328 ELECTRICAL APPARATUS

the motor has similar characteristics as the direct-current series
motor.

In this1 case we may assume the stator reduced to the rotor by
the ratio of effective turns.

Let then, in the motor shown diagrammatically in Fig. 153 :

EQ and — j$o, 7o and -j/o, ZQ = impressed e.m.fs., currents
and self -inductive impedance of stator circuits, assumed as two-
phase, and reduced to the rotor circuits by the ratio of effective
turns, GJ

E! and - jEl} /i, and - #1, Zi = impressed e.m.fs. currents
and self -inductive impedance of rotor circuits,

Z = mutual-inductance impedance,

S '== speed; and, s = 1 — S = slip,

B = brush angle,

c = ratio of effective stator turns to rotor turns.

If, then:

$ and — j£l = impressed e.m.fs., / and —jf = currents of
motor, it is:

/i = /, (H2)

/o = c/, (113)

c#o + #i = #; (114)

and, stator, by equation (7) :

E0 = Zo/o + Z(J0 - 1 1 cos 0 - jli sin 0); (115)

rotor:'

El = ZJ1 + Z (/i - /o cos 0 + jh sin 6) - jSZ (- j/i + /o

sin0 -fj/ocos 0); (116)

and, e.m.f. of rotation:

$'i = - jSZ (~jh + !« sin 0 + jh cos 0) . (117)

Substituting (112), (113) in (115), (116), (117), and- (115), (116)
in (114) gives:

+~^i) + Z (1 + c2 - 2 c cos 0) + SZ (or - 1

where :

<r = cos 0 — ,? sin 0, (119)

and:

(c2Z0 + Zi) = Z (1 + c2 - 2 c cos 0) + £Z (or - I)]7