you will also
obtain a sine curve by plotting the time on the hori-
zontal and the projection of the crank on the verti-
cal. The curve I in Fig. i has been so obtained.
We may, however, save ourselves the trouble of



plotting this curve, for we can represent the alter-
nating current more directly by the projection on
the vertical of a line OI (Fig. 2) revolving with a
constant angular speed round the fixed centre O.

The length of OI represents to any convenient
scale the maximum value of the current, or the
crest of the current wave, and its projection repre-
sents its instantaneous value. You see that for

FIG. 2.

half a revolution this value is positive, and for the
other half of the revolution it is negative.

In this diagram, which is called a "clock dia-
gram," we must therefore make a projection in
order to find the instantaneous value of the current.
This is less laborious than the plotting of a sine
curve, but it is possible to represent the current in


a still more simple way. Those of you who are
familiar with Zeuner's valve diagram will immedi-
ately see how this can be done. Instead of draw-
ing the circle round O as centre, we draw it passing
through O. The diameter of this circle (Fig. 3)


FIG. 3.

represents to any convenient scale the maximum
value of the current. Then the instantaneous cur-
rent is given directly by the length of the revolv-
ing line between O and the circle. To obtain the
negative values of the current, we reproduce the
circle on the opposite side; this in the figure is
shown dotted.

To illustrate the use of any of these graphic
methods of representing alternating currents, let
us suppose that we have to solve the following
problem : We have an iron core wound with two
independent coils, each carrying an alternating


current. The two currents shall have the same
frequency, that is to say, the time which elapses
between two succeeding positive maxima or nega-
tive maxima shall be the same for both currents,
but the maxima in the two currents shall not occur
at the same moment. In other words, the phase
of one current shall lag behind that of the other,
just as in a two-cylinder steam engine one crank
lags behind the other. Now the problem we have
to solve is : what will be the magnetization of the
core at any instant? To find this we must of
course know the instantaneous value of the excit-
ing power, or the ampere turns resulting from the
action of both currents combined ; we must, in fact,
find what resultant current acting alone will have
the same effect as the two given currents acting
together. Let, in Fig. i, the curves I and II rep-
resent the two currents, or better still the ampere
turns of these currents, then the ampere turns of
the resultant current are found by plotting the
algebraical sum of the ordinates. Thus we obtain
curve III. It is self-evident, and needs, therefore,
no elaborate proof, that this curve can also be
obtained from Fig. 2 if in that figure we draw a



parallelogram of currents (precisely in the same
way as in mechanics we draw a parallelogram of
forces), and use the resultant O III to plot the sine
curve. You see that we can combine currents in the
same way as mechanical forces. I have proved this
for the case that the currents flow in two independ-
ent coils, but a glance at Fig. 4 will show you that it


FIG. 4.

also holds good if the two currents are sent through
the same coil. Here we have two machines, Ai
and A2, mechanically coupled, and therefore pro-
ducing currents of the same frequency. These
currents, I and II, flow into one circuit containing
a coil C. It is evident that in the circuit BCD
there flows only one current, which is the algebraic
sum of I and II.

Now let us change the arrangement to that


shown in Fig. 5. Here we have to do with only a
single current, for both machines and coil C are
coupled in series ; but we have to do with two elec-

FIG. 5.

tromotive forces, namely, those of the machines.
I assume that the coil C in itself has no electromo-
tive force. In this case also it is self-evident that
the current which will be forced through C is due
to the algebraic sum of the two electromotive
forces, and that all I have said about the determi-
nation of the resultant current is directly applicable
to that of the resultant electromotive force. In
other words, we may use any of the three graphic
methods of representing currents also for represent-
ing electromotive forces.

These graphic methods of investigation, and es-
pecially those based on the clock diagram, are so


useful and so simple that I shall employ them fre-
quently in the course of these lectures in preference
to analytical methods, and it is therefore expedient
to familiarize you at the outset with the clock dia-
gram. For this purpose I select, by way of exam-
ple, a case which is very frequently met with, and
which is represented by Fig. 6. Lest you should

FIG. 6.

think that this case has merely theoretical impor-
tance, I may at once say that a certain deduction
which flows naturally from its consideration is of
great practical importance in motors driven by
multiphase currents, since on it depends the start-
ing torque of such motors. If you compare Figs.
5 and 6 you will find that they only differ in this :
that an electromagnet S has been substituted for the
machine A2. The circuit represented in Fig. 6


consists of a machine A, giving an alternating elec-
tromotive force, a resistance B, consisting of a
bank of glow lamps, and an electromagnet S. This
electromagnet has a property which is technically
called "self-induction/' and, before going further,
I must briefly explain to you what is meant by
self-induction. You know that an electromotive
force is set up in a wire whenever the wire cuts
across magnetic lines of force. Since the wire
must necessarily form part of a closed circuit (for
if the circuit were not closed there could be no cur-
rent), the cutting of lines must be accompanied by
an increase or decrease in the number of lines or
total induction threading through the circuit, and
we may therefore also say that whenever the total
induction through a circuit changes, there is an
electromotive force set up in the circuit which is
the greater the more rapid the change. In fact,
the rate of change, that is, number of lines added
or withdrawn per second, multiplied with the num-
ber of turns of wire, gives the electromotive force
set up in the coil. Going back to Fig. i, we have
seen that the curve I represents the current as a
function of the time. Suppose there is no other


coil wound over the core, then the ordinates of the
curve represent to a suitable scale also the exciting
power on the core, and it is obvious that the mag-
netization of the core, or, to speak correctly, the
total induction passing through it, will change
more or less in accordance with the curve I. If
the permeability were constant, the induction would
be strictly proportional to the exciting power, and
by the selection of a suitable scale the curve repre-
senting induction could be made to coincide with
the current curve I. Now for low values of the
induction, say between zero and 3,000 or 4,000
lines per square centimetre, we may regard the
permeability of soft, well-annealed wrought-iron as
approximately constant, and if we do not press the
induction beyond this point, we may without any
great error assume that the current curve I also
represents the total induction through the core.
For the points where the current passes through
zero, and which momentarily interest us the most,
the assumption is, of course, quite correct. But if
the curve I represents the total induction, then the
geometrical tangent to it at any point represents
the change of induction in unit time, or, as I said


just now, the rate of change of induction at the par-
ticular moment represented by the point on the
curve. Thus, reading off the time on the horizon-
tal axis, we can, by drawing the tangent to the
current curve at the corresponding points, find the
rate at which the total induction changes at each
moment. I said just now that the rate of change,
multiplied with the number of turns in the coil,
gives the electromotive force generated at any in-
stant in the coil, and it will now be clear to you
that this electromotive force, which we call the
"electromotive force of self-induction," must be
proportional to the geometrical tangent to the cur-
rent curve. The steeper this line, the greater is
the electromotive force. Thus you see that when
the current is either a positive or negative maxi-
mum, the tangent is horizontal, and therefore at
those moments the electromotive force of self-
induction is zero. On either side of maximum cur-
rent it has a definite value, but this value is posi-
tive on one side and negative on the other side of
maximum current, since the slope of the tangent
changes from upward to downward when passing
this point. Where the current curve intersects the


horizontal axis, the slope of the tangent is evi-
dently greatest, and we therefore see that the elec-
tromotive force of self-induction is a maximum
when the current passes through zero, and it is
itself zero when the current is a maximum. This
then is, in general terms, the relation between the
current curve and the curve giving the electromo-
tive force of self-induction. It remains yet to de-
termine the exact nature of the latter. We have
seen that the ordinates of the electromotive force
curve are proportional to the geometric tangent
drawn to the current curve. Now how do we draw

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Online LibraryGisbert KappAlternating currents of electricity: their generation, measurement, distribution, and application → online text (page 1 of 7)