The value of a given waveform at any instant time is termed as ___________

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Examoogle · Accepted Answer

Instantaneous value

Explanation: The instantaneous value of a waveform is the specific magnitude of a quantity (such as voltage or current) at a precise, unique point in time. It represents the value of the signal as it varies continuously across the time axis.

Working Principle: In AC circuits, electrical quantities like voltage $v(t)$ and current $i(t)$ are time-varying functions. The instantaneous value is obtained by evaluating these functions at a specific time instant $t=t_0$. For a sinusoidal source, this is given by $v(t) = V_m \sin(\omega t + \phi)$, where the value changes dynamically as $t$ progresses.

Key Formulas: $v(t) = V_m \sin(\omega t)$ — Instantaneous voltage of a pure sine wave; $i(t) = I_m \sin(\omega t - \phi)$ — Instantaneous current of a lagging load

Key Points: Instantaneous values are used to derive other metrics like RMS and Average values.; The instantaneous power in an AC circuit is the product of instantaneous voltage and current, $p(t) = v(t) 	imes i(t)$.; For DC circuits, the instantaneous value is constant and equal to the steady-state value.

Advantages: Allows for precise analysis of circuit behavior at any specific point in a cycle.; Essential for calculating instantaneous power consumption in non-linear loads.

Disadvantages: Usually fluctuates too rapidly for standard analog meters to display.; Requires high-speed sampling for accurate digital observation.

Applications: Protection relay operations in power systems.; Waveform synthesis and digital signal processing.; Power quality monitoring and harmonic analysis.

Additional Info: Cycle: One complete set of positive and negative variations.. Period (T): The time taken to complete one full cycle.. Instantaneous value is distinct from Peak (Maximum), RMS, or Average value.

Answer: B is correct — The value of a waveform at a specific instant of time is known as the instantaneous value.

Exam Tip: Remember that while instantaneous values vary, AC meters usually display the Root Mean Square (RMS) value, which is effectively the equivalent heating value of DC.

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