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)
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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)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7186c19-f484-472d-921d-33d7fb24a522%2F4ecdda88-0ec5-4c95-9ce5-161ee41cf32a%2F9jx92x_processed.png&w=3840&q=75)
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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