104 ELEMENTS OF ELECTRICAL ENGINEERING

or, reduced, _

/ = V1252 + 33.52
= 129.4 amp.

Thus, the volt-ampere input,

Q = el = 220 X 129.4

= 28,470.

The e.m.fs. acting upon the two motor circuits respectively are
Ei = IZl = (125 - 33.5 j] (1.09 - 0.11 j) = 132.8 - 50.4 j

and
E' = iz = (125 - 33.5 j} (0.55 + 0.55;) = 87.2 + 50.4 j.

Thus, the tangents of their phase angles are

50 4

tan $1 = + T^Q = + 0.30; hence, 0i = + 21°;

KA 4

tan 0' = - —^ = - 0.579; hence, 0' = - 30°;

o/ ..£

and the phase difference,

0 = ^ - 0' = 51°.

The absolute values of these e.m.fs. are

ei = V132.8 + 50.42 = 141.5
and

e' = V87.22 - 50.42 = 100.7;

thus, the torque is

D = aetf' sin 6
= 11,100 a;

and the apparent torque efficiency is

_ D 11,100 a
*'-~0" 28,470 - °^9a'

Hence, comparing this with the quarter-phase motor, ttie
relative torque is

JP-_ 11,100 a

Do ""12,100 a "" u>y '

and the relative torque per volt-ampere, or relative apparent;
torque efficiency, is

it 0.39 a

770 0.388 a

= 1.005.