Let in t seconds, the coil rotates through an angle θ = ω t, and in this deflected position, the flux component perpendicular to the plane of the coil,
Consequently, the flux linkage of the coil in this deflected position is given by:
Now, according to faraday’s law of electromagnetic induction, the induced emf in the coil is equal to the rate of change of flux linkage of the coil. Consequently, the instantaneous induced emf ( e )at time, when θ =ω t, is given by:
Now, the induced emf e has a maximum value of Em, when sin θ = sin 90o = 1, i.e.
Where f is the frequency of the rotation of the coil
Therefore from equations above, we get:
Now the current I at any time t in the coil is proportional to the induced emf e in the coil. Hence, the induced alternating current is given by:
Where Im is the maximum value of current