SINGLE-PHASE COMMUTATOR MOTORS 833

in the field conductors an e.m.f. of self-inductance, which is not
useful but wattless, and therefore harmful in lowering the ppwer-
factor, hence must be kept as low as possible. 1

This e.m.f. of self-inductance of the field, e0, is proportional
to the field strength, <i>, to the number of field turns, no, and to
the frequency, /, of the impressed e.m.f. :

e0 = 27r/n0$10-8, (1)

while the useful e.m.f. generated by the field in the armature
conductors, or " e.m.f. of rotation," e, is proportional to the field
strength, 3>, to the number of armature turns, ni, and to the fre-
quency of rotation of the armature, /0:

= 2

10~8.

(2)

This later e.m.f., e, is in phase with the magnetic flux, <3>, and
so with the current, i, in the series motor, that is, is a power e.m.f.,
while the e.m.f. of self -inductance, e0, is wattless, or in quadrature
with the current, and the angle of lag of the motor current thus
is given by:

.tan 6 =

^r

(3)

where ir = voltage consumed by the motor resistance. Or ap-
proximately, since ir is small compared with e (except at very
low speed):

tan 8 =

6

and, substituting herein (1) and (2):

-/ r'

tan 6 =

Jo n\

(4)

(5)

Small angle of lag and therewith good power-factor therefore
require high values of /o and n\ and low values of / a-nd nQ.
High /o requires high motor speeds and as large number of
poles as possible. Low / means low impressed frequency; there-
fore 25 cycles is generally the highest frequency considered for
large commutating motors.
High ni and low nQ means high armature reaction and low
field excitation, that is, just the opposite conditions from that
required for good commutator-motor design.
Assuming synchronism, /o = /, as average nciotor speed—750
revolutions with a four-pole 25-cycle motor—an armature reac-