SINGLE-PHASE INDUCTION MOTOR 113
y — gf — jjy — primary exciting admittance of shaded poles
(assuming total pole shaded).
If the reluctivity of the shaded portion of the pole is the same
as that of the unshaded; then Yf = Y; in general, if
b = ratio of reluctivity of shaded to unshaded portion of
pole,
F = 67,
b either = 1, or, sometimes, b > 1, if the air gap under the
shaded portion of the pole is made larger than that under the
unshaded portion.
Yi = gi — jbi = self-inductive admittance of the revolving
secondary or armature,
¥2 = </2 — jbz = self-inductive admittance of the stationary
secondary or shading coil, inclusive its exter-
nal circuit, where such exists.
Z0? YI and F2 thus refer to the self-inductive impedances, in
which the energy component is due to effective resistance, and
Y and Y' refer to the mutual inductive impedances, in which the
energy component is due to hysteresis and eddy currents.
a = shaded portion of pole, as fraction of total pole; thus
(1 — a) = unshaded portion of pole.
If:
<?o = impressed single-phase voltage,
El = voltage induced by flux in unshaded portion of pole,
j£2 = voltage induced by flux in shaded portion of pole,
Jo = primary current,
it- is then:
<30 = Ei + #2 4- £0/0. (62)
The secondary current in the armature under the unshaded
portion of the pole is:
/i = #iFx. (63)
The primary exciting current of the unshaded portion of the
pole:
/oo = T-~>
JL — d
thus:
Jo = h + /oo = #, | Fx + T-F~- (65)
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