Frequency is calculated by

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Examoogle · Accepted Answer

$f = \frac{1}{T}$

Explanation: Frequency ($f$) is defined as the number of cycles completed per unit of time, typically measured in Hertz (Hz). It is the reciprocal of the Time Period ($T$), which is the duration required to complete one full cycle.

Working Principle: In periodic waveforms, such as sinusoidal A.C. signals, the time period $T$ represents the time taken for one complete oscillation. Since frequency counts the number of oscillations occurring in one second, the relationship is inverse: if an event takes less time to complete, the frequency of occurrence is higher.

Key Formulas: $f = \frac{1}{T}$ — Relationship between frequency and time period; $\omega = 2\pi f = \frac{2\pi}{T}$ — Relationship between angular frequency and time period

Key Points: The SI unit of frequency is Hertz (Hz), where 1 Hz = 1 cycle per second.; Time period ($T$) is measured in seconds (s).; This relationship holds true for all periodic signals, including sine, square, and triangular waves.

Advantages: Simple mathematical inverse relationship.; Easily measurable using oscilloscopes or frequency counters.

Disadvantages: Only applicable to periodic waveforms.; Instantaneous frequency may vary in non-stationary signals.

Applications: Power system analysis (e.g., 50Hz/60Hz grid frequency).; Communication systems for signal modulation and tuning.; Digital electronics for clock speed synchronization.

Additional Info: In India, the standard power line frequency is 50 Hz, corresponding to a time period of $T = \frac{1}{50} = 0.02$ seconds or 20 milliseconds.. Option B ($f=V/T$) is dimensionally incorrect as it incorporates voltage (or velocity).. Option A and D are incorrect as they do not represent the reciprocal relationship of frequency to time.

Answer: C is correct — Frequency is defined as the reciprocal of the time period, mathematically expressed as $f = \frac{1}{T}$.

Exam Tip: Always verify units when dealing with formulas; frequency is always in $s^{-1}$ (Hz), ensuring consistency with the time period $T$ in seconds.

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