What formula represents the instantaneous voltage at any given degree in an AC cycle?

The formula that represents the instantaneous voltage in an alternating current (AC) circuit at any given degree of the cycle is derived from the sinusoidal representation of AC voltage. The instantaneous voltage can be expressed as a function of time or phase angle using the peak voltage, denoted as Vpk.

In an AC system, voltage varies sinusoidally, and one common representation is through the sine function, especially when starting from zero at the beginning of a cycle (0 degrees). The relationship described in the correct formula indicates how the voltage builds from zero up to its maximum value (the peak voltage) as a sine wave progresses through its 360-degree cycle.

This means that at any angle θ, the instantaneous voltage Vi can be calculated by multiplying the peak voltage Vpk by the sine of the angle θ. This accurately captures the periodic nature of AC voltage, where it fluctuates between positive and negative values as it cycles through its wave.

The other options, while they incorporate Vpk, do not correctly represent the behavior of AC voltage. The cosine function is more relevant when analyzing voltage that starts at its maximum value (which occurs in a different phase), and the division and tangent functions do not appropriately model the oscillation of voltage over time. Hence, the