Q$4.(25$ pts$)$ A $240-$y series DC motor has a full load current of $80$ A $.$ It has a field winding of $24$ turns per pole. The armature resistance is $0\mathrm{.}12$ ohm and the field resistance is $0\mathrm{.}09$ ohm $.$ The magnetization curve for this motor can be considered as approximately linear and some data of the magnetization curve are given in the following table when the speed is $1000\frac{r}{m}in.$ Answer the following questions:

$\backslash$table$[[\backslash$table$[[$Armature$],[$voltage$,$ Ea $($V$)]],95,150,220,240,],[$MMF $($A$.$turns$),1140,1800,$g$.,,220]]$

a$)$ Calculate the speed of the motor under full load conditions. $($Ignore armature reaction$)$

b$)$ By neglecting rotational and stray losses, calculate the output power$-$of the motor under the conditions in part $($a$)$

c$)$ By neglecting rotational and stray losses, calculate the forque of the motor under the conditions in part $($a$)$

d$)$ By neglecting rotational and stray losses, calculate the efficiency of the motor under the conditions in part $($a$)$