The average voltage is what multiplied by the peak value of one alternation?

The average voltage is what multiplied by the peak value of one alternation?

• A. 0.636 x peak
• B. 1.0 x peak
• C. 0.5 x peak
• D. 2 x peak

Answer: (A)

The average value of a full-wave rectified sine is 2/π times the peak, which is about 0.636 of the peak. If you take v(t) = Vp sin θ and find the average of its absolute value over a full cycle, you compute (1/2π) ∫0 to 2π |Vp sin θ| dθ. The integral of |sin θ| over a full cycle is 4, so the average becomes (Vp/(2π)) × 4 = 2Vp/π ≈ 0.636 Vp. So the correct description is that the average voltage is 0.636 times the peak value.

The average value of a full-wave rectified sine is 2/π times the peak, which is about 0.636 of the peak. If you take v(t) = Vp sin θ and find the average of its absolute value over a full cycle, you compute (1/2π) ∫0 to 2π |Vp sin θ| dθ. The integral of |sin θ| over a full cycle is 4, so the average becomes (Vp/(2π)) × 4 = 2Vp/π ≈ 0.636 Vp. So the correct description is that the average voltage is 0.636 times the peak value.