Alternating voltage may be generated by rotating a coil in a magnetic field or by rotating a magnetic field within a stationary coil. The value of the voltage generated depends, in-each case, upon the number of turns in the coil, strength of the field and the speed at which the coil or magnetic field rotates.

*Equations of the Alternating Voltages and Currents:*
Consider a rectangular coil having N turns and rotating in a uniform magnetic field with an angular velocity of ω radian / second as shown in Figure. Maximum flux Φ

_{m}is linked with the coil when its place coincides with the X-axis.
In time t seconds, this coil rotates through an angle

*θ*= ωt.
In this deflected position, the component of the flux which is perpendicular to the plane of the coil is Φ = Φ

_{m}cos ωt.
Hence, flux linkages of the coil at any time are NΦ = NΦ

_{m}cos ωt.
According to Faraday's Laws of Electromagnetic Induction, the e.m.f induced in the coil is given by the rate of change of flux-linkage of the coil. Hence, the value of the induced e.m.f at this instant (i.e where

*θ*= ωt) or the instantaneous value of the induced e.m.f is
e = ωNΦ

_{m}sin ωt volt ----------(i)
When the coil has turned through 90° i.e. when θ = 90°, then sin θ = 1, hence ‘e’ has maximum value, say E

_{m}. Therefore, from above equation we get
E

_{m}= ωNΦ_{m}= 2лfNB_{m}A volt
f= frequency of rotation of the coil in rev/second. Substituting this value of E in Eq (i) we get

e = E

_{m}sin ωt
Similarly, the equation of the induced alternating current is

i = I

_{m}sin ωt
provided the coil circuit has been closed through a resistive load.