Page 95 - Electric Machinery Fundamentals

TRANSFORMERS 71

appearing at one end of each winding in Figure 2-4 tell the polarity of the voltage
and cutTent on the secondary side of the transformer. The relationship is as
follows:

1. If the primary voltage is positive at the dotted end of the winding with respect
to the undotted end, then the secondary voltage will be positive at the dotted
end also. Voltage polarities are the same with respect to the dots on each side
of the core.
2, If the primary current of the transformer flows into the dotted end of the pri-
mary winding, the secondary current will flow out of the dotted end of the
secondary winding.
The physical meaning of the dot convention and the reason polarities work out
this way will be explained in Section 2.4, which deals with the real transformer.
(
Power in an Ideal Transformer
The real power Pin supplied to the transformer by the primary circuit is given by
the equation

(2-6)
where Op is the angle between the primary voltage and the primary current. The
real power P out supplied by the transformer secondary circuit to its loads is given
by the equation

(2-7)

where f)s is the angle between the secondary voltage and the secondary current.
Since voltage and current angles are unaffected by an ideal transformer, Op = Os = fJ.
The primary and secondary windings of an ideal transfonner have the same power
facto,
How does the power going into the primary circuit of the ideal transformer
compare to the power coming out of the other side? It is possible to find out
through a simple application of the voltage and current equations [Equations (2-4)
and (2- 5)J. The power out of a transformer is

Pout = Vs I cos () (2-8)
s
Applying the tUll1s-ratio equations gives Vs = V pIa and Is = alp, so
_lie
Po", - a (alp) cos e

I Pout = VpIp cos e - Pin I (2-9)

Thus. the output power of an ideal transformer is equal to its input powel: