For an input signal of v(t) = Vm sin (ωt) V, the average value of a half-rectified sine wave is:

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MPPKVVCL Indore JE Electrical 21 August 2018 Official Paper
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  1. \(\rm\frac{V_m}{2 \pi}\)
  2. \(\rm\frac{2 V_m}{\pi}\)
  3. \(\rm\frac{V_m}{\pi}\)
  4. \(\rm\frac{V_m}{4 \pi}\)

Answer (Detailed Solution Below)

Option 3 : \(\rm\frac{V_m}{\pi}\)
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Detailed Solution

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Half wave rectifier

qImage537

Case 1: During +ve half cycle

Diode is forward biased, hence short-circuited

Vo = Vs

Case 2: During -ve half cycle

Diode is reverse biased, hence open-circuited

Vo = 0 

The output waveform is shown below:

qImage538

The average value of a half-rectified sine wave is:

\(V_{o(avg)}={1\over 2\pi}\int_{0}^{\pi}V_m\space sin\omega t\space d\omega t\)

\(V_{o(avg)}={V_m\over 2\pi}(1-cos\pi)\)

\(V_{o(avg)}={V_m\over \pi}\)

Hence, the correct answer is option 3.

Mistake Points Full wave rectifier

qImage539

The average value of a full-rectified sine wave is:

\(V_{o(avg)}={2V_m\over \pi}\)

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