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

Half wave rectifier

Case 1: During +ve half cycle

Diode is forward biased, hence short-circuited

V_o = V_s

Case 2: During -ve half cycle

Diode is reverse biased, hence open-circuited

Vo = 0 

The output waveform is shown below:

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

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

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