CHAPTER XIV. 

THE ALTERNATING-CURRENT TRANSFORMER. 

126. The simplest alternating-current apparatus is the 
transformer. It consists of a magnetic circuit interlinked 
with two electric circuits, a primary and a secondary. The 
primary circuit is excited by an impressed E.M.F., while in 
the secondary circuit an E.M.F. is induced. Thus, in the 
primary circuit power is consumed, and in the secondary 
a corresponding amount of power is produced. 

Since the same magnetic circuit is interlinked with both 
electric circuits, the E.M.F. induced per turn must be the 
same in the secondary as in the primary circuit ; hence, 
the primary induced E.M.F. being approximately equal to 
the impressed E.M.F., the E.M.Fs. at primary and at sec- 
ondary terminals have approximately the ratio of their 
respective turns. Since the power produced in the second- 
ary is approximately the same as that consumed in the 
primary, the primary and secondary currents are approxi- 
mately in inverse ratio to the turns. 

127. Besides the magnetic flux interlinked with both 
electric circuits — which flux, in a closed magnetic circuit 
transformer, has a circuit of low reluctance — a magnetic 
cross-flux passes between the primary and secondary coils, 
surrounding one coil only, without being interlinked with 
the other. This magnetic cross-flux is proportional to the 
current flowing in the electric circuit, or rather, the ampere- 
turns or M.M.F. increase with the increasing load on the 
transformer, and constitute what is called the self-induc- 
tance of the transformer ; while the flux surrounding both 


194 ALTERNATING-CURRENT PHENOMENA. 

coils may be considered as mutual inductance. This cross- 
flux of self-induction does not induce E.M.F. in the second- 
ary circuit, and is thus, in general, objectionable, by causing 
a drop of voltage and a decrease of output. It is this 
cross-flux, however, or flux of self-inductance, which is uti- 
lized in special transformers, to secure automatic regulation, 
for constant power, or for constant current, and in this 
case is exaggerated by separating primary and secondary 
coils. In the constant potential transformer however, the 
primary and secondary coils are brought as near together as 
possible, or even interspersed, to reduce the cross-flux. 

As will be seen by the self-inductance of a circuit, not 
the total flux produced by, and interlinked with, the circuit 
is understood, but only that (usually small) part of the flux 
which surrounds one circuit without interlinking with the 
other circuit. 

128. The alternating magnetic flux of the magnetic 
circuit surrounding both electric circuits is produced by 
the combined magnetizing action of the primary and of the 
secondary current. 

This magnetic flux is determined by the E.M.F. of the 
transformer, by the number of turns, and by the frequency. 
If 

<£ = maximum magnetic flux, 
N= frequency, 
n = number of turns of the coil ; 

the E.M.F. induced in this coil is 

E= V2 *• JVfc * 10 -8 = 4.44 .Afo* 10 -'volts; 


hence, if the E.M.F., frequency, and number of turns are 
determined, the maximum magnetic flux is 


To produce the magnetism, $, of the transformer, a 
M.M.F. of 5 ampere-turns is required, which is determined 


ALTERNATING-CURRENT TRANSFORMER. 195 

by the shape and the magnetic characteristic of the iron, in 
the manner discussed in Chapter X. 

For instance, in the closed magnet circuit transformer, 
the maximum magnetic induction is ($> = & /S, where S 
= the cross-section of magnetic circuit. 

129. To induce a magnetic density, ($>, a M.M.F. of 3CTO 
ampere-turns maximum is required, or, 3COT / V2 ampere- 
turns effective, per unit length of the magnetic circuit ; 
hence, for the total magnetic circuit, of length, /, 

/3C 
& = — :r- ampere-turns ; 


« *V2 
where n = number of turns. 

At no load, or open secondary circuit, this M.M.F., CF, is 
furnished by the exciting current, T00, improperly called the 
leakage current, of the transformer ; that is, that small 
amount of primary current which passes through the trans- 
former at open secondary circuit. 

In a transformer with open magnetic circuit, such as 
the "hedgehog" transformer, the M.M.F., &, is the sum 
of the M.M.F. consumed in the iron and in the air part of 
the magnetic circuit (see Chapter X.). 

The energy of the exciting current is the energy con- 
sumed by hysteresis and eddy currents and the small ohmic 
loss. 

The exciting current is not a sine wave, but is, at least 
in the closed magnetic circuit transformer, greatly distorted 
by hysteresis, though less so in the open magnetic circuit 
transformer. It can, however, be represented by an equiv- 
alent sine wave, f00, of equal intensity and equal power with 
the distorted wave, and a wattless higher harmonic, mainly 
of triple frequency. 

Since the higher harmonic is small compared with the 


196 ALTERNATING-CURRENT PHENOMENA. 

total exciting current, and the exciting current is only a 
small part of the total primary current, the higher harmonic 
.can, for most practical cases, be neglected, and the exciting 
current represented by the equivalent sine wave. 

This equivalent sine wave, 7^, leads the wave of mag- 
netism, 3>, by an angle, a, the angle of hysteretic advance of 
phase, and consists of two components, — the hysteretic 
energy current, in quadrature with the magnetic flux, and 
therefore in phase with the induced E.M.F. = I00 sin a; and 
the magnetizing current, in phase with the magnetic fluXj 
and therefore in quadrature with the induced E.M.F., and 
so wattless, = I00 cos a. 

The exciting current, 700, is determined from the shape 
and magnetic characteristic of the iron, and number of 
turns ; the hysteretic energy current is — 

Power consumed in the iron 


I00 sin a 


Induced E.M.F. 


130. Graphically, the polar diagram of M.M.Fs. ot a 
transformer is constructed thus : 


Fig. 94. 


Let, in Fig. 94, O® = the magnetic flux in intensity and 
phase (for convenience, as intensities, the effective values 
are used throughout), assuming its phase as the vertical; 


ALTERNATING-CURRENT TRANSFORMER. 197 

that is, counting the time from the moment where the 
rising magnetism passes its zero value. 

Then the resultant M.M.F. is represented by the vector 
QS, leading O<b by the angle &O® = a. 

The induced E.M.Fs. have the phase 180°, that is, are 
plotted towards the left, and represented by the vectors 
OZT; and OE±. 

If, now, ft' = angle of lag in the secondary circuit, due 
to the total (internal and external) secondary reactance, the 
secondary current II , and hence the secondary M.M.F., 
JF1= «j /L, will lag behind £•[ by an angle ft1, and have the 
phase, 180° + ft', represented by the vector O^1. Con- 
structing a parallelogram of M.M.Fs., with Off as a diag- 
onal and Oif1 as one side, the other side or O'S0 is the 
primary M.M.F., in intensity and phase, and hence, dividing 
by the number of primary turns, n0, the primary current is 
/.-*./*.. 

To complete the diagram of E M.Fs. , we have now, — 

In the primary circuit : 

E.M.F. consumed by resistance is 70r0, in phase with fot and 
represented by the vector OEr0 • 

E.M.F. consumed by reactance is IoX0, 90° ahead of I0, and 
represented by the vector OEx0 ; 

E.M.F. consumed by induced E.M.F. is E', equal and oppo- 
site to E'o, and represented by the vector Off. 

Hence, the total primary impressed E.M.F. by combina- 
tion of OEr0, OEx0, and OE' by means of the parallelo- 
gram of E.M.Fs. is, 

E0 = ~OE0, 

and the difference of phase between the primary impressed 
E.M.F. and the primary current is 

ft0 = E0O50. 
In the secondary circuit : 

Counter E.M.F. of resistance is 1^ in opposition with Iv 
and represented by the vector OJS'r^ ; 


198 


AL TERNA TING-CURRENT PHENOMENA, 


90° behind 7X, and 


Counter E.M.F. of reactance is 
represented by the vector OE^x^ 

Induced E.M.Fs., E( represented by the vector OE-[. 

Hence, the secondary terminal voltage, by combination 
of OEr^ OEx{ and OE^ by means of the parallelogram of 

E.M.Fs. is -==• 

A = M»II 

and the difference of phase between the secondary terminal 
voltage and the secondary current is 


As will be seen in the primary circuit the " components 
of impressed E.M.F. required to overcome the counter 
E.M.Fs." were used for convenience, and in the secondary 
circuit the "counter E.M.Fs." 


Er, 


Fig. 95. Transformer Diagram with 80° Lag in Secondary Circuit. 

131. In the construction of the transformer diagram, it 
is usually preferable not to plot the secondary quantities, 
current and E.M.F., direct, but to reduce them to corre- 
spondence with the primary circuit by multiplying by the 
ratio of turns, a = n0/ nv for the reason that frequently 
primary and secondary E.M.Fs., etc., are of such different 


AL TERA?A TING-CURRENT TRANSFORMER. 


19!) 


magnitude as not to be easily represented on the same 
scale; or the primary circuit may be reduced to the sec- 
ondary in the same way. In either case, the vectors repre- 
senting the two induced E.M.Fs. coincide, or OE-^ = OE^. 


Fig. 96. Transformer Diagram with 50° Lag in Secondary Circuit. 

Figs. 96 to 107 give the polar diagram of a transformer 
having the constants — 


r0 = .2 ohms, 
x0 = .33 ohms, 
f! = .00167 ohms, 
*! = .0025 ohms, 
g0 = .0100 mhos, 

for the conditions of secondary circuit, 


= .0173 mhos, 
= 100 volts, 
= 60 amperes, 
=10 degrees. ? 


20° lead in Fig. 99. 
50° lead " 100. 
80° lead " 101. 


ft' = 80° lag in Fig. 95. 

50° lag " 96. 

20° lag " 97. 

O, or in phase, " 98. 

As shown with a change of /?/ the other quantities E0, Iv 
I0, etc., change in intensity and direction. The loci de- 
scribed by them are circles, and are shown in Fig. 102, 
with the point corresponding to non-inductive load marked. 
The part of the locus corresponding to a lagging secondary 


200 ALTERNATING-CURRENT PHENOMENA. 


Fig. 97. Transformer Diagram with 20° Lag in Secondary Circuit 


Fig. 98. Transformer Diagram with Secondary Current in Phase with E.M.F. 


Fig. 99. Transformer Diagram with 20° Lead in Secondary Current. 


ALTERNATING-CURRENT TRANSFORMER. 201 


(To EO 

Fig. 100. Transformer Diagram with 50° Lead in Secondary Circuit. 


Fig. 101. Transformer Diagram with 80° Lead in Secondary Circuit. 


Fig. 102. 


202 


AL TERNA TING-CURRENT PHENOMENA. 


current is shown in thick full lines, and the part correspond- 
ing to leading current in thin full lines. 

132. This diagram represents the condition of constant 
secondary induced E.M.F., £"/, that is, corresponding to a 
constant maximum magnetic flux. 

By changing all the quantities proportionally from the 
diagram of Fig. 102, the diagrams for the constant primary 
impressed E.M.F. (Fig. 103), and for constant secondary 
terminal voltage (Fig. 104), are derived. In these cases, 
the locus gives curves of higher order. 


Fig. 103. 


Fig. 105 gives the locus of the various quantities when 
the load is changed from full load, /j = 60 amperes in a 
non-inductive secondary external circuit to no load or open 
circuit. 

a.) By increase of secondary resistance ; b.} by increase 
of secondary inductive reactance ; c.) by increase of sec- 
ondary capacity reactance. 

As shown in a.), the locus of the secondary terminal vol- 
tage, J5lt and thus of E0, etc., are straight lines; and in 
b.) and c.}, parts of one and the same circle a.} is shown 


AL TERNA TING-CURRENT TRANSFORMER. 


203 


in full lines, b.} in heavy full lines, and c.} in light full lines. 
This diagram corresponds to constant maximum magnetic 
flux ; that is, to constant secondary induced E.M.F. The 
diagrams representing constant primary impressed E.M.F. 
and constant secondary terminal voltage can be derived 
from the above by proportionality. 


Fig. 104. 


133. It must be understood, however, that for the pur- 
pose of making the diagrams plainer, by bringing the dif- 
ferent values to somewhat nearer the same magnitude, the 
constants chosen for these diagrams represent, not the mag- 
nitudes found in actual transformers, but refer to greatly 
exaggerated internal losses. 

In practice, about the following magnitudes would be 
found : 


r0 = .01 ohms ; 
x0 = .033 ohms ; 
ri = .00008 ohms j 


#! = .00025 ohms ; 
g0 = .001 ohms ; 
b0 = .00173 ohms ; 


that is, about one-tenth as large as assumed. Thus the 
changes of the values of E0, Elt etc., under the different 
conditions will be very much smaller. 


204 


ALTERNATING-CURRENT PHENOMENA. 


Symbolic Method. 

134. In symbolic representation by complex quantities 
the transformer problem appears as follows : 

The exciting current, 700, of the transformer depends 
upon the primary E.M.F., which dependance can be rep- 
resented by an admittance, the " primary admittance," 
°f tne transformer. 


Fig. 105. 

The resistance and reactance of the primary and the 
secondary circuit are represented in the impedance by 

Z0=r0- jx0, and Zl=rl- j xl . 

Within the limited range of variation of the magnetic 
density in a constant potential transformer, admittance and 
impedance can usually, and with sufficient .exactness, be 
considered as constant. 

Let 

n0 = number of primary turns in series ; 
#1 = number of secondary turns in series ; 
a = — = ratio of turns ; 

Y0 = g0 4- jb0 = primary admittance 

Exciting current . ~i I 

Primary counter E.M.F. ' 


.VVWvVl 


rw^ww 


ALTERNATING-CURRENT TRANSFORMER. 205 

Z0 = r0 — j x0 = primary impedance 7. — — 

E.M.F. consumed in primary coil by resistance and reactance. ^ -n-f '" ' j**/\. 

Primary current ~ / 

Z± = r± —jx1= secondary impedance 

__ E.M.F. consumed in secondary coil by resistance and reactance . 
Secondary current 

where the reactances, x0 and ^ , refer to the true self -induc- 
tance only, or to the cross-flux passing between primary and 
secondary coils ; that is, interlinked with one coil only. 
Let also 

Y = g -\-jb- total admittance of secondary circuit, 

including the internal impedance ; 
E0 = primary impressed E.M.F. ; 
E ' = E.M.F. consumed by primary counter E.M.F. ; 
£i = secondary terminal voltage ; 
EI = secondary induced E.M.F. ; 
I0 = primary current, total ; 
/oo = primary exciting current ; 
/i = secondary current. 

Since the primary counter E.M.F.,-£"', and the second- 
ary induced E.M.F., E^, are proportional by the ratio of 

turns, a, 

E ' = — a E{. (1) 

The secondary current is : 

/i = **/, (2) 

consisting of an energy component, gE^, and a reactive 
component, b E^. 

To this secondary current corresponds the component of 
primary current, 

•7o = ~a a* 

The primary exciting current is — 

I«>=YOE>. (4) 

Hence, the total primary current is : 


206 AL TERNA TING-CURRENT PHENOMENA. 

(6) 


The E.M.F. consumed in the secondary coil by the 
internal impedance is Z-J^. 

The E.M.F. induced in the secondary coil by the mag- 
netic flux is EI. 

Therefore, the secondary terminal voltage is 


or, substituting (2), we have 

£, = £,' {I- Z,Y} (7) 

The E.M.F. consumed in the primary coil by the inter- 
nal impedance is Z0 I0. 

The E.M.F. consumed in the primary coil by the counter 
E.M.F. is E'. 

Therefore, the primary impressed E.M.F. is 

E0 = E' + Z0S0, 
or, substituting (6), 


(8) 

\°/ 


136. We thus have, 

primary E.M.F., E0 = - aE{ j 1 + Z0 Y0 + ^Z J , (8) 

secondary E.M.F., E^ = E{ { 1 - Zl Y}, (7) 

primary current, I0 = — — -{Y+a*Y0}, (6) 

secondary current, /i = YEl't (2) 

as functions of the secondary induced E.M.F., EJ, as pa- 
rameter. 


ALTERNATING-CURRENT TRANSFORMER. 207 

From the above we derive 

Ratio of transformation of E.M.Fs. : 


. 1-Z.K 

Ratio of transformations of currents : 


(10) 


From this we get, at constant primary impressed 
E.M.F., 

E0 = constant ; 

secondary induced E.M.F., 


E.M.F. induced per turn, 
E 1 

n0 -\ \ 7 y \ 

secondary terminal voltage, 


primary current, 

^ 4- Y 
, . EA Y+a*Y0 _ w ^^ y° 


secondary current, 

Y 


At constant secondary terminal voltage, 
-fi1! = const. ; 


208 AL TERNA TING-CURRENT PHENOMENA. 

secondary induced E.M.F., 

F1 - £l 

1-^F' 
E.M.F. induced per turn, 


^1-Z.F' 
primary impressed E.M.F., 


primary current, 

/ 

secondary current, 


136. Some interesting conclusions can be drawn from 
these equations. 

The apparent impedance of the total transformer is 


(14) 


Substituting now, — = V, the total secondary admit- 

tance, reduced to the primary circuit by the ratio of turns, 
it is 


Y0-\-Y' is the total admittance of a divided circuit with 
the exciting current, of admittance Y0, and the secondary 


AL TERN A TING-CURRENT TRANSFORMER. 


209 


current, of admittance Y1 (reduced to primary), as branches. 
Thus : 


is the impedance of this divided circuit, and 


That is : 


(17) 


The alternate-current transformer, of primary admittance 
Y0 , total secondary admittance Y, and primary impedance 
Z0 , is equivalent to, and can be replaced by, a divided circuit 
with the branches of admittance Y0 , the exciting current, and 
admittance Y' = Y/a2, the secondary current, fed over mains 
of the impedance Z0, the internal primary impedance. 

This is shown diagrammatically in Fig. 106. 


Yog 

z 


Fig. 106. 


137. Separating now the internal secondary impedance 
from the external secondary impedance, or the impedance of 
the consumer circuit, it is 

4 -£.+ *! (18) 


where Z = external secondary impedance, 


(19) 


210 ALTERNATING-CURRENT PHENOMENA. 

Reduced to primary circuit, it is 


= Z/ + Z7. (20) 

That is : 

An alternate-current transformer, of primary admittance 
Y0, primary impedance Z0, secondary impedance Zv and 
ratio of turns a, can, when the secondary circuit is closed by 
an impedance Z (the impedance of the receiver circuit), be 
replaced, and is equivalent to a circtiit of impedance Z ' = 
a?Z, fed over mains of the impedance Z0-\- Z^, where Z^ = 
a2Zlt shunted by a circuit of admittance Y0, which latter 
circuit branches off at the points a — b, between the impe- 
dances Z and Z-. 


Generator I, Transformer I 


Fig. 107. 

This is represented diagrammatically in Fig. 107. 

It is obvious therefore, that if the transformer contains 
several independent secondary circuits they are to be con- 
sidered as branched off at the points a, i, in diagram 
Fig. 107, as shown in diagram Fig. 108. 

It therefore follows : 

An alternate-current transformer, of x secondary coils, of 
the internal impedances Z^, Z^1, . . . Z-f, closed by external 
secondary circuits of the impedances Z1, Zn, . . . Zx, is equiv- 
alent to a divided circuit of x + 1 branches, one branch of 


AL TERN A TING-CURRENT TRANSFORMER. 
Generator Transformer 


211 


Fig. 108. 

admittance Y0) the exciting current, the other branches of the 
impedances ZJ + Z7, ZJ1 + Zn, . . . 2f + Zx, the latter 
impedances being reduced to the primary circuit by the ratio 
of turns, and the whole divided circuit being fed by the 
primary impressed E.M.F. £0, over -mains of the impedance 
Z0- 

Consequently, transformation of a circuit merely changes 
all the quantities proportionally, introduces in the mains the 
impedance Z0 + Z^, and a branch circuit between Z0 and 
Z^, of admittance Y0. 

Thus, double transformation will be represented by dia- 
gram, Fig. 109. 


212 A L TERN A TING- CURRENT PHENOMENA . 

With this the discussion of the alternate-current trans- 
former ends, by becoming identical with that of a divided 
circuit containing resistances and reactances. 

Such circuits have explicitly been discussed in Chapter 
VIII., and the results derived there are now directly appli- 
cable to the transformer, giving the variation and the con- 
trol of secondary terminal voltage, resonance phenomena, etc. 

Thus, for instance, if Z/ = Z0, and the transformer con- 
tains an additional secondary coil, constantly closed by a 
condenser reactance of such size that this auxiliary circuit, 
together with the exciting circuit, gives the reactance — x0, . 
with a non-inductive secondary circuit Z^ = rv we get the • 
condition of transformation from constant primary potential 
to constant secondary current, and inversely, as previously 
discussed. 

Non-inductive Secondary Circuit. 

138. In a non-inductive secondary circuit, the external 
secondary impedance is, 


or, reduced to primary circuit, 

Assuming the secondary impedance, reduced to primary 
circuit, as equal to the primary impedance, 

* is> Y ' i r 


Substituting these values in Equations (9), (10), and (13), 
we have 

Ratio of E.M.Fs. : 


(r0 — jx0} 
4- ra—jx0 


ALTERNATING-CURRENT TRANSFORMER. 213 


+ r0-jx0 f r0-jx0 Y| . . . \ . 

R + r0 — jx0 \ R + rn — /#„ 


or, expanding, and neglecting terms of higher than third 
order, 

— jx0 

^ 


or, expanded, 

J|= - « 1 1 + 2 r° ^'^ + (r, -y^)(.% 

Neglecting terms of tertiary order also, 


£t 

Ratio of currents : 

^- = - - 

/I ^ 

or, expanded, 

~=-- 

/! a 

Neglecting terms of tertiary order also, 


Total apparent primary admittance : 


R + r0— jx 
(r0 -jx0} + R (r0- 


= {R + 2 (r0 - y x0} - & (go +jb0} -2 R (r0 - Jx0) 


214 ALTERNATING-CURRENT PHENOMENA. 

or, 

b0}- 2 (r0 -Jx0}( 


Neglecting terms of tertiary order also : 
Zt=R 

Angle of lag in primary circuit : 

tan S>0 = ^ , hence, 
rt 

2^+Rb0 + 2r0b0-2Xogo-2 
tan S>0 = a 


Neglecting terms of tertiary order also : 
'R 


139. If, now, we represent the external resistance of 
the secondary circuit at full load (reduced to the primary 
circuit) by R0, and denote, 


2 r0 _ _ . Internal resistance of transformer _ percentage 

R0 ~ External resistance of secondary circuit ~ na^ resistance, 

2 X0 _ __ ratjQ Internal reactance of transformer _ percentage 
J£ ' External resistance of secondary circuit nal reactance 

X*.- h - ratio - percentage hysteresis, 

,, , , . Magnetizing current percentage magnetizing cur- 

•KO °o= g = -10 Totalsecondarycurrent = rent^ 

and if d represents the load of the transformer, as fraction 
of full load, we have 


ALTERNATING-CURRENT TRANSFORMER. 215 


and, 


**.-«. 

a 

Substituting these values we get, as the equations of the 
transformer on non-inductive load, 
Ratio of E.M.Fs. : 


or, eliminating imaginary quantities, 


H"-"^) 


Ratio of currents : 

+ (h +> 

d 


2 f 

. ^ 

or, eliminating imaginary quantities, 


1 f 

a \ 


i i h i 


216 ALTERNATING-CURRENT PHENOMENA. 

Total apparent primary impedance : 
Z, = 


or, eliminating imaginary quantities, 


Angle of lag in primary circuit : 


That is, 

An alternate-current transformer, feeding into a non-induc- 
tive secondary circuit, is represented by the constants : 

R0 = secondary external resistance at full load ; 

p = percentage resistance ; 

q = percentage reactance ; 

h = percentage hysteresis ; 

g = percentage magnetizing current ; 

d = secondary percentage load. 

All these qualities being considered as reduced to the primary 
circuit by the square of the ratio of turns, a2. 


ALTERNATING-CURRENT TRANSFORMER. 


217 


140. As an instance, a transformer of the following 
constants may be given : 


e0 =1,000; 
a = 10 ; 


£0= 120; 

p = .02 • 


q = .06 ; 
h = .02 ; 
g = .04. 


Substituting these values, gives : 
100 


= 

" 


V(i.oou + .02 </)2 + (.0002 + .06 <ty 


*-^-£- 


.1 ii V/Y 1.0014 + — Y + ( — - 
\\ d J \ d 


. 0002 . 


- -.0004- 


tan w, 


^- 


1.9972 + . 


Fig. 110. Load Diagram of Transformer. 


218 ALTERNATING-CURKENT PHENOMENA. 

In diagram Fig. 110 are shown, for the values from 
d = 0 to d= 1.5, with the secondary current ix as abscis- 
sae, the values : 

secondary terminal voltage, in volts, 

secondary drop of voltage, in per cent, 

primary current, in amps, 

excess of primary current over proportionality with 

secondary, in per cent, 
primary angle of lag. 

The power-factor of the transformer, cos w0, is .45 at 
open secondary circuit, and is above .99 from 25 amperes, 
upwards, with a maximum of .995 at full load. 


ALTERNATING-CURRENT TRANSFORMER. 219