$3.$ The data sheet for a wound field separately excited dc motor gives the following parameters Va$,$rated $=220$ V Ia$,$rated $=10$ A Vf$,$rated $=120$ V Ra $=1\mathrm{.}5$ Rf $=120$ Kb $=0\mathrm{.}215$ V$/$RPM rated $=100$ rad$/$s where Kb is the motor back emf constant, which is simply Ka$$d$.$ For clarity, this is to say Kb $$ Ka$$d $($a$)$ Calculate the torque being developed under rated conditions and the no load speed $($b$)$ Repeat part $($a$)$ if the armature voltage is reduced to $200$ V and determine if rated speed can be achieved. If rated speed can be achieved, clearly state why in your answer. Similarly, if rated speed cannot be achieved, clearly state why and determine a value Vf which will allow rated speed to be achieved. $($c$)$ Suppose we wish to ensure operation at twice the rated speed. Calculate the value of Vf which will allow us to achieve this while still operating under rated conditions