Derive the relationship between Synchronous speed (Ns) and frequency (f) of alternator.
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Derivation of Relationship Between Synchronous speed (Ns) and Frequency (f) of Alternator:

Let, Ns = rotor speed in rpm (synchronous speed) P = number of rotor poles f = frequency of emf in Hz Consider a stator conductor that is successively swept by the N and S poles of 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 it. This means that one complete cycle of emf is generated in the conductor as pair of poles passes it. Hence : 

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