AC Generator and Voltage Generation

The AC generator is a device that converts mechanical energy into electrical energy. It consists of a coil of wire, referred to as an armature, which rotates in a magnetic field. The voltage generated in the coil is determined by the area of the coil, the strength of the magnetic field, and the angular speed at which the coil rotates.

Voltage Variation

The voltage generated in the AC generator does not remain constant but varies over time. This variation is due to the sinusoidal nature of the generated voltage. The correct option, option D, states that the voltage generated varies sinusoidally.

Sinusoidal Variation

The sinusoidal variation of the generated voltage can be understood by considering the motion of the coil in the magnetic field. As the coil rotates, the area of the coil that is perpendicular to the magnetic field changes. This change in area results in a change in the magnetic flux through the coil. According to Faraday's law of electromagnetic induction, a changing magnetic flux induces an electromotive force (EMF) in the coil.

Faraday's Law of Electromagnetic Induction

Faraday's law states that the magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux through the coil. Mathematically, this can be expressed as:

EMF = -N * dΦ/dt

where EMF is the induced electromotive force, N is the number of turns in the coil, and dΦ/dt is the rate of change of magnetic flux.

Sinusoidal Voltage Generation

As the coil rotates, the rate of change of magnetic flux through the coil is not constant. It varies sinusoidally with time. Therefore, the induced EMF and the generated voltage also vary sinusoidally. This sinusoidal variation is commonly known as alternating current (AC).

Conclusion

In summary, the voltage generated in an AC generator coil varies sinusoidally due to the changing magnetic flux through the coil as it rotates in a magnetic field. This variation is in accordance with Faraday's law of electromagnetic induction.