1. Consider a permanent-magnet dc motor with the following parameters:
Rₐ = 0.35 Ohm, Lₐ = 1.5 mH, kₑ = 0.5 V/rad/s, kₜ = 0.5 Nm/A, and Jₘ = 0.02 kg m². The rated torque of this motor is 4 Nm.
Plot the steady-state torque-speed characteristics for V = 100 V, 60 V, and 30 V.

2. The motor above is driving a load whose torque requirement remains constant at 3 Nm, independent of speed. Calculate the armature voltage Vs to be applied in steady-state if this load is to be driven at 1,500 rpm.