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The average of all the instantaneous values of a sinusoidal quantity over a cycle is:
- a)0.707 times its maximum value
- b)Unity
- c)Maximum
- d)Zero
Correct answer is option 'D'. Can you explain this answer?
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The average of all the instantaneous values of a sinusoidal quantity o...
The average value of a sinusoidal wave is zero
The rms value of a sinusoidal wave is
The rms value of a sinusoidal wave is
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The average of all the instantaneous values of a sinusoidal quantity o...
Explanation:
In order to understand why the average of all the instantaneous values of a sinusoidal quantity over a cycle is zero, we need to have a basic understanding of the properties of a sinusoidal waveform.
Sinusoidal Waveform
A sinusoidal waveform is a repetitive waveform that is characterized by its amplitude, frequency, and phase. It can be represented by the equation:
y(t) = A sin (ωt + φ)
- y(t) represents the instantaneous value of the sinusoidal waveform at time t.
- A represents the amplitude of the waveform, which is the maximum value it reaches.
- ω represents the angular frequency of the waveform, which is equal to 2π times the frequency.
- φ represents the phase shift of the waveform.
Average Value of a Sinusoidal Waveform
The average value of a sinusoidal waveform over a cycle can be calculated by finding the area under the waveform and dividing it by the time period of the waveform.
For a sinusoidal waveform, the positive and negative areas cancel out over a complete cycle, resulting in an average value of zero.
This can be visually understood by considering that the waveform is symmetrical about the x-axis, and the positive and negative areas are equal in magnitude but opposite in sign. Therefore, when these areas are summed together, they cancel each other out.
Conclusion
Based on the properties of a sinusoidal waveform and the cancellation of positive and negative areas over a complete cycle, the average of all the instantaneous values of a sinusoidal quantity over a cycle is zero (option D).
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The average of all the instantaneous values of a sinusoidal quantity over a cycle is:a)0.707 times its maximum valueb)Unityc)Maximumd)ZeroCorrect answer is option 'D'. Can you explain this answer?
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