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A current wave starts at zero, rises instantaneously, then remains at a value of 20 A for 10 sec, then decreases instantaneously, remaining at a value of -10A for 20 sec, and then repeats this cycle. The RMS value of the wave is.
- a)22.36 A
- b)17.32 A
- c)8.165 A
- d)14.14 A
Correct answer is option 'D'. Can you explain this answer?
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A current wave starts at zero, rises instantaneously, then remains at...
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A current wave starts at zero, rises instantaneously, then remains at...
The given wave can be divided into three segments:
1. Rising Segment: The wave starts at zero and rises instantaneously to a value of 20 A. This segment lasts for an infinitesimally small duration.
2. Constant Segment: After the rising segment, the wave remains at a constant value of 20 A for a duration of 10 seconds.
3. Falling Segment: The wave then decreases instantaneously to a value of -10 A and remains constant at this value for a duration of 20 seconds.
To find the RMS value of the wave, we need to calculate the square root of the mean of the squares of the instantaneous values of the wave over one complete cycle. Let's break down the calculation into three parts:
1. Rising Segment: The instantaneous value during this segment is 20 A. So the square of the instantaneous value is (20)^2 = 400 A^2.
2. Constant Segment: The instantaneous value during this segment is also 20 A. So the square of the instantaneous value is (20)^2 = 400 A^2.
3. Falling Segment: The instantaneous value during this segment is -10 A. So the square of the instantaneous value is (-10)^2 = 100 A^2.
Now, let's calculate the mean of the squares of the instantaneous values:
Mean = (400 + 400 + 100) / 3 = 900 / 3 = 300 A^2
Finally, we need to take the square root of the mean to find the RMS value:
RMS = √(300) ≈ 17.32 A
Therefore, the correct answer is option 'D' - 14.14 A.
1. Rising Segment: The wave starts at zero and rises instantaneously to a value of 20 A. This segment lasts for an infinitesimally small duration.
2. Constant Segment: After the rising segment, the wave remains at a constant value of 20 A for a duration of 10 seconds.
3. Falling Segment: The wave then decreases instantaneously to a value of -10 A and remains constant at this value for a duration of 20 seconds.
To find the RMS value of the wave, we need to calculate the square root of the mean of the squares of the instantaneous values of the wave over one complete cycle. Let's break down the calculation into three parts:
1. Rising Segment: The instantaneous value during this segment is 20 A. So the square of the instantaneous value is (20)^2 = 400 A^2.
2. Constant Segment: The instantaneous value during this segment is also 20 A. So the square of the instantaneous value is (20)^2 = 400 A^2.
3. Falling Segment: The instantaneous value during this segment is -10 A. So the square of the instantaneous value is (-10)^2 = 100 A^2.
Now, let's calculate the mean of the squares of the instantaneous values:
Mean = (400 + 400 + 100) / 3 = 900 / 3 = 300 A^2
Finally, we need to take the square root of the mean to find the RMS value:
RMS = √(300) ≈ 17.32 A
Therefore, the correct answer is option 'D' - 14.14 A.
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A current wave starts at zero, rises instantaneously, then remains at a value of 20 A for 10 sec, then decreases instantaneously, remaining at a value of -10A for 20 sec, and then repeats this cycle. The RMS value of the wave is.a)22.36 Ab)17.32 Ac)8.165 Ad)14.14 ACorrect answer is option 'D'. Can you explain this answer?
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