The repetition of a variable quantity, recurring at equal intervals, is known as

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Cycle

Explanation: A cycle is defined as one complete set of positive and negative values of an alternating quantity. When a waveform repeats its pattern of variation at regular intervals, the full sequence from the starting point through its maximum, minimum, and back to the start is known as a cycle.

Working Principle: In AC circuits, a rotating vector or phasor completes one full revolution of 360 degrees (or $2\pi$ radians). The physical quantity (voltage or current) associated with this motion traverses through a full positive alternation and a full negative alternation, constituting one single cycle of the signal.

Key Formulas: $T = \frac{1}{f}$ — The period (time for one cycle) is the reciprocal of frequency.; $f = \frac{1}{T}$ — Frequency is the number of cycles completed in one second.

Key Points: One cycle consists of one positive and one negative alternation.; The duration of one cycle is called the Time Period ($T$).; The number of cycles occurring per second is termed Frequency ($f$), measured in Hertz (Hz).; A cycle represents the smallest repeating unit of a periodic waveform.

Advantages: Allows for standardized measurement of AC signal properties.; Facilitates the analysis of periodic functions using Fourier series.

Applications: Power system frequency analysis (50Hz or 60Hz).; Communication systems signal processing.; Rotating machinery speed calculations.

Additional Info: Instantaneous value: The value of the quantity at any specific moment in time.. Waveform: The shape of the graph plotted as a function of time.. Period: The specific duration required to complete one cycle.

Answer: C is correct — A cycle is the complete set of positive and negative values of an alternating quantity.

Exam Tip: Always remember that in India, the standard power frequency is 50 Hz, meaning 50 complete cycles occur every second.

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