Principle: The AC generator is based on the principle that change in loop’s orientation and effective area of loop as it rotates in magnetic field, leads to induction emf and current.
Basic Elements and working:
It consists of a coil mounted on a rotor shaft. The axis of rotation of the coil is perpendicular to the direction of the magnetic field. The coil (called 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. The ends of the coil are connected to an external circuit by means of slip rings and brushes.
When the coil is rotated with a constant angular speed \(\omega\), the angle \(\theta\) between the magnetic field vector B and the area vector A of the coil at any instant t is \(\theta = \omega t\) (assuming \(\theta = 0^\circ\) at t = 0). As a result, the effective area of the coil exposed to the magnetic field lines changes with time, the flux at any time t is
\(\phi B = BA \ cos \ \theta = BA \ cos \ \omega t\)
From Faraday’s law, the induced emf for the rotating coil of N turns is then,
\(\varepsilon = -N \frac {d \phi _B}{dt} = - NBA \frac{d}{dt} (cos\ \omega t)\)
Thus, the instantaneous value of the emf is
\(\varepsilon = NBA \omega \ sin \ \omega t\)
Where \(NBA \omega\) is the maximum value of the emf which occurs when \(sin\ \omega t = \pm1\). If we denote \(NBA \omega \ \text{as} \ \varepsilon_0\), then
\(\varepsilon = \varepsilon _0 \ sin \omega t\)
Since the value of the sine function varies between +1 and –1, the sign, or polarity of the emf changes with time. The emf has its extremum value when \(\theta = 90^ \circ \ \text{or}\ \theta = 270 ^\circ\) , as the change of flux is greatest at these points.
Thus expression of instantaneous value of emf is
\(\varepsilon = \varepsilon_0 \ sin (\omega t)\)
