368

ELECTRICAL APPARATUS

gives the impressed e.m.f., OE, nearer in phase to 01 than with
0$ in phase with 01.

In this manner, if the e.m.fs. of self-inductance are not too
large, unity power-factor can be produced, as shown in Fig. 178.

Let 01 = total current, OEf = impedance voltage of the
motor, OE = impressed e.m.f. or supply voltage, and_assumed
in phase with 01. OE then must be the resultant of OE' and of
OEi, the -voltage of rotation plus that of alternation, and resolv-
ing therefore OEZ into two components, OE\ and OEQ, in quadra-

FIG. 179.—Single-phase commutator-motor diagram with secondary
excitation.
ture with each other, and proportional respectively to the e.m.f.
of rotation and the e.m.f. of alternation, gives the magnetic flux,
0$, in phase with the e.m.f. of rotation, OEi, and the component
of current in the field, 01', and in the non-inductive resistance,
01", in phase and in quadrature respectively with 0<i>, which
combined make up the total current. The projection of the
e.m.f. of rotation OEi on 01 then is the power component of
the e.m.f., which does the work of the motor, and the quadra-
ture projection of, OEi, is the compensating component of the
e.m.f. of rotation, which neutralizes the wattless component of
the e.m.f. of self-inductance.
Obviously such a compensation involves some loss of power
in the non-inductive resistance, r0, shunting the field coils, and as
the power-factor of the motor usually is sufficiently high, such
compensation is rarely needed.
In motors in which some of the circuits are connected inductively
in scries with the others the diagram is essentially the same, except