;

* t. \

'i :

I

rl

H

i!

'

" !

i

444

ELECTRICAL APPARATUS

to the alternating current, i, the resultant current in the arma-
ture coil, r, is:

Jo

. 7T

sin -
n

• sin (6 - r - 00) - 1

(13)

and the ratio of heating, of the resultant current, i0, compared
with the current, -~, of the same machine as direct-current gen-
erator of the same output, thus is:

j0\

-
2/

6/o)~1

sm

(14)

Averaging (14) over one half wave gives the relative heating
of the armature coil, r, as:

1 f- ^o2 ,a 1 f »

*-;%-;!

Integrated, this gives:

4k
n sin

>~T-00) -1 de> (15)

16 ft cos

sn2

. sin

n n

243. Herefrom follows the local heating in any armature
coil, r, in the coils adjacent to the leads by substituting r = ± ~,
and also follows the average armature heating by averaging

£ ^x . ^

7Tfromr = — - to r = H—*
T n n

The average armature heating of the n-phase converter there-
fore is:

or, integrated :

r = .. ^

+ 1 -

2 • ,

n2sm2 -

(17)
v '