30 ELECTRICAL APPARATUS

The leakage reactance, x2, of the inner squirrel cage is that due
to the flux produced by the current in the inner squirrel cage,
which passes between the two squirrel cages, and does not in-
elude the reactance due to the flux resulting from the current,
Js, which passes beyond the outer squirrel cage, as the latter is
mutual reactance between the two squirrel cages, and thus meets
the reactance, xi.

It is then, at slip s:

/.-*•

/o = /2 + h + YQE. (3)

and:

E = E} + y#j (/i + /2). (5)

The leakage flux of the outer squirrel cage is produced by the
m.m.f. of the currents of both squirrel cages, /i + 72, and the
reactance voltage of this squirrel cage, in (5), thus isjxi (Ii + J2).

As seen, the difference between EI and E^ is the voltage in-
duced by the flux which leaks between the two squirrel cages, in
the path of the reactance, x^ or the reactance voltage, 0:2/2; the
difference between $ and $i is the voltage induced by the rotor
flux leaking outside of the outer squirrel cage. This has the
m.m.f. Ji + /a, and the reactance x\9 thus is the reactance voltage
#1 (/i + /2). The difference between $Q and $ is the voltage
consumed by the primary impedance: Zo/0. (4) and (5) are the
voltages reduced to full frequency; the actual voltages are ,5
times as high, but since all three terms in these equations are
induced voltages, the s cancels.

21. From the equations (1) to (6) follows:

(7)

(9)