Problem $5$:

a$)$ A shunt connected DC motor needs to provide $P_{\text{o}\text{u}\text{t}}=1000W$ of power to a mechanical load. The magnetization curve for the motor is shown below. If the supplied voltage is $225$ V $,$ what is the speed of the motor in rad$/$sec and torque on the motor assuming negligible rotational losses given $R_A=10,R_{\text{a}\text{d}\text{j}}=5,$ and $R_F=25.$ You may assume that the motor is operating in its normal operating range. $(10$ points$)$

b$)$ What would be the output power if $R_{\text{a}\text{d}\text{j}}$ changed to $50$ assuming the same load is connected? $(10$ points$)$