Write down formula of induced emf in AC generator and discuss how its vary with time.

Explanation

Formula of induced emf in AC generator is,
`epsilon=epsilon_0 sin omegat=epsilon_0 sin (2pivt)`….(1)
Note the Eq.(1) give the instantaneous value of the emf and e varies between `+epsilon_0` and `-epsilon_0` periodically. In the figure different stage of generator is given along with emf `to` time graph.

emf produced at different interval of time can be found as follow:
Stage 1: When `omegat=0^@`, the plane of the coil is perpendicular to `vecB, sin omegat=sin0^@=0`, so that `epsilon=0`
Stage 2: When `omegat=pi/2` the plane of the coil is parallel to field `vecB, sin omegat = "sin"pi/2=1`, so that `epsilon=epsilon_0` .
Stage 3: When `omegat=pi` , the plane of the coil is again perpendicular to B, `sin omegat=sinpi=0`, so that `epsilon=0`
State 4: When `omegat=(3pi)/2` the plane of the coil is again parallel to `vecB`, `sin omegat = "sin" (3pi)/2=-1`, so that `epsilon=-epsilon_0`
Stage 5: When `omegat=2pi`, the plane of the coil again becomes perpendicular to `vecB` after completing one rotation, `sinomegat=sin2pi=0`, so that `epsilon=0`