mean power taken up in the transformer at no load. To
obtain the true mean ordinate of the power onrve we have to
integrate the whole area included between the power curve
and the time axis, and to reckon those areas which lie above
the time axis as positive and those which lie below as negative.
The total area of the positive and negative parts algebraically
added, and divided by the length of the axis representing one
complete period, gives us the true mean ordinate of the power
curve. Hence, we can, from the transformer diagram taken on
open secondary circuit, determine the mean power taken op in
the transformer. The amount dissipated in heat in the copper
of the primary circuit is generally an exceedingly small
fraction of the total loss, and hence the mean power obtained
as above is practically the value of the power taken up in the
iron core.
The analytical expression of this feict is as follows: Taking
the fundamental equation for the transformer on open
secondary circuit, viz.,
at
we multiply the equation all through by ^ and obtain
a t
or «itid«=Rt,*d«+SNiti<£6.
If this last equation is integrated between the limits 0 to
T
±, where T is the complete periodic time, and each integral
Q
multiplied by = , we obtain an expression for the mean power
given to the transformer during one half-period. Thus,
The first term on the left hand side represents the true
mean power given to the transformer in one half-period. The
second term represents the power dissipated as heat in the
primary circuit in one half-period, and the third term repre*
sents the power dissipated on eddy currents and hysteresis in
THE INDUCTION COIL AND TRAN8F0BMBR. 558
the core in the same time. If a horizontal line is taken, and
from an origin distances are set off right and left to represent
the varying values of the primary current i during the period,
and vertical ordinates corresponding to these abscisssB taken
lio represent the values of the induction density h in the core
at the same instant, then a curve wiU be defined which will be
A cyclic curve, and will give us the total core loss per cycle
when the numerical value of its area is multiplied by the
iEM^tor Ni S. If the iron core is well laminated, eddy current
loss will be practically absent ; and the value of this area,
therefore, will give us the true hysteresis loss in the iron.
4000
IIOAO
^
t
7
1001
/
/
/
^ 0
/
/
5
innn
/
/
/
/
y
/
zwo
L
r
^
•^
8000
4000
482 10 1 284
3IaffnetUififf Force,
Flo. 195. — Hysteresis Curve of a Gauz Transfonuer.
Hence, such a curve is called the hysteresis curve of the core.
In Fig. 195 is shown the hysteresis curve of the Ganz trans-
iormer, so obtained from the current and induction curves of
ithe same transformer as given in Fig. 170.
In order to obtain the correct numerical value of the
hysteresis loss per cycle it must be noted that if all the quan-
tities 8, i and b are measured in C.G.S. measure, the value of
•{he integral SIHi f idb will give us, when taken round one
complete cycle, the value of the core loss in ergs during one
554 THE INDUCTION COIL AND TRANSFORMER.
complete period. And this value has to be divided by 10^ to-
reduce it to joules. Since the integral ^l^Aidh can be
written / (Nt)(2(S&), we see that the core loss per cycle in
joules can at once be obtained by taking the area of a loop
curve, the horizontal ordinates of which represent the periodic-
values of the primary ampere-turns, and the vertical ordinates
the corresponding total core induction during one complete
period, taken in a unit equal to 10^ G.G.S. units of magnetic
induction.
If the frequency is n, then n times the above integral gives-
the loss in the core per second ; and this should have the same
numerical value as the mean ordinate of the power curve
which measures the same quantity. The practical rule»
therefore, for obtaining the core loss in the transformer due to
the hysteresis and eddy current loss which may be present
is as follows : Draw two axes at right angles ; on the hori-
zontal axis set off right and left from the origin distances
which represent the primary ampere-turns for the different
instants during one complete period. At these points set up ordi-
nates which represent the total induction in the core measured
in imits each equal to 10^ C.6.S. units of magnetic induction,
and complete the looped curve defined by these ordinates.
The area of this curve, measured in terms of the area of
a rectangle one side of which is the length taken to represent
one ampere-turn and the other side is the length taken to
represent 10^ C.Q.S. units of induction, will give the value
of the core loss per cycle in joules, and multiplication of
this value by the frequency n will give the mean loss of
power in the core in tvatts. The number so obtained will
agree closely with the value of the mean ordinate of the
power curve in those cases in which the copper loss in the
primary circuit when the transformer is not loaded can be
neglected.
The form of this hysteresis loop will depend upon the manner
in which the magnetic induction in the core varies with the
magnetising force, and, as we shall see presently, the area
of this hysteresis loop depends, amongst other things, upon
the form of the curve of primary impressed electromotive^
force.
THE INDUCTION COIL AND TEAN8F0BMEB. 555
§ 6. The Efficiency of Transfennera — ^If the secondary
circnit of the transformer is closed through a resistance, and
the transformer is therefore loaded up, the power given to the
primary circuit in part reappears in a transformed form in the
external secondary circuit. As by far the most frequently
presented case in practice is that in which the resistance
which closes the secondary circuit consists of incandescence
lamps or other practically non-inductive resistances, we shaU,
therefore, in the first instance assume that the external
secondary circuit is an inductionless resistance. Under these
conditions the secondary current is, to a close approximation,
in step or synchronism with the secondary electromotive force,
and the mean power given to the extermd secondary drouit is
measured by the product of the mean-square value of the
secondary current strength and the mean-square value of the
potential difference of the secondary terminals. If we denote
by Ps the power thus given up to the external secondary
circuit, and similarly by P^ the power given up to the primary
circuit, the ratio of Pa to Pi is called the efficiency of the trans-
former. This efficiency is generally expressed as a percentage,
and will be denoted by the symbol c Hence
The difference between Pi and P, is represented by the
power lost in the core and dissipated in the copper circuits of
the transformer. If the symbol Cj stands for the mean-square
value ( v^mean^) of the primary current, and G2 for that of the
secondary currents at any time, and if Bi and B, are the resis-
tances of these circuits when warm and at that time, then the
power wasted in the primary and secondary circuits respec-
tively is Ci^ Bs a^d Cs' Bs, and if H is the core loss, viz., the
hysteresis and eddy-current loss, then
Pi-P,=Ci«B-fCa«B, + H,
on the assumption that there are no eddy-current losses or
energy dissipations in the copper circuits, or in the iron case
or framework of the transformer.
One of the most important measurements, therefore, which
it is necessary to make in connection with transformers is the
}
666 THE INDUCTION COIL AND TRAN8F0RMSB.
measurement of the power given to the primary oirouit. We
shall defer to a later chapter on transformer testing a full
discussion of the various methods which can be employed for
determining either the magnitude of the quantity P^ or of the
difference Pi - P, in the case of a transformer at any load. It
may suffice to state at present that one way in which this
measurement can be made is by means of a properly oon-
structed wattmeter, which measures directly the power P|
given to the primary circuit. The objection to this method is
that any error made in evaluating P^ appears to the same
extent and percentage in the ratio of P, to Pj, and therefore in
the efficiency. Hence other methods have been devised for
measuring directly the difference Pj - P^. However the value
of the efficiency may be determined, the results are best set
down in the form of an efficiency curve as follows: Each
transformer is constructed to give safely a certain output of
power to the secondary external circuit, which is called its
full load, and is stated generally in watts or kilowatts. The
load on the secondary circuit in any other cases can be
expressed as a fraction of the full load. To draw an efficiency
curve for any transformer, a horizontal line is taken, on
which are marked off the decimal fractions of the full load,
and at these points are set up ordinates which represent the
p
percentage efficiencies at these loads, viz., the value of 100;^
Pi
where Pi is the power given to the primary circuit and P9 is
the power given to the external secondary circuit. The ex-
tremities of these ordinates delineate the efficiency ourve«
In Figs. 196 and 197 are shown the efficiency curves of
various transformers. It will be seen that the chief difference
is that the more modern transformer has a higher efficiency
at the low loads. A good transformer of any moderate size
should have at least 80 per cent, efficiency at one-tenth load.
And larger transformers of 15 and 20-kilowatt size and
upwards will reach to 90 per cent, efficiency or more at one-
tenth of full load.
Another method of delineating the efficiency is to plot the
difference Pi - Ps in terms of P, ; in other words, to plot a
curve the abscissas of which represent the secondary output
P2, and the ordinates of which represent the total loss of
THE INDUCTION COIL AND TRANSFORMER. 557
100
^
1 80
1 00
«0
80
0
ie^
fc
5
=
-r
—
-la-
w
^
^
—
W
/^
y^
f/
f
•12'8'4'60'T«8
Fraetions nf FuU Secondary Load,
Flo. 196. — Efficiency Curves of Tiunafomiera.
l-O
LOO
«^
^
_
^^^
^^^
80
00
40
■ —
W
<:"
Ij
20
0
f
1
1 -S '8 '4 -5 -0 '7 '8
Fractiom of FuU Secondary Load,
Fig. 197. — ^Efficiency Curves of Transformers.
11>
In the above diagrams, horizontal distances represent the decimal
fractions of full secondary load, and vertical ordinates the percentage
efficiency corresponding thereto. The numbers against the curves refer
to the following transformers : —
- 5
If
9r f crittui/i xr»u8iuruicr ... ...
11 II ••• •••
xooo bype.
1885 type
rewound.
- 15
»
II II ••• •••
1892 type.
- 15
»>
II II ••• •••
1892 type
rewound.
- 20
II
II II ••• •••
1892 type.
- 6 kUowatt
Mordey Transformer
1892 type.
- 4-5
II
Thomson -Houston Transformer ...
1892 type.
- 4
II
Kapp Transformer
1892 type.
- 3
tt
" Hedgehog" (Swinburne) Transformer
1892 type.
- 6-5
»i
Westinghouse Transfonner
1892 type^
558 THJS INDUCTION COIL AND TRANSFORMER.
^
power in the transformer, viz.,
P, - Pj. In Fig. 198 is shown
such a curve drawn for a
6,500 - watt Westinghouse
transformer. The ordinates
of the upper curve give the
vahie of Pi— Pa corresponding
to the secondary output P^.
One important question
which arises in this connec-
tion is whether the true iron
core loss by hysteresis remains
constant at all loads of the
transformer. This was at one
time denied. It has, how-
ever, been shown by careful
experiments that the hys-
teresis loss in the iron core
is sensibly constant at all
loads.*
The proof of this was
obtained by careful measure-
ments made of the total
energy loss P -P^ for various
transformers. This value was
plotted down, as in Fig. 198,
in terms of the secondary out-
put P,. On the same diagram
was drawn a curve represent-
ing the total copper loss or
C*B loss for the primary
- The reader may be referred t»
a Paper by the author in the Pro-
ceedingt of the Institution of Elec-
trical Engineers, VoL XXL, 1892,
entitled ** Experimental BesearchtP
on Alternate • Current Tranafor-
mers/' for full information on the
experimental methods by which this
question has been settled. See
also The EUetrtcian, VoL XXX.,
pp. 97, 120. 162, 446.
sxivM xscn
THB INDUCTION COIL AND TEANSFOBMEB. 669
and seoondftry circuits taken together. These two curves
are found to be sensibly parallel to each other through-
out their whole range, and hence the true iron core loss or
iiystereais loss is a constant quantity at all loads. This is
a necessary consequence of the fieust that in constant potential
iransformers as designed for ordinary electric lighting work
the induction in the core is constant at all loads, and this in
turn is a consequence of the fact that the resultant mag-
netising force in the core is constant for all loads. Generally
speaking, we may state that for all fiurly well designed closed
iron drouit constant-potential transformers the iron core loss is
constant for all loads. This enables us to determine the
efficiency curve for any transformer of this description by three
measurements. If we measure the total power loss in the
transformer at no load we have the quantity which is constant
ai all loads. Call this loss in watts w. If, then, we measure
the resistances of the primary and secondary circuits and
<x)rrect these values so as to obtain the true resistances Bi
and Ba of the copper circuits at the final temperature reached
by the transformer when working, we can calculate the copper
losses Gi'Bi and Ca'Bt lor various values of the output of the
transformer. We can determine the value of the primary
current Ci corresponding to any value of the secondary current
€s to a sufficient approximation for this purpose by taking it as
N
•equal to CSt =—, where N^ and N^ are the number of turns of
the primary and secondary circuits respectively. Hence, the
total copper loss in the transformer is very approximately
«qualto
and the total power P^ given to the primary circuit conse-
quently corresponding to any secondary output C^ Va, where
Ysis the secondary terminal potential difference, is given
by the equation
and Pg-C,Vg.
Hence the ratio of P9 to Pi, or the efficiency at various
560 THE INDUCTION COIL AND TRANSFORMER.
00
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THB INDUCTION COIL AND TBAN8F0BMER. 661
loads, can be calculated. This is a convenient and fairly
accurate method to adopt in the case where we are testing
large transformers. It is sometimes very difficult or impos-
sible then to obtain the necessary non-inductive load in the
form of incandescence lamps for very large loads such as 40
or 50 kilowatts, and in that case the above procedure may be
' followed. The table on page 560 gives the results of a large
number of transformer efficiency measurements made by the
author in 1892, employing many forms of transformers then
in use.
The table shows particularly what a great advance was
made in transformer manufacture in the course of the seven
years between 1885 and 1892.
In the case of larger transformers the efficiency curves can
be made still more square-shouldered, and efficiencies of
over 90 per cent, obtained at one-tenth load.
Since the core loss at no load is an important factor in.
determining the efficiency of the transformer, it is obvious
that no transformer can have a high efficiency at light loads
unless the core loss is small. The iron core loss or no-load
loss in the case of transformers of 80 kilowatt size and
upwards can now be made to be less than 1 per cent, of
the full secondary output. That is to say, it is possible to
make the iron core loss of a 50-kilowatt transformer not
more than 400 watts. In the case of smaller transformers,
fix>m 1 to 15 kilowatts, the core loss will in general be from 8
to 1*8 per cent, of the full secondary output. Thus, a 1-kilo-
watt transformer, or one capable of giving out 1,000 watts in its
external secondary circuit, is a fairly good one if it has a core
loss of not more than 80 watts, or 8 per cent, of its full load ;
a 6-kilowatt transformer if it has a core loss of not more than
120 watts, or 2 per cent. ; and a 15-kilowatt transformer is
good if its core loss does not exceed 225 watts, or 1*5 per
cent. These figures will be a guide to the reader to know what
the core loss may be expected to be found in various cases.
We shall consider presently the causes which affect the
magnitude of the core losses.
§ 6* Current Diagram of a Transformer. — ^Let a horissontal
line be taken on which are set off distances proportional to
00
i
^
N
o
3
»
5
A
•
I
1
A'*
4
o
o
{
o
\
5
\
o
\
i
lN3UUn3 3U3dW>r
I.II1UIIA3 im^Hv
66S
THE INDUCTION COIL AND TRANSFORMER. 563
the power ontput on the external secondary circuit, that is, to
the secondary load of a transformer, and let ordinates at these
points be drawn to any scale representing the magnitudes of
the primary and secondary currents, the scale of the primary
current ordinates being taken so that if one unit of length
represents one ampere of primary current, and the scale of the
N
secondary current so that one unit of length represents ^
times the corresponding secondary current, then we shall
•delineate the lines called the current curves. For any closed
•circuit transformer of constant potential type these current
are nearly two lines running nearly parallel to each other as
shown in Fig. 199. If C^ stands for the mean-square value
of the primary current, and C, for that of the secondary
^surrent, and if Ni and N, are the numbers of the primary and
eecondary turns respectively, then experiment shows that a
good type of closed magnetic circuit constant potential trans-
former C^ - »- Gg is a nearly constant quantity, and that this
•difference is practically the same as the mean-square value of
4ihe primary current when the transformer is not loaded. Let
ihis last be called e^. Then
or Cini=»OiNi-0,Na.
In other words, the difference of the primary and secondary
ampere-turns at all loads is a constant quantity, and is equal
to the ampere-turns at no load. This is merely the expression
of the fact that the magnetomotive force acting on this
magnetic circuit is a constant quantity, and that therefore the
induction is constant as well. This is, however, not the case
for open-circuit transformers. In Fig. 200 is shown the
current curves for a Swinburne "Hedgehog" transformer, and
it will be seen that the difference of the primary and secondary
ampere-turns is not constant, but increases as the load dimi-
nishes. This is a consequence of the fia>ct that in the open
circuit transformer the difference of phase between the primary
.and secondary currents is considerable at light loads, but
Jjecomes less as the transformer is loaded up, and that Uiere-
oo2
504 THE INDUCTION COIL AND TRANSFORMER.
Table A. — Test of a WestinghouM Transforfner.
Power, 6,500 watts. Secondary volts, 100.
Frequency used, 82'6 periods per second.
Average final temperature of transformer, 96*F.
Volts on primary circuit (Vi)= 2,400 (kept constant).
Primary circuit resistance ==5*95 ohms at 96'F.
Secondary circuit resistance =0*0108 ohm at WF.
Secondary Circuit
Primary Circuit.
|i:
& J
Power
Power
6 • ^
M 3
Tolta.
Axnperes.
taken out
in watts.
Volts.
Amperes.
given in
watts
1010
0
0
2,400
0-060
95
95
0
100-9
1-00
101
tt
0-100
205
104
49-3
100*8
1-98
200
ft
0140
306
106
66-4
100-8
2-94
296
,)
0-180
401
105
73-7
100-7
3-87
390
0218
493
103
79-1
1007
4-79
482
}9
0-2E0
697
116
80-7
100-7
8-00
806
yi
0-382
920
114
87-6 -
100-4
10-16
1,019
}}
0-472
1,139
120
89-6
100-3
13-07
1,311
19
0-580
1,440
129
91-1
1001
18-00
1,802
))
0-800
1,930
128
93-4
100-1
19-90
1,992
II
0-880
2,118
126
941
100-0
21-93
2,195
II
0-960
2,330
127
94-1
100-0
24-74
2,474
II
1-080
2,609
135
948
1000
29-66
2,966
II
1-286
3,006
130
95-8
99-8
37-20
3,713
1-610
3,870
157
96-0
99-6
4200
4,179
II
1-810
4,324
146
967
99-3
46-65
4,633
II
2-002
4,792
150
96-9
99-2
£0-40
5,000
II
2160
5,174
174
967
990
5216
5.164
yi
2-240
5,422
268
95-3
98-9
65-60
5,499
II
2-383
5,702
203
S6-1
98-8
57-68
5,700
II
2-478
5,885
185
969
98-9
59-32
5,867
M
2-650
6,041
174
97-3
98-7
61-32
6,053
II
2-633
6,271
218
967
98-8
6216
6,142
II
2-672
6.344
202
£6-8
98-7
63-00
6.218
II
2-700
6,426
208
96-8
987
64-00
6,317
If
2-750
6,522
205
96-9
98*6
64-74
6,384
»>
2-776
6,598
214
96-9
fore there must be an increase in mean-square or maximum
value of the primary current, so that its greater value at light
loads is a compensation for the greater difference of phase
between the primary and the secondary current. This is on
the assumption that the secondary chrcuit is a pra<5tically non-
inductive circuit. K the carefully-drawn current diagram ot
TEE INDUCTION COIL AND TRANSFORMER, 565
Table B. — Te$t of a Swinburne " Hedgehog " Tranrformer.
Power, 3,000 watta. Secondaiy volts, 100.
Frequency used, 81*1 periods per second.
Average final temperature of transformer, 145^.
Volts on primary circuit (¥1)= 2,400 (kept constant).
Primary circuit resistances 24*00 ohms at 145*'F.
Secondary circuit resiBtanceB 0*051 ohm at 146''F.
Scoondary Clrcnit.
Primary Circuit.
11
ik
8.1 ss
1 " I
Volts.
Amperes.
Power
taken out
in watta,
Wa.
Volta.
Amperes
Power
given in
watta Wi
101-8
0
0
2,400
0-7f6
121
121
0
101-7
100
102
II
0-761
213
111
47-9
1016
2-97
301
}i
0-786
414
113
72 7
101-3
4 84
490
1}
0-811
608
118
80-6
101-3
600
(07
II
0-829
730
19.3
83-1
101-2
8-00
810
If
0-862
943
133
85-9
1010
10-20
1,0/0
ii
0-915
1,161
131
886
100-9
12-00
1.211
II
0 960
1,361
150
890
100-6
14-00
1,408
II
1013
1,551
143
90-8
100-3
16-87
1,5-2
If
1-066
1,760
158
91-1
1000
17-89
1,';89
II
1-133
1,951
162
91-7
100-0
19-80
3,980
11
1197
2,129
149
93-0
99-9
21 -1:2
2,180
II
1,260
2,344
164
930
99-7
23-66
2,369
II
1-321
2,525
166
93-3
995
25-46
2,534
II
1-397
2.732
1&8
92-8
99-3
26-46
2,628
11
1-430
2,823
195
93-2
991
27-42
2,718
II
1-465
2.914
196
93-4
99-0
28-28
2,8C0
II
1-600
2,988
188
93-7
98-9
29-26
2,896
II
1-532
3,103
207
95-3
990
30-20
2,9:0
11
1-666
3,185
195
94-0
any oloeed-circuit transfonner of constant-potential type are
examined, it will be seen that the difference between the ordi-
nates of the primary and secondary current curves or lines
increases slightly very near the origin, and as we shall see pre-
sently this is an indication of the fact that the primary current
is for all loads, except very small ones, practically in exact
opposition, as regards phase, to the secondary current. As an
example of the measurements of a complete test of a closed
circuit and open circuit transformer, we give on page 564
and above, in Tables A and B, the figures obtained for a
Westinghouse and Swinburne transformer respectively.
666 THE INDUCTION COIL AND TBAN8F0RMEK
% 7- The Power Factor of Transformers. — ^If under any
conditions of load on the secondary circuit we measure the
true power P^ being taken up by the primary circuit, and also
the mean-square ( V'mean*) value A of the primary current
and the mean-square value Y of the primary terminal potential
difference, the ratio of Pi to the product A V is called the
^ower factor of the transformer at that load. The product
A Y is often called the apparent power or apparent watts given
to the transformer, and the value of Pi is the true power
or true watts given to the transformer. Hence the power
fEtctor (F) is defined thus : —
Power fac-\ ^ True power in watts given to the transformer
^^ (F) / Apparent power in watts given to the transformer
The above relation may be symbolically expressed by
writing
^"rv ^' Pi = (FA)Y.
This last mode of writing it exposes the appropriateness of
the term '' power factor" ; since we see that it is a factor by
which the value of the total mean-square value of the current
must be multiplied to obtain that current which, when multi-
plied by the mean-square value of the potential difference
Y, will give the true mean power being taken up in the
circuit. Thus, if the power factor is denoted by F, this
signifies that the portion FA of the current A is effective in
conveying power, and the remainder (1 - F) A is ineffective,
or, as it is sometimes called, is the wattless component of the
current. Hence, we may, in imagination, divide the apparent
power AY into two portions: a ps^ FAY, which is a measure
of the true power given to the circuit ; and a part (1 - F) AY,
which is the wattless or powerless portion.
The true power P^ is obtained from the correct wattmettf
reading, and the apparent power AY is the value of the product
of the readings of an electrostatic voltmeter used to measure
the mean-square value of the potential difference and that of
an alternating-current ammeter used to measure the mean-
square value of the current. A very important constant with
respect to any transformer is its power factor at no load or on
open secondary circuit, and the Table on page 567 gives the
THB INDUCTION COIL AND TBAN8F0BMEB. 567.
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So
568 THE INDUCTION COIL AND TRANSFORMER.
values of the no-load power £B.ctor for various types of trans-
formers taken on certain alternators.
Generally speaking, it is found that the power factor of
most closed iron circuit transformers has a value lying between
0*5 and 0*8, but that for induction coils on open-circuit
transformers, such as the << Hedgehog" transformer, the power
factor is about one-tenth of the value for closed iron circuit
transformers.
It must not be supposed, however, that the power factor of
an induction coil or transformer has a constant and fixed
value for any particular transformer. The value of the power
factor is affected to a very considerable degree by the form of
the curve of primary terminal potential difference, and may
vary within wide limits according as the curve is varied in
form.
Power Factors of Transformers taken off different Altematon at
tJie same Primary Voltage,
Size in
Kilow'ttB
Power Factor.
Magnetising Current!
in Amperes.
Transformer.
On
Thomson-
Houston
Alternator
On
Mordey
Alternator
On
Thomson-
Houston
Alternator
On
Mordey
Alternator
Mordey-Brush ...
Thomion-Houston
Mordey-Brush ...
60
30
18
0-609
0-49J
0686
0-704
0-636
0-761
0-668
0-662
0-326
0-623
0*660
0*332
In the Table above are given the power factors at no
load of three transformers taken off a Mordey alternator
having an E.M.F. curve similar to that shown in Fig. 175,
and a Thomson-Houston alternator having an E.M.F. curve
of the land shown in Fig. 174, and it will be seen that the
power factors and magnetising currents of the transformers
are quite different in the two cases.
We must not, therefore, regard the power factor as an
absolute constant for the transformer, but as a function to
some degree of the form of the primary E.M.F. curve, although
at the same time dependent essentially upon the nature of
the magnetic circuit of the transformer.
TEE INDUCTION COIL AND TRANSFORMER. 669
If the primary E.M.F. cnrve and current curve were both
simple periodic or sine carves, then the power fia>ctor would be
«imply the cosine of the angle of lag of the current behind the
-electromotive force. If the transformer has its secondary
•circuit loaded up, the power factor approximates to unity as
this loading takes place.
In the case of most closed-circuit transformers a very little
loading-up of the secondary circuit causes the power factor to
become unity, but in the case of an open-circuit transformer,
whilst the loading-up of the transformer increases the power
factor, it never actually reaches unity.
Table 0. — Test of a Westingliouse Transformer,
Primary Yolts, 2,400 (kept constant).
Secondary volts at no load = 101*0.
^
Copper Lowes in Watte.
1^
Primary WatU.
g
r
fi
^•^S
it
22?
•§9
CO
CDm
&
go
0-060
0
0
0
0
0
0
95
120
0-79
0100
1*00
0042
0
0
0
01
205
240
0-86
0140
1-98
0*083
0-1
0
0
0*2
306
336
0-91
0*180
2-94
0*122
0*2
01
0
0-2
401
432
0-93
0*218
3-87
0161
0*3
0-2
0
0*3
493
523
0-94
0-250
4-79
0-199
0*4
0-2
1
0-3
697
600
0-99
0-382
8-00
0-333
0*9
0-7
2
0-3
920
917
l-OO
•0-472
10-15
0*423
1*3
11
2
0*6
1,139
1,133
1-00
0-680
13*07
0*545
2-0
1-8
4
07
1,440
1.392
103
0-800
18*00
0*750
3 8
3-5
7
0*9
1,930
1,920
1-00
0-880
19-90
0*830
4-6
4-3
9
0*9
2,118
2,112
100
0-960
21-93
0*914
5-5
5-2
11
1*0
2,330
2,304
1-01
1*080
24-74
1*031
6-9
6-6
14
1-0
2,609
2,592
1-01
1-285
29*66
1*238
9 8
9-5
19
1-0
3,096
3,086
1-00
1-610
37-20
1-560
15-4
14*9
30
1-2
3,870
3,864
100
1*810
42*00
1*750
195
19*0
39
1-5
4,324
4,344
0*99
2-002
46*65
1*945
23-5
23*5
47
1-7
4,792
4,805
100
2-160
50*40
2-100
23-7
27*5
55
1*8
5,174
5,184
100
2-240
5216
2-171
29*8
29*5
59
2*0
5,422
5,376
1-01
2*383
55*60
2*320
33-9
33-5
67
21
5,702
5,719
1-00
2-478
57*68
2*404
36-5
36-0
73
2-2
5,885
5,947
0-99
•2-550
59-32
2*474
38-7
38-1
77
2-1
6,041
6,120
0-99
2-633
61-32
2*560
41-2
40-6
82
2-3
6,271
6,319
0 99
2-672
62*16 ! 2-594
42*5
41-8
84
2-2
6,344
6,413
0-99
.2-700
63*00 ; 2-623
43*3
42*9
86
2-3
6,426
6,480
0-99
2760
6400
2-665
45 0
44*2
89
2-3
6,522
6,600
0-99
Si'TJb
64*74
2-700
46-8
45-3
91
2-4
6,598
6,660
100
67a TEE INDUCTION COIL AND TRANSFOHMEB,.
This may best be illustrated by giving the figures of test of
two transfonriers, one of the closed-circuit type (Westinghouse)
and one of the open-circuit type (Swinburne) {see Tables C
and D). It will be seen that a very small loading of the
closed-circuit type suffices to bring the power factor up to
unity.
Hence it follows that for closed-circuit transformers the
apparent power given to the transformer is equal to the real
power at and beyond about one-tenth of full load. In Fig. 201
are shown three curves illustrating the gradual rise of the
power factor towards unity in the case of three types of
transformer. In the case of an open-circuit transformer at
no stage of the load is the true power taken up by the
transformer identical in value with the apparent power given
to the transformer.
Table D. — Test of a Swinburne " Hedgehog " Transformer.
Primary volts, 2,400 (kept const ant).
Secondary volts at no load =102 '00.
-*-
Copper Losaea iu Watts.
^i
Primary Watta.
^.
1"
Is
^:^
£?8
it
c X
1
g
«t*
1
0-756
0
0
13-7
0
14
0
121
1,816
0-07
0-761
1-02
0-042 14-0
0-1
14
01
228
1,829
0-13
0-786
2-98
0-124 14-9
0-5
15
0-2
4'.0
1,886
0-22
0-811
4-84
0-202 , 15-8
1-2
17
0-4
621
1,948
0-32
0-829
6-00
0-250 16-5
18
18
0-6
730
1,988
0-37
0-862
800
0-333 , 17-8
33
21
0-8
943
2,067
046
0-911
10-00
0-417 19-9
5-1
25
1-0
1,152
2,188
0-53
0-960
12-00
0-500 22-6
73
30
1-2
1,353
2,301
0-59
1-013
14-00
0-584 24-7
10-C
35
1-3
1,538
2,432
0-65
1-066
15-88
0-663 27-2
12-9
40
1.6
1,746
2,659
0-68
1-133
17-89
0-746 30-9
16 3
47
1-7
1,932
2,720
0-71
1-197
19-80
0-825 34-5
20-0
55
1-9
2,129
2,873
0-74
1-260
21-63
0-902 38-2
24 0
62
2-1
2,320
3,022
0-77
1-321
23-68
0-983 42-0
28 3
70
2-4
2,510
3,172
0-79
1-395
26-46
1-C60
46-6
331
80
2-7
2,706
3,350
0-81
1-426
26-38
1-098
48-9
35-4
84
2-9
2,829
3,422
0-83
1-460
27-28
1-136
51-2
38 0
89
3-0
2,890
3,601
0-83
1-498
28-21
1-175
54-0
40-8
95
3-0
2,993
3,596
0-83
1-529
29-19
1-216
56 1
43-6
100
3-2
3,042
3,666
0-83
1-567
30-33
1-262