Let the area of the coil be A and the magnetic field be B. Let N be the number of turn in the armature. Let θ be the angle between the area and the magnetic field. If ω is the constant angular velocity of the rotation of the coil then θ = ωt.
The magnetic flux linked with the coil is:
From Faraday’ law the induced emf by rotating coil is given by:
where ε0 = NBAω is called the peak value of the emf or the maximum emf.
If ν is the frequency of rotation of the armature then: ω = 2πν. Therefore
ε = ε0 sin 2πνt
This is the expression for the alternating emf produced by a generator. As the time increases the emf ε increases from zero to +ε0 and then falls to zero. Then it becomes negative and reaches -ε0. Then gradually it increases to become zero. This completes one cycle of AC.
