Answer Posted / anip upanshu

Vdc = 2Vp/π
Vri = 2Vp/π - Vpsinωt
Vri^2 = 4Vp^2/π^2 - (4Vp^2/π)sinθ + Vp^2sin^2θ
Vr = √(1/π)[4πVp^2/π^2 + (4Vp^2/π)(cosπ - cos0) -
(1/2)Vp^2(π - 0 -cosπsinπ + cos0sin0)]
Vr = Vp√(1/π)[4π/π^2 + (4/π)(cosπ - cos0) + (π/2)]
Vr = Vp√[4/π^2 + (4/π^2)(- 1 - 1) + (1/2)]
Vr = Vp√[1/2 - 4/π^2]
Vr/Vdc = (π/2)√[1/2 - 4/π^2]
Vr/Vdc = √(π^2/8 - 1)
Vr/Vdc ≈ 0.4834258 ≈ 48.3%

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