Final answer:
Neither the two value split phase motor nor the resistance split phase motor is suitable for speed control using a variable autotransformer. These motors are designed to run at a fixed speed determined by the supply frequency, and other motor types like AC motors with VFDs or DC motors with variable voltage inputs are better suited for speed control.
Step-by-step explanation:
To answer the question of which single phase motor can successfully be used with a variable autotransformer for speed control, we need to understand the characteristics of the motors in question. A two value split phase motor has separate windings for starting and running, and it does not lend itself well to speed control via a variable autotransformer because of the potential for damaging the starting winding. A resistance split phase motor uses a resistor to create a phase shift for starting torque but it is also not suitable for speed control using a variable autotransformer due to the resistor's fixed value which would interfere with the ability to vary speed smoothly. In general, variable autotransformers are not ideal for speed control of split phase motors because these motors are designed to operate at a fixed speed determined by the supply frequency. For speed control, other types of motors such as variable frequency drives (VFDs) for AC motors or DC motors with variable voltage input, are more suitable. Therefore, the answer to the question is c) neither.