ALTERNATING-CURRENT MOTORS 305
S = speed, as fraction of synchronism, that is, ratio of fre-
quency of rotation to frequency of alternation.
It is then:
E.m.f. consumed by self-inductive impedance, ZQ!Q.
E.m.f. consumed by mutual-inductive impedance, Z (J0 + /i
cos r) since the m.m.f. acting in the direction of the axis of the
stationary coil is the resultant of both currents. Hence:
#o = Zo/o + Z (Jo + ll cos r). (3)
In the rotating circuit, it is:
; E.m.f. consumed by self-inductive impedance, Zifi.
I E.m.f. consumed by mutual-inductive impedance or "e.m.f. of
? alternation'7: Zr (Ji + 70 cos r). (4)
| E.m.f. of rotation, -jSZ"IQ sin r. (5)
I Hence the impressed e.m.f.:
j E, = zji + Z1 (II + Jo cos T) -jSZ"Iv sin r. (6)
;;„:/ In a structure with uniformly distributed winding, as used in
induction motors, etc., Zr = Z" = Z, that is, the exciting im-
pedance is the same in all directions.
Z is the reciprocal of the "exciting admittance/' Y of the in-
duction-motor theory.
In the most general ease, of a motor containing n circuits, of
which some are revolving, some stationary, if:
&, Ik) %k = impressed e.m.f., current and self-inductive im-
pedance respectively of any circuit, k.
Z1, and Zu = exciting impedance parallel and at right angles
respectively to the axis of a circuit, i,
Tjf = space angle between the axes of coils k and i} and
S = speed, as fraction of synchronism, or -"frequency of
rotation.77
It is then, in a coil, i:
Et = Zili + Z^h cos rfc« - jSZ" ^ /* sin Tjb*, (7)
i i
where:
ZiJi = e.m.f. of self-inductive impedance; (8)
n
Z^klk COST*:* = e.m.f. of alternation; (9)
"1'
/£'. = - jSZu}kIk sin T// = e.m.f. of rotation; (10)
i
which latter = 0 in a stationary coil, in which S = 0.
20