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The rms value is _________ times he maximum value
- a)1.414
- b)0.5
- c)2
- d)0.707
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The rms value is _________ times he maximum valuea)1.414b)0.5c)2d)0.70...
Introduction:
The rms (root mean square) value is a measure of the average power of an AC (alternating current) signal. It is used to calculate the effective value of an AC signal, which is equivalent to the DC (direct current) value that would produce the same amount of power in a resistive load.
Explanation:
The rms value of an AC signal is calculated by taking the square root of the average of the squares of the instantaneous values of the signal over a complete cycle. Mathematically, it can be represented as:
rms = sqrt((1/T) * ∫[t1 to t2] (x(t)^2) dt)
Where:
- T is the time period of one complete cycle of the signal.
- x(t) is the instantaneous value of the signal at time t.
Maximum Value:
The maximum value of an AC signal is the peak value of the waveform. For a sinusoidal waveform, the peak value is equal to the amplitude of the waveform.
Relationship between rms and maximum value:
The rms value of an AC signal is related to its maximum value by a constant factor. This factor depends on the waveform shape.
For a sinusoidal waveform, the rms value is approximately equal to 0.707 times the maximum value. This constant factor is derived from the mathematical relationship between the rms value and the peak value of a sine wave.
Mathematically, it can be represented as:
rms = 0.707 * Vmax
Where:
- rms is the rms value of the sinusoidal waveform.
- Vmax is the maximum value or peak value of the sinusoidal waveform.
Reasoning:
The correct answer to the given question is option 'D', which states that the rms value is 0.707 times the maximum value.
This is a widely used relationship in electrical engineering to calculate the rms value of a sinusoidal waveform based on its peak value. It is important to understand this relationship to accurately calculate power, current, and voltage values in AC circuits.
Conclusion:
The rms value of an AC signal is 0.707 times the maximum value for a sinusoidal waveform. This relationship is derived from the mathematical properties of a sine wave and is widely used in electrical engineering calculations.
The rms (root mean square) value is a measure of the average power of an AC (alternating current) signal. It is used to calculate the effective value of an AC signal, which is equivalent to the DC (direct current) value that would produce the same amount of power in a resistive load.
Explanation:
The rms value of an AC signal is calculated by taking the square root of the average of the squares of the instantaneous values of the signal over a complete cycle. Mathematically, it can be represented as:
rms = sqrt((1/T) * ∫[t1 to t2] (x(t)^2) dt)
Where:
- T is the time period of one complete cycle of the signal.
- x(t) is the instantaneous value of the signal at time t.
Maximum Value:
The maximum value of an AC signal is the peak value of the waveform. For a sinusoidal waveform, the peak value is equal to the amplitude of the waveform.
Relationship between rms and maximum value:
The rms value of an AC signal is related to its maximum value by a constant factor. This factor depends on the waveform shape.
For a sinusoidal waveform, the rms value is approximately equal to 0.707 times the maximum value. This constant factor is derived from the mathematical relationship between the rms value and the peak value of a sine wave.
Mathematically, it can be represented as:
rms = 0.707 * Vmax
Where:
- rms is the rms value of the sinusoidal waveform.
- Vmax is the maximum value or peak value of the sinusoidal waveform.
Reasoning:
The correct answer to the given question is option 'D', which states that the rms value is 0.707 times the maximum value.
This is a widely used relationship in electrical engineering to calculate the rms value of a sinusoidal waveform based on its peak value. It is important to understand this relationship to accurately calculate power, current, and voltage values in AC circuits.
Conclusion:
The rms value of an AC signal is 0.707 times the maximum value for a sinusoidal waveform. This relationship is derived from the mathematical properties of a sine wave and is widely used in electrical engineering calculations.
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Community Answer
The rms value is _________ times he maximum valuea)1.414b)0.5c)2d)0.70...
We know that the rms value is 1/√2 times the maximum value, hence the rms value is 0.707 times the maximum value.
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The rms value is _________ times he maximum valuea)1.414b)0.5c)2d)0.707Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The rms value is _________ times he maximum valuea)1.414b)0.5c)2d)0.707Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The rms value is _________ times he maximum valuea)1.414b)0.5c)2d)0.707Correct answer is option 'D'. Can you explain this answer?.
The rms value is _________ times he maximum valuea)1.414b)0.5c)2d)0.707Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The rms value is _________ times he maximum valuea)1.414b)0.5c)2d)0.707Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The rms value is _________ times he maximum valuea)1.414b)0.5c)2d)0.707Correct answer is option 'D'. Can you explain this answer?.
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