Single-phase full bridge controlled rectifier (B-2) with resistive DC load For input v(t) = V_m sin(ωt), the average DC output voltage V_dc equals:

Introduction / Context:
The single-phase full bridge controlled rectifier produces a controllable average DC voltage by delaying the firing of each thyristor pair by angle α. With a resistive DC load, conduction occurs over each half-cycle after firing, and the average can be computed by integrating the instantaneous output.

Given Data / Assumptions:

• Full bridge (B-2) controlled rectifier.
• Input v(t) = V_m sin(ωt).
• Resistive DC load; commutation at natural current zeros.

Concept / Approach:
The instantaneous output is the line-to-line rectified segment selected by the fired devices. For symmetric firing at α in each half-cycle, the average over 0 to π for a resistive load yields the familiar expression V_dc = (2 V_m / π) cos α (valid for 0 ≤ α ≤ 90°; for larger α the average reduces accordingly and reaches zero at α = 90° for discontinuous conduction assumptions).

Step-by-Step Solution:
Compute average over a half-cycle: V_dc = (1/π) ∫{α}^{π} V_m sin(θ) dθ − (1/π) ∫{π+α}^{2π} V_m sin(θ) dθ.Symmetry results in V_dc = (2 V_m / π) cos α.Thus the mean DC output decreases with α and is maximum at α = 0°.

Verification / Alternative check:
For α = 0°, V_dc = 2 V_m / π (same as uncontrolled bridge). For α = 90°, V_dc ≈ 0, matching the integral.

Why Other Options Are Wrong:

• (V_m/π)(1 + cos α) corresponds to a semi-converter, not a full bridge.
• “Independent of α” is incorrect for a controlled bridge.
• Zero for all α contradicts observed control.
• (2 V_m/π) is only for α = 0°.

Common Pitfalls:

• Mixing semi-converter and full bridge formulas.
• Confusing RMS and average values.

Final Answer:
(2 V_m / π) cos α