Explanation :
A=2, separately excited dc machine
$ {\mathrm R}_\mathrm a\approx0,230\;\mathrm V,5\;\mathrm{kW},\mathrm N=1200\;\mathrm{rpm} $
For ware winding,
$ 230=\frac{\mathrm\phi\times4\times1200\times{\mathrm Z}_1}{60\times2}\;\;...(\mathrm i) $
For lap winding,
$ \mathrm V=\frac{\mathrm\phi\times4\times1200\times{\mathrm Z}_1}{60\times4}\;\;\;...(\mathrm{ii}) $
Dividing equation (i) by equation (ii)
$ \begin{array}{l}\frac{\;230}{\mathrm V}=\frac42\\\Rightarrow\;\mathrm V=115\;\mathrm V\end{array} $
For power :
Wave:
Total conductor in single path $ =\frac{\mathrm Z}2 $
Let, resistence of $ \frac{\mathrm Z}2 $ conductor = R
Total resistence,
$ {\mathrm P}_1=\frac{\mathrm V_1^2}{{\mathrm R}_1}=\frac{\mathrm V_1^2}{(\mathrm R/2)}\;\;\;...(\mathrm i) $
Lap :
Total conductor in single path $ =\frac{\mathrm Z}4 $
Let resistence of single path $ =\frac{\mathrm R}4 $
Total resistence $ =\frac{\mathrm R/2}4=\frac{\mathrm R}8 $
$ {\mathrm P}_2=\frac{\mathrm V_2^2}{{\mathrm R}_2}=\frac{\mathrm V_2^2}{(\mathrm R/8)}\;\;...(\mathrm{ii}) $
By equarion (i) and (ii)
$ \begin{array}{l}\frac{{\mathrm P}_1}{{\mathrm P}_2}=\frac{\mathrm V_1^2/(\mathrm R/2)}{\mathrm V_2^2/(\mathrm R/8)}\\\;\;\;\;\;\;=\frac{(230)^2}{\mathrm R/2}\times\frac{\mathrm R/8}{(715)^2}=1\end{array} $