The average load voltage across a resistive load of a single-phas
A. <span class="math-tex">\(\frac{{200}}{{\sqrt 2 \pi }}\cos \alpha \)</span>
B. <span class="math-tex">\(\frac{{\sqrt 2 \times 200}}{\pi }\cos \alpha \)</span>
C. <span class="math-tex">\(\frac{{\sqrt 2 \times 200}}{\pi }\left( {1 + \cos \alpha } \right)\)</span>
D. <span class="math-tex">\(\frac{{200}}{{\sqrt 2 \pi }}\left( {1 + \sin \alpha } \right)\)</span>
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
Concept:
Rectifier:
A rectifier is a device that converts alternating signal (AC) into the DC signal.
Rectifiers are 3 types in both 1-phase and 3-phase circuits.
1. Half-wave rectifier
2. Full-wave rectifier (Midpoint and bridge rectifiers)
3. Half/ Semi converter.
Single-phase semi converter:
In the half-controlled rectifier configuration, the average DC load voltage is controlled using two thyristors and two diodes.
Rectification process:
The waveform below showing the result of the rectification of half controller.
- During the positive half cycle of the input waveform, current flows along the path of SCR1 and D2, and back to the supply.
- During the negative half cycle of VIN, conduction is through SCR2 and D1 and back to the supply.
Formula:
The average value of output voltage is
\({V_{avg}} = \frac{{{V_m}}}{\pi }\left( {1 + \cos \alpha } \right)\)
\({V_m} = \;\sqrt 2 \;{V_{rms}}\)
The average value of load current is
\({I_{avg}} = \frac{{{V_m}}}{{\pi R}}\left( {1 + \cos \alpha } \right)\)
Calculation:
Given that,
Input voltage VIN = 200 V
frequency f= 50 Hz
The average value of the output voltage
\({V_{avg}} = \frac{{{V_m}}}{\pi }\left( {1 + \cos \alpha } \right)\)
\({V_m} = \;\sqrt 2 \;{V_{IN}}\)
\(\begin{array}{l} {V_m} = \;\sqrt 2 \; \times 200\\ {V_{avg}} = \frac{{\sqrt 2 \times 200}}{\pi }\left( {1 + \cos \alpha } \right) \end{array}\)
