A separately excited DC machine drives a mechanical load at constant torque from $0$ rpm to $1500$ rpm $.$ The supply voltage, $V_{DC},$ is varied and the field current, $I_f,$ is kept constant.

The parameters for the DC machine are:

$K^{\text{'}}=0\mathrm{.}8,I_f=2A,R_A=2\mathrm{.}4$

$($i$)$ Draw the equivalent circuit diagram for a separately excited DC machine and highlight which parts represent the armature winding and the field winding.

$($iii$)$ Calculate the minimum and maximum values of $V_{DC}$ to give constant torque from $0$ to $1500$ rpm $.$