ALTERNATING-CURRENT MOTORS 325
and a wattless or reactive component:
i"o = +jc (Ai sin 6 - A2 cos 0); (99)
where:
7"o = i'o - #"0. (100)
The reactive component, i"0, is zero, if:
Ai sin 0 — A2 cos e = o; (101)
hence:
. tan 0i = + 4~2' (102)
AI
In this case, that is, with brush angle, 0i, the secondary im-
pressed voltage, cEj does not change the reactive current, but
adds or subtracts, depending on the sign of c, energy, and so
raises or lowers the speed of the motor: case (1).
The power component, i'o, is zero, if:
Ai cos 6 + At sin 6 = o, (103)
hence:
tan 02 = - 4™* (104)
A.2
In this case, that is, with brush angle, 02, the secondary im-
pressed voltage, cEj does not change power or speed, but pro-
duces wattless lagging or leading current. That is, with the
brush position, 02, the polyphase shunt motor can be made to
produce lagging or leading currents, by 'varying the voltage im-
pressed upon the secondary, c$, just as a synchronous motor
can be made to produce lagging or leading currents by varying
its field excitation, and plotting the stator current, Jo, of such a
polyphase shunt motor, gives the same V-shaped phase charac-
teristics as known for the synchronous motor.
These two phase angles or brush positions, 0i and 02, are in
quadrature with each other.
There result then two distinct phenomena from the insertion
of a voltage by commutator, into an induction-motor armature:
a change of speed, in the brush position, 0i, and a change of phase
angle, in the brush position, 02, at right angles to 0i.
For any intermediate brush position, 0, a change of speed so
results corresponding to a voltage:
c$ cos (0i - 0);