The AC voltage waveform is in the positive direction for some period of time and in the negative direction for some period of time. What is the name given to this waveform?

The waveform described, which has both positive and negative directions, is commonly referred to as a sine wave. This type of waveform is characterized by its smooth and continuous oscillation, representing alternating current (AC) effectively.

A sine wave is defined mathematically as a continuous waveform that exhibits a periodic oscillation with a specific frequency and amplitude. Its shape is derived from the trigonometric function sine, which naturally oscillates between a maximum positive and a maximum negative value over one complete cycle. This oscillation is essential for AC applications, as it allows for the flow of current in both directions, which is fundamental to how alternating current operates.

Understanding the sine wave is crucial in electrical studies because it serves as the basis for more complex waveforms. In contrast, other waveforms such as the square wave, triangle wave, and cosine wave either do not exhibit this dual-directionality in a single cycle in the same manner or represent different forms of signal generation used in various applications. Thus, recognizing a sine wave is vital for grasping basic principles of electricity and AC systems.