Principle: Based on electromagnetic induction — when a coil rotates in a uniform magnetic field, the magnetic flux through it changes continuously, inducing an alternating emf.

Derivation:

At time $t$, angle of coil with $\vec{B}$: $\theta = \omega t$

Magnetic flux:

$$\Phi = NBA\cos\omega t$$

Induced emf by Faraday's law:

$$\varepsilon = -\frac{d\Phi}{dt} = -NBA(-\sin\omega t)\omega$$

$$\boxed{\varepsilon = NBA\omega\sin\omega t = \varepsilon_0\sin\omega t}$$

where $\varepsilon_0 = NBA\omega$ is the peak (maximum) emf.

Labelled diagram components: Armature coil, strong permanent magnets (N-S poles), slip rings, brushes, external load.

Source of energy: Mechanical energy (provided by rotating the coil using water turbine, steam turbine, etc.) is converted to electrical energy.