State the basic principle behind the working of an ac generator. Briefly describe its working and obtain the expression for the instantaneous value of emf induced.

Principle: Whenever magnetic flux linked through a coil changes an emf is induced. Alternatively: ac generator is based on the phenomenon of electromagnetic induction. Working: The coil (armature) is mechanically rotated in the uniform magnetic field by some external means. The rotation of the coil causes the magnetic flux through it to change. So an emf is induced in the coil. Expression for induced emf Flux linked with the coil at any instant of time is- \[\begin{aligned} & \phi_{B}=B A \cos \omega t \\ & \epsilon=-N \frac{d \phi_{B}}{d t} \\ & \epsilon=-N B A \frac{d}{d t}(\cos \omega t) \end{aligned} \] Thus, instantaneous value of emf is \(\displaystyle \epsilon=N B A \omega \sin \omega t\)