The frequency of induced e.m.f in the armature conductors depends upon speed and the number of poles.
Let, N = rotor speed in r.p.m
P = number of rotor poles.
f = frequency of induced e.m.f in Hz.
Consider a stator conductor that is successively swept by the N and S poles of the rotor. If a positive voltage is induced when a N-pole sweeps across the conductor, a similar negative voltage is induced when a S-pole sweeps by. This means that one complete cycle of emf is generated in the conductor as a pair of pole passes through it, one N pole and the adjoining S-pole. The same is true for every other armature conductor.
Number of cycles/revolution = Number of pairs = P/2
Number of revolutions/second = N/60
Number of cycles/second = (P/2) × (N/60)
But number of cycles of e.m.f per second is its frequency.
∴ f = PN/120
It may be noted that N is the synchronous speed. For a given alternator, the number of rotor poles is fixed and, therefore, the alternator must run at synchronous speed to give an output of desired frequency. For this reason, an alternator is sometimes called synchronous generator.