$250$V R$\_($a$)+$ R$\_($s$)=0\mathrm{.}07$ ohm DC series connected motor, under some load which requires constant power, armature current is $50$ amp. Magnetization characteristics of the machine is given by following equation at constant speed of n$=1200$ rpm Ea$=1\mathrm{.}6*$ I$\_($F$)$ volt.

$($shaft speed $=$ mechanical speed$)$ mechanical load has the characteristic of having constant power at all speeds. $($ armature and field currents are the same$)$

a$)$ Calculate the shaft speed for the above described operation

b$)$For the shaft speed of $1453$ rpm$,$ what will be the terminal voltage $?$