Consider the following statements:1.RMS value of sinusoidal current is its peak value divided by √2.2.Average value of sinusoidal current over one cycle is zero.3.Form factor of sine wave is1.11.Which of the above statements is/are correct?
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For a sine wave x(t)=Xm sinωt, the RMS value is Xm/√2. The average of a rectified sine over a half cycle is 2Xm/π, giving sine-wave form factor RMS/average-rectified ≈1.11. Key relation: Xrms=Xm/√2; Xavg(rectified)=2Xm/π; form factor≈1.11.
Exam focus: Check whether the question asks full-cycle average or rectified average. Common trap: Using the half-cycle average as the full-cycle average is a common error.
Formula / Key Relation
Xrms=Xm/√2; Xavg(rectified)=2Xm/π; form factor≈1.11.
Detailed Explanation
Correct Answer: D - 1, 2 and 3 Quick Concept Explanation For a sine wave x(t)=Xm sinωt, the RMS value is Xm/√2. The average of a rectified sine over a half cycle is 2Xm/π, giving sine-wave form factor RMS/average-rectified ≈1.11. Key relation: Xrms=Xm/√2; Xavg(rectified)=2Xm/π; form factor≈1.11.Exam focus: Check whether the question asks full-cycle average or rectified average. Common trap: Using the half-cycle average as the full-cycle average is a common error. Statement-wise Verification Statement 1 - Correct.RMS value of sinusoidal current is its peak value divided by √2.RMS value of sinusoidal current is its peak value divided by √. Statement…
Correct Answer: D - 1, 2 and 3
Quick Concept Explanation
For a sine wave x(t)=Xm sinωt, the RMS value is Xm/√2. The average of a rectified sine over a half cycle is 2Xm/π, giving sine-wave form factor RMS/average-rectified ≈1.11. Key relation: Xrms=Xm/√2; Xavg(rectified)=2Xm/π; form factor≈1.11.
Exam focus: Check whether the question asks full-cycle average or rectified average. Common trap: Using the half-cycle average as the full-cycle average is a common error.
Statement-wise Verification
Statement 1 - Correct. RMS value of sinusoidal current is its peak value divided by √2. RMS value of sinusoidal current is its peak value divided by √.
Statement 2 - Correct. Average value of sinusoidal current over one cycle is zero. 2. Average value of sinusoidal current over one cycle is zero.
Statement 3 - Correct. Form factor of sine wave is 1.11. The average of a rectified sine over a half cycle is 2Xm/π, giving sine-wave form factor RMS/average-rectified ≈1.11.
Core Concept
For a sine wave x(t)=Xm sinωt, the RMS value is Xm/√2. The average over a complete cycle is zero because positive and negative halves cancel. The average of a rectified sine over a half cycle is 2Xm/π, giving sine-wave form factor RMS/average-rectified ≈1.11.
Formula / Key Relationship
Xrms=Xm/√2; Xavg(rectified)=2Xm/π; form factor≈1.11.
Why the Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 3. Option B is incorrect because it omits correct statement(s) 1. Option C is incorrect because it omits correct statement(s) 2.
Exam Shortcut / Approach
Check whether the question asks full-cycle average or rectified average.
Common Mistake
Using the half-cycle average as the full-cycle average is a common error.
Quick Revision
RMS Average and Form Factor is linked with Sinusoidal Waveforms, AC Fundamentals and Basic Electrical Engineering. Check whether the question asks full-cycle average or rectified average.
Quick Trick
Check whether the question asks full-cycle average or rectified average.
Why Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 3. Option B is incorrect because it omits correct statement(s) 1. Option C is incorrect because it omits correct statement(s) 2.
Common Mistake
Using the half-cycle average as the full-cycle average is a common error.
Exam Tip
Check whether the question asks full-cycle average or rectified average.
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