$(5$ points each$)$ A DC motor can be modeled as a resistance, inductance, and a voltage source. The voltage is dependent on the generator speed, and the torque is dependent on the generator current. For DC machines, the inductance can be ignored for steady$-$state analysis. The circuit model is shown.

a$.$ Suppose the motor is spinning at $1300$ rpm and producing $6$ Nm $.$ Find the motor mechanical power.

b$.$ Find the electrical losses.

c$.$ Find the minimum required terminal voltage.

d$.$ Find the motor's efficiency