306

ELECTRICAL APPARATUS

The power output of the motor is the sum of the powers of all
the e.m.fs. of rotation, hence, in vector denotation:

i i

and herefrom the torque, in synchronous watts:

D = ~ = - F [jZu fk h sin rk\ I j1.

o — i

The power input, in vector denotation, is:
Po = ft [Ei,

and therefore:

(11)

(12)

(13)

Po1 = true power input;

Po7' = wattless volt-ampere input;

Q — vPo1 + Po? = apparent, or volt-ampere
input;

P

«--: = ejfficiency;

jTo

^ = apparent efficiency;
V

~-.. = torque efficiency;

Jr o

D

Q

= apparent torque efficiency;

Po1 . ,
-y == power-i actor.
y
From the ?i circuits, i = 1, 2 . . .71, thus result n linear
equations, with 2 n- complex variables, /; and jg?t-.
Hence n further conditions must be given to determine the
variables. These obviously are the conditions of operation of
the n circuits.
Impressed e.m.fs. Ei may be given.
Or circuits closed upon themselves #* = 0.
Or circuits connected in parallel dE* = CkEkj where c* and c&