Single-phase fully controlled bridge converter (R load) At what firing angles does a single-phase full converter (full-controlled bridge) produce its maximum average output voltage and its minimum (most negative) average output voltage?

Introduction / Context:
This question tests understanding of how the firing angle controls the average DC output of a single-phase fully controlled bridge (full converter) feeding a resistive load. Knowing the cosine control law is essential for rectifier design, motor control, and power supply engineering.

Given Data / Assumptions:

• Single-phase full-controlled bridge converter.
• Ideal thyristors and purely resistive load for clarity.
• Firing angle denoted by α (degrees).

Concept / Approach:

The average output voltage of a full converter is controlled by the firing angle as:

where Vm is the peak of the supply phase voltage. The cosine term directly sets sign and magnitude of the average DC output.

Step-by-Step Solution:

Verification / Alternative check:

Plotting Vdc_avg versus α shows a cosine curve with maximum at 0° and minimum at 180°. The sign reversal beyond 90° is consistent with inversion (power flow reversal) capability of a full converter.

Why Other Options Are Wrong:

180° and 0° reverses the true order. Pairs involving 90° or 45° do not correspond to extrema of the cosine function; 90° gives zero average, not an extremum.

Common Pitfalls:

Confusing the full converter with a half-controlled converter (which cannot produce negative average V). Also mixing up RMS and average values leads to wrong conclusions.

Final Answer:

0° and 180° respectively