Q.Describe the principle, construction and working of a single phase A.C. generator.

A single-phase AC generator (alternator) converts mechanical rotational energy into alternating electrical energy by rotating a coil in a magnetic field, inducing a sinusoidal emf $e = e_0\sin\omega t$ by Faraday's law of electromagnetic induction.

Principle

It works on the principle of electromagnetic induction: when the magnetic flux linked with a coil changes with time (here, because the coil is mechanically rotated in a uniform magnetic field), an emf is induced in the coil, given by Faraday's law $e = -N\dfrac{d\phi}{dt}$.

Construction

The main parts of a single-phase AC generator are:

1. Armature — a coil of many turns of insulated copper wire wound on a laminated soft-iron core; this is where the emf is induced.
2. Field magnet — a strong permanent magnet or an electromagnet that provides the uniform magnetic field $B$ in which the armature rotates.
3. Slip rings — two metal rings, insulated from each other and from the shaft, fixed to and rotating with the two ends of the armature coil.
4. Brushes — stationary carbon/graphite contacts that press against the slip rings and connect the rotating coil to the stationary external circuit.
5. A prime mover (turbine, engine, etc.) supplies the mechanical energy that rotates the armature/shaft.

Working and derivation of emf

Let the coil of $N$ turns and area $A$ be rotated with constant angular velocity $\omega$ in a uniform field $B$. Take $t=0$ when the plane of the coil is perpendicular to $B$ (flux maximum). At time $t$, the coil has turned through angle $\theta = \omega t$, and the flux linked is

$\phi = NBA\cos\omega t$

By Faraday's law, the induced emf is

$e = -\dfrac{d\phi}{dt} = NBA\omega\sin\omega t$

i.e. …