Problem $5$: A series connected DC motor needs to provide an output torque of $15$ Nm with negligible

rotational losses. The motor has resistance values of RA$=3$ and RF $=22$ while the magnetization curve

for the motor is linear with M $=150$ V$/$A and $$m $=125$ rad$/$sec$.$ The motor is connected to a motor

controller that can provide a VT from $50$ V to $350$ V$.$

a$)$ What is the smallest value of VT for which the motor will still be able to turn for the desired

torque? $(5$ points$)$

b$)$ Derive an expression for the efficiency in terms of VT$.$ Your answer should be in the

following form where Vo is a number. What is Vo $?(10$ points$)$

$1001$ o

T

V

V

$$

$$

$$

c$)$ What is the most efficient VT and the motor speed corresponding to this V T$?(5$ points$)$