Torque vs speed curves for electric motors are which shape?

• A. Linear
• B. Parabolic
• C. Exponential
• D. Useless

Answer: (A)

Torque versus speed for a DC motor under a fixed supply voltage forms a straight line. This comes from the motor equations: the back-EMF is proportional to speed, and the armature current is determined by the remaining voltage after subtracting that back-EMF and dividing by the armature resistance. Since torque is proportional to current, substituting these relationships gives a linear relation between torque and speed with a negative slope: as torque increases, speed decreases in a simple, proportional way. The line crosses the torque axis at the stall torque (maximum torque at zero speed) and crosses the speed axis at the no-load speed (maximum speed at essentially zero torque). Because of this linear relation, shapes like parabolic or exponential curves don’t fit the standard DC motor model under constant voltage, and a line best represents the relationship.