Pb$3-$ The constant$-$speed magnetization curve for a $25-kW,250-V$ dc machine at a speed of $1500\frac{r}{m}in$ is shown in Fig. $1.$ This machine is separately excited and has an armature resistance of $100m.$ This machine is to be operated as a de generator while driven from a synchronous motor at constant speed. $(8$ Marks$)$

a$.$ What is the rated armature current of this machine? $(2$ Marks$)$

b$.$ With the generator speed held at $1500\frac{r}{m}in$ and if the armature current is limited to its rated value, calculate the maximum power output of the generator and the corresponding armature voltage for constant field currents of

$($i$)1\mathrm{.}0$ A $,$

$(2\mathrm{.}0$ A

$($ii$)2\mathrm{.}5$ A $.(6$ Marks $)$

$\backslash$table$[[\frac{E_8}{?},V_4(v),P(w),],[1,,,],[2,,,],[25,,,]]$