A $15-$hp$,230-$V$,1800$ r$/$min shunt DC motor has a full$-$load armature current of $60$ A when operating at rated conditions. The armature resistance of the motor is Ra$=0\mathrm{.}15$R$\_$a $=0\mathrm{.}15\backslash ,\backslash$OmegaRa$=0\mathrm{.}15,$ and the field resistance RfR$\_$fRf$$ is $8080\backslash ,\backslash$Omega$80.$ The adjustable resistance in the field circuit RadjR$\_\{$adj$\}$Radj$$ may be varied over the range from $0$ to $200\backslash$Omega$$ and is currently set to $9090\backslash ,\backslash$Omega$90.$ Armature reaction may be ignored in this machine. The magnetization curve for this motor, taken at a speed of $1800$ r$/$min$,$ is given in tabular form below:

EAE$\_$AEA$,$ V$8\mathrm{.}5150180215226242$IfI$\_$fIf$,$ A$0\mathrm{.}000\mathrm{.}801\mathrm{.}001\mathrm{.}281\mathrm{.}442\mathrm{.}88$

$($a$)$ What is the speed of this motor when it is running at the rated conditions specified above?

$($b$)$ The output power from the motor is $15$ hp at rated conditions. What is the output torque of the motor?

$($c$)$ What are the copper losses and rotational losses in the motor at full load $($ignore stray losses$)?$

$($d$)$ What is the efficiency of the motor at full load?

$($e$)$ If the motor is now unloaded with no changes in terminal voltage or RadjR$\_\{$adj$\}$Radj$,$ what is the no$-$load speed of the motor?

$($f$)$ Suppose that the motor is running at the no$-$load conditions described in part $($e$).$ What would happen to the motor if its field circuit were to open? Ignoring armature reaction, what would the final steady$-$state speed of the motor be under those conditions?

$($g$)$ What range of no$-$load speeds is possible in this motor, given the range of field resistance adjustments available with RadjR$\_\{$adj$\}$Radj$?$