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Equation 11-11 Average Value of a Half-Cycle Sine Wave The average value of a sine wave is determined for a half-cycle because the average over a full cycle is zero. The equation for a sine wave is v = V₂ sin 0 The average value of the half-cycle is the area under the curve divided by the distance of the curve along the horizontal axis (see Figure B-20). Figure B-2 Vp 72π Area under the half-cycle of a sinusoidal voltage wave. To find the area, we use integral calculus. Vavg 0 = = || 1 7T Vavg *V,sin 0 de = 6 area TT V₂ ㅠ (-cos 6 Cos 0)|5 [-cos T-(-cos 0)] = -co = (2) = 2V₁ = 0.637V₂ π [-(-1)-(-1)]

Equation 11-11 Average Value of a Half-Cycle Sine Wave The average value of a sine wave is determined for a half-cycle because the average over a full cycle is zero. The equation for a sine wave is v = V₂ sin 0 The average value of the half-cycle is the area under the curve divided by the distance of the curve along the horizontal axis (see Figure B-20). Figure B-2 Vp 72π Area under the half-cycle of a sinusoidal voltage wave. To find the area, we use integral calculus. Vavg 0 = = || 1 7T Vavg *V,sin 0 de = 6 area TT V₂ ㅠ (-cos 6 Cos 0)|5 [-cos T-(-cos 0)] = -co = (2) = 2V₁ = 0.637V₂ π [-(-1)-(-1)]

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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In your textbook, Equation 11-11 defines Vavg = 0.637 VPEAK. Derive this relationship.

I don't remember how to do this. Please help! Please write legibly or type in equation form. Thanks!

Equation 11-11 Average Value of a Half-Cycle Sine Wave The average value of a sine wave is determined for a half-cycle because the average over a full cycle is zero. The equation for a sine wave is v = V₂ sin 0 The average value of the half-cycle is the area under the curve divided by the distance of the curve along the horizontal axis (see Figure B-20). Figure B-2 Vp 72π Area under the half-cycle of a sinusoidal voltage wave. To find the area, we use integral calculus. Vavg 0 = = || 1 7T Vavg *V,sin 0 de = 6 area TT V₂ ㅠ (-cos 6 Cos 0)|5 [-cos T-(-cos 0)] = -co = (2) = 2V₁ = 0.637V₂ π [-(-1)-(-1)]
Transcribed Image Text:Equation 11-11 Average Value of a Half-Cycle Sine Wave The average value of a sine wave is determined for a half-cycle because the average over a full cycle is zero. The equation for a sine wave is v = V₂ sin 0 The average value of the half-cycle is the area under the curve divided by the distance of the curve along the horizontal axis (see Figure B-20). Figure B-2 Vp 72π Area under the half-cycle of a sinusoidal voltage wave. To find the area, we use integral calculus. Vavg 0 = = || 1 7T Vavg *V,sin 0 de = 6 area TT V₂ ㅠ (-cos 6 Cos 0)|5 [-cos T-(-cos 0)] = -co = (2) = 2V₁ = 0.637V₂ π [-(-1)-(-1)]
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