114

ELECTRICAL APPARATUS

The secondary current under the shaded portion of the pole is:
/'i = #27:. (66)

The current in the shading coil is:

I* = #2F2. (67)

The primary exciting current of the shaded portion of the pole

thus:

/f __
oo —

Jo = J'l + /oo + h =

(68)

from (65) and (69) follows:

* r, + £ Y +

Mi a

F1 + ~F+Y2|; (69)

(Z

(70)

1-a

and this gives the angle, <£, of phase displacement between the two
component voltages, ft and $2.
. If, as usual, 6 = 1, and
if a — 0.5, that is, half the pole is shaded, it is:

E, _ Yi + 2Y + Yz

#2~ Fx + 27 "' (il)

74. Assuming now, as first approximation, ZQ = 0, that is,
neglecting the impedance drop in the single-phase primary coil—
which obviously has no influence on the phase difference between
the component voltages, and the ratio of their values, that is,
on the approximation of the devices to polyphase relation—then
it is:

ft + #2 = <?0; (72)

thus, from (70):

ft =

r, + - Y + F2

a

(73)