AL DC generator (Dynamo)

There is no general equation for the emf produced by a generator. The equation that you quoted is one for the induced emf produced in a rectangular coil in a uniform magnetic field. In general, induced emf depends on the configuration of both the coil and magnetic field.

As you know, the induced emf can be rectified into dc by means of a pair of communtators connected to the rotating coil. The equation is therefore the same except the absolute value of the sine function is used.

i.e. induced emf from a dc generator = NBAwlsin wtl