178

ELECTRICAL APPARATUS

ill,

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> li

.
MS

4
'V

105. Let, in a general alternating-current transformer :

secondary
" — -- ~

J_.
s = ratio

primary

, ,, ,. „

frequency, or slip ;

H J' *

thus, if:

/ = primary frequency, or frequency of impressed e.m.f.,
sf = secondary frequency;

and the e.m.f. generated per secondary turn by the mutual flux
has to the e.m.f. generated per primary turn the ratio, s,

s = 0 represents synchronous motion of the secondary;

s < 0 represents motion above synchronism—driven by external

mechanical power, as will be seen;
s = I represents standstill;
s > I represents backward motion of the secondary,

that is, motion against the mechanical force acting between
primary and secondary (thus representing driving by external
mechanical power).
Let:

n0 = number of primary turns in series per circuit;
HI = number of secondary turns in series per circuit;

a = ~ = ratio of turns ;

Y = g — jb = primary exciting admittance per circuit;

where:

where:

where:

g = effective conductance;
6 = susceptance;
ZQ = r0 +• j#o = internal primary self-inductive impedance
per circuit,
rQ = effective resistance of primary circuit;
XQ = self-inductive reactance of primary circuit;
n = TI + >jxi — internal secondary self-inductive im-
pedance per circuit at standstill, or for s ~ 1,
7*1 = effective resistance of secondary coil;
Xi = self-inductive reactance of secondary coil at stand-
still, or full frequency, s = 1,