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Why AC output is a sine wave?

Updated: 11/1/2022
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The AC supply is sinusoidal by the electricity being produced in a rotating machine - the alternator - that spins coils of wired across a magnetic field. The voltage is proportional to the rate at which the coil is cutting across the field so maximum at the infinitesimally small point at which it is moving perpendicular to the field; minimum when moving for an equally tiny moment along the field lines. Since the coil is rotating, the voltage at any one point is therefore proportional to the instantaneous angle of the coil with the field. So we now have an angular relationship that is changing continuously through the full 360 º of each rotation, hence the voltage follows the sine of the angle, by basic trigonometry. Each complete turn (360º) therefore gives 1 complete cycle with the 0V crossings where the wire is effectively moving along the magnetic field lines for an extremely brief moment.

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Q: Why AC output is a sine wave?
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