182 ELECTRICAL APPARATUS

and separating the real and imaginary quantities :

~-j (r0 (ri + r)

a Z]c

- j -^-g Oo(xi + x) — £ fa + r)) + (r0b - E00) ' ,

L Ct 2» & * J J

+ r , ffi • r^^i + *) . 6i i

-J- + Kj- , L-^^F- + -J I'

Neglecting the exciting current, or rather considering it as
a separate and independent shunt circuit outside of the trans-
former, as can approximately b3 done, and assuming the primary
impedance reduced to the secondary circuit as equal to the
secondary impedance :

Y - n ^° - 7

/ o — u, ™ — x/i.

Substituting this in the equations of the general transformer
we get:

#o = n0e 1 1 + —2 [ri fa + r) + sxl (XL + x)]

I %k

- ^ [an (a* + *)-*i (f! + r)] }»

106. The true power is, in symbolic representation:

P =

denoting :

-. w

gives:
Secondary output of the transformer:
/ 2
Pi = Will}1 = (~^\ r = sro;