:n

160 ELECTRICAL APPARATUS
sufficiently flexible, as by belting, etc., so that the motors can
drop into exact step with each other and maintain step by their
synchronizing power.
It is of interest, then, to examine the synchronizing power of
two induction motors which are connected in multiple with
their secondaries on the same rheostat and operated from the
same primary impressed voltage.
95. Assume two equal induction motors with their primaries
connected to the same voltage supply and with their secondaries
connected in multiple with each other to a common resistance,
r, and neglecting for simplicity the exciting current and the vol-
tage drop in the impedance of the motor primaries as not mate-
rially affecting the synchronizing power.
Let Zi = TI + jxi = secondary self-inductive impedance at
full frequency; $ = slip of the two motors, as fraction of syn-
chronism; CQ = absolute value of impressed voltage and thus,
when neglecting the primary impedance, of the voltage generated
in the primary by the rotating field.
If then the two motor secondaries are out of phase with each
other by angle 2 r, and the secondary of the motor 1 is behind in
the direction of rotation and the secondary of the motor 2
ahead of the average position by angle ry then:
$1 = seQ (cos r + j sin r) = secondary generated
l^m.f. of the first motor, (1)
$2 = seQ (cos r — j sin r) = secondary generated
e.m.f. of the second motor. (2)
And if /i = current coming from the first, JT2 = current coming
from the second motor secondary, the total current, or current
in the external resistance, r, is:
/ = /t + /2; (3)
it is then, in the circuit comprising the first motor secondary
and the rheostat, r,
#1 - hZ - IT = 0, (4)
in the circuit comprising the second motor secondary and the
rheostat, r,
& - hZ - IT = 0, (5)
where
Z « TI + js