Page 104 - Electric Machinery Fundamentals

80 ELECTRIC MACHINERY FUNDAMENTALS

where CPs = total average secondary flux
<PM = flux component linking both primary and secondary coils
<PLS = secondary leakage flux
With the division of the average pIimary flux into mutual and leakage com-
ponents, Faraday's law for the primary circuit can be reexpressed as

(2-21)

The first term of this expression can be called er(t), and the second term can be
called eLP(t), If this is done, then Equation (2- 21) can be rewritten as
(2-22)
(
The voltage on the secondary coil of the transformer can also be expressed
in terms of Faraday's law as
d<ps
vs(t) = NSdt
= N d<PM + N d<PLS (2-23)
5 dt S dt
= es(t) + eLS(t) (2-24)

The primary voltage due to the mutual flux is given by
_ d<PM
ep(t) - Np dt (2- 25)
and the secondary voltage due to the mutual flux is given by

(2-26)

Notice from these two relationships that

Therefore,

(2- 27)

This equation means that the ratio oj the primary voltage caused by the mutual
flux to the secondary voLtage caused by the mutual flux is equal to the turns ratio
of the transformer. Since in a well-designed transformer cPM » c:PLP and
</>1>1» cPLS' the ratio of the total voltage on the primary of a transformer to the to-
tal voltage on the secondary of a transformer is approximately