362 ELECTRICAL APPARATUS

impressed voltage, /, to the field strength, $, and to the number of
field turns, n^

10~8. (26)

3. The impedance voltage of the motor:

' e' = JZ (27)'

and: Z = r + jx,

-where r = total effective resistance of field coils, armature with
commutator and brushes, and compensating winding, x — total
self -inductive reactance, that is, reactance of the leakage flux of
armature and compensating winding — or the stray flux passing
locally between the armature and the compensating conductors
— plus the self-inductive reactance of the field, that is, the reac-
tance due to the stray field or flux passing between field coils
and armature.

In addition hereto, x comprises the reactance due to the quad-
rature magnetic flux of incomplete compensation or overcom-
pensation, that is, the voltage generated by the quadrature flux,
<£', in the difference between armature and compensating con-
ductors, n\ — n% or n^ — n\.

Therefore the total supply voltage, E, of the motor is :

E = ei + eQ + e'

= 2 Tr/on^ 10-8 + 2 JT/n^ 10~8 + (r + jx) I. (28)

Let, then, R = magnetic reluctance of field circuit, thus
$ = -~ = the magnetic field flux, when assuming this flux as in
phase with the excitation 7, and denoting:
= x0 (30)
JL\j
as the effective reactance of field inductance, corresponding to
the e.m.f. of alternation:
S = ~ = ratio of speed to frequency, or speed
* as fraction of synchronism,
/ (31)
c = ™. = ratio of effective armature turns to
nQ field turns;