## Theory of AC generator:

Consider a coil PQRS free to rotate in a uniform Magnetic field B. The axis of rotation of the coil is perpendicular to the field B. The flux through the coil when its normal makes an angle θ with the field is given by

Rotating coil in a magnetic field |

If the coil rotates with an angular velocity ω and turns through an angle θ in time t, then

θ=ωt ∴ Ф= BAcos ωt

As the coil rotates, the magnetic flux linked with its changes. An induced EMF is set up in the coil which is given by

ε= - dΦ/dt = - d(BA cos ωt)/dt = BAω sin ωt

If the coil has N turn , then the total induced EMF will be

ε=NBAω sin ωt

Thus the induced EMF varies sinusoidal with time t. The value of induced EMF is maximum when the sinωt=1 or ω=90

i.e. when the plane of the coil is parallel to the field B. Denoting this maximum value by εo, we have

εo=NBAω

∴ε=εo sinωt=εo sin 2πft

where f is the frequency of rotation of the coil and uniform magnetic field.

Induced EMF in rotating coil |

In fig shows how the induced EMF ε between the two terminals of the coil varies with time. We consider the following special cases:

- When ωt = 0, the plane of the coil is perpendicular to B,sinωt=sin0=0 so that ε=0
- When ωt=π/2, the plane of the coil is parallel to field B,sinωt=sinπ/2=1, so that ε=εo
- When ωt = π, the plane of the coil is again perpendicular to B,sinωt=sinπ=0 so that ε=0
- When ωt=3π/2, the plane of the coil again parallel to B, sinωt=sin3π/2=-1 so that ε = -εo
- When ωt=2π, the plane of the coil again become perpendicular to B after completing one rotation,sinωt = sin2π=0 so that ε=0

As the coil continues to rotate in the same sense, the same cycle of change repeats again and again. The graph between EMF ε and time t is a sine curve . Such an EMF is called

*sinusoidal*or*alternating EMF.*Both the magnitude and direction of this EMF change regularly with time.