E.M.F. equation of an elementary alternator single phase
Let us assume that this generator has an armature winding consisting of a total number of full pitched concentrated coils C, each coil having a given number of turns Nc. Then the total number of turns in any given phase of a single-phase generator armature is
N p = CNc
According to Faraday's law of electromagnetic induction the average voltage induced in a single turn of two coil sides is
The voltage induced in one conductor is 2ϕ/(1/n) = 2ϕs, where n=speed of rotation in r.p.s, for a 2 pole generator. Furthermore, when a coil consisting of Nc turns rotates in a uniform magnetic field, at a uniform speed, the average voltage induced in an armature coil is
where ϕ is the number of lines of flux (in Webers) per pole, Nc is number of turns per coil, n is the relative speed in revolutions/second (rps) between the coil of Nc turns and the magnetic field ϕ.
A speed n of 1 rps will produce a frequency f of 1 Hz. Since f is directly proportional and equivalent to n, (for a 2-pole generator) for all the series turns in any phase,
The effective rms value of a sinusoidal ac voltage is 1.11 times the average value. The effective ac voltage per phase is