SINGLE-PHASE COMMUTATOR MOTORS 363

substituting (30) and -(31) in (28):

E = cSxd + jxQI + (r+jx) I

_ ......

j (X

(32)
(33)

(34)

(35)
The useful work of the motor is done by the e.m.f. of rotation:

or:

r =

(

and, in absolute values:

f) ~g

The power-factor is given by:

and, since this e.m.f., Ei, is in phase with the current, f} the
useful work, or the motor output (inclusive friction, etc.), is:

(36)

(r + cS#o)2 + (a? +
and the torque of the motor is:

— p.

D = -g =

(r + c&Eo)2 + (x + £0)2
For instance, let :

e — 200 volts, c = — = 4,
Z = r + jx = 0.02 + 0.06 j, x<> = 0.08;

10,000

(37)

then.

^ _
1 + 16

amp.,

P =

32,000 S

(1 + 16 S)2 + 49
32,000

(1 + 16 S)2 + 49

: kw.,

. kw.

11
m