Basic principle of working of AC generator:

Basic principle of working of $\mathrm{AC}$ generator is electromagnetic induction. A copper coil known a armature is rotated in a strong magnetic field and emf is induced in the coil according to the Faraday's laws of electromagnetic induction and the direction of induced emf is determined by Fleming's right hand rule.
Working of ac generator:

Main components of ac generator are:
(i) Armature, (ii) Field magnet, (iii) slip ring (iv) Brush Armature $\left(\mathit{A}\mathit{B}\mathit{C}\mathit{D}\right)$ is a copper coil wound on a soft iron core. The armature is rotated by a turbine.
The armature is placed in between poles of a strong permanent magnet (NS) known as field magnet.
Two ends of armature coil are connected to the slip rings $({\mathit{R}}_{1.}$ and ${\mathit{R}}_2)$. Carbon brushes $({\mathit{B}}_{1.}$ and ${\mathit{B}}_2)$ kept just in firm contact with the rings. External circuit is connected with the brushes.
When armature rotates in the magnetic field induced emf is generated which is supplied to the external circuit through the brushes.
Expression of instantaneous emf induced:
If the armature has $\mathrm{N}$ number of turns, then magnetic flux through the coil is
$\mathit{\varphi }=\mathit{N}\left(\overrightarrow{\mathit{B}}\cdot \overrightarrow{\mathit{A}}\right)$
$=\mathit{N}\mathit{B}\mathit{A}\cos \mathit{\theta }$
If $\mathit{\omega }$ is the angular velocity, then emf induced
$\mathit{\epsilon }=-\frac{\mathit{d}\mathit{\varphi }}{\mathit{d}\mathit{t}}$