Final answer:
A four-pole motor will have a higher RPM than a six-pole motor when operated with the same power source due to the direct relationship between the number of poles and the synchronous speed of an induction motor.
Step-by-step explanation:
When considering which induction motor will have a higher RPM when operated with the same power source, it is important to understand the relationship between the number of poles and the speed of the motor. The synchronous speed of an induction motor, which is the maximum speed it can reach under no load condition and is solely dependent on the frequency of the power source and the number of poles the motor has, can be determined by the formula:
N_s = (120 × f) / P
where N_s is the synchronous speed in RPM, f is the power supply frequency in Hertz (Hz), and P is the number of poles.
Given that the frequency (f) remains the same, the motor with fewer poles will have a higher synchronous speed. Therefore, a four-pole motor will have a higher RPM compared to a six-pole motor. Hence, the correct answer to the student's question is A. Four-pole motor.