In the formula Ns = 60f ÷ P, what does P represent in the synchronous speed calculation?

• A. Number of poles per phase
• B. Number of poles total
• C. Number of pairs of poles per phase
• D. Number of rotor slots

Answer: (C)

The main idea here is that synchronous speed depends on how many magnetic pole pairs the machine has, together with the supply frequency. The formula Ns = 60 f ÷ P uses P as the number of pole pairs because each pole pair corresponds to two poles and determines how many times the stator’s magnetic field completes a full cycle per electrical cycle.

If you start from the standard form Ns = 120 f / P_total (where P_total is the total number of poles) and let P_pairs = P_total / 2, you get Ns = 120 f / (2 P_pairs) = 60 f / P_pairs. So the P in this equation is the number of pole pairs, i.e., the pairs of poles (often described per phase in a three‑phase machine).

This is why the best answer is the number of pairs of poles per phase. The other options refer to volts of poles per phase, total poles, or rotor slots, which don’t match how the formula relates speed to pole structure.