An AC voltage is given by v(t) = 100 sin(ωt). Then1.Peak voltage is 100 V.2.RMS voltage is 100/√2.3.RMS value ≈ 70.7 V.4.Average value over full cycle is 100 V.Which of the above statements is/are correct?

Correct Answer: C - 1, 2 and 3 only

Quick Concept Explanation

The average of a rectified sine over a half cycle is 2Xm/π, giving sine-wave form factor RMS/average-rectified ≈1.11. For v(t)=100 sinωt, Vm=100 V and Vrms=Vm/√2≈70.7 V. The full-cycle average of a sine wave is zero. 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.
  Peak voltage is 100 V.
  For v(t)=100 sinωt, Vm=100 V and Vrms=Vm/√2≈70.7 V.
• Statement 2 - Correct.
  RMS voltage is 100/√2.
  For v(t)=100 sinωt, Vm=100 V and Vrms=Vm/√2≈70.7 V.
• Statement 3 - Correct.
  RMS value ≈ 70.7 V.
  For v(t)=100 sinωt, Vm=100 V and Vrms=Vm/√2≈70.7 V.
• Statement 4 - Incorrect.
  Average value over full cycle is 100 V.
  The correct principle is: The full-cycle average of a sine wave is zero.

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.

Step-by-Step Check

For v(t)=100 sinωt, Vm=100 V and Vrms=Vm/√2≈70.7 V. The full-cycle average of a sine wave is zero.

Why the Other Options Are Wrong

Option A is incorrect because it omits correct statement(s) 3. Option B is incorrect because it includes incorrect statement(s) 4 and omits correct statement(s) 1, 3. Option D is incorrect because it includes incorrect statement(s) 4.

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

Peak RMS and Average Values is linked with Sinusoidal Voltage, AC Fundamentals and Basic Electrical Engineering. Check whether the question asks full-cycle average or rectified average.