Question

A single-phase half wave controlled rectifier, operating at 120 V rms and 60 Hz ac supply, has a firing angle of 60°. The average value of its output voltage is
1. \(\frac {45\sqrt 2}{\pi} V\)
2. \(\frac {45\sqrt 3}{\pi} V\)
3. \(\frac {90\sqrt 2}{\pi} V\)
4. \(\frac {90\sqrt 3}{\pi}V\)

Answer 1

Correct Answer - Option 3 : \(\frac {90\sqrt 2}{\pi} V\)

Concept:

The average output voltage of the single-phase halfwave rectifier with a resistive load is given by

\({V_0} = \frac{{{v_m}}}{{2\pi }}\left( {1 + cosa} \right)\)

Where 

vm = peak value of source voltage, a = firing angle

Calculation:

Given that

Source voltage Vin = 120 V rms, firing angle a = 600

From the source voltage peak value vm = \(\sqrt 2\times {120} V\)
The average output value of a single-phase half-wave rectifier is given by

⇒ \({V_0} = \frac{{\sqrt 2 \times 120}}{{2\pi }}\left( {1 + \frac{1}{2}} \right)\)

=  \({V_0} = \frac{{\sqrt 2 \times{120}}}{{2\pi }} \times \frac{3}{2}\)

= \(\frac {90\sqrt 2}{\pi} V\)