Question

With the help of a labelled diagram, describe the principle and working of an ac generator. Hence, obtain an expression for the instantaneous value of the emf generated.

Answer 1

Principle: It is based on Faraday's law of electromagnetic induction. When a coil in a uniform magnetic field is rotated along an axis perpendicular to the field, the magnetic flux associated with the coil changes, and an induced emf is created across its ends.

Working: When the coil begins to rotate with the arm AB travelling up and the arm CD moving down, cutting the magnetic lines of force, the induced current is set up in these arms along the AB and CD directions, according to Fleming's right-hand rule. As a result, an effective induced current flows in the direction of ABCD.

If the coil has a big number of turns, the current created in each turn adds up to produce a large amount of current across the coil. After half a rotation of the coil, its arm CD begins to move upward and its arm AB begins to move downward. As a result, the induced currents in the coil are reversed in the direction of DCBA. As a result, the polarity of the current in each arm changes every half rotation. A current that changes direction at equal intervals of time is referred to as an alternating current. A split ring type commutator must be used instead of a slip ring commutator to obtain direct current.

Emf induced in a coil:

Consider a coil of N turns and area A being rotated at a constant angular velocity ω in a magnetic field of flux density B, its axis being perpendicular to the field. When the normal to the coil is at an angle θ to the field, the flux through the coil is,

BAN cosθ = BAN cosωt, since θ = ωt.

E = `-(dphi)/(dt)`

E = `-(d(BAN costheta))/(dt)`

E = BANω sin(ωt)

The maximum value of the e.m.f (E₀) is when θ = ωt = 90° (that is, the coil is in the plane of the field as shown in Figure) and is given by,

E₀ = BANω

Therefore, the maximum value of induced emf will be
E₀ = BANω.