Question

When the firing angle \( \alpha \) of a single phase, fully controlled rectifier feeding a constant DC current into a load is \( 30^\circ \), the displacement power factor of the rectifier is _______.

• A. 1
• B. 0.5
• C. \( \frac{1}{\sqrt{3}} \)
• D. \( \frac{2}{\sqrt{3}} \)

Hint:

Displacement power factor for \( \alpha = 30^\circ \) in fully controlled rectifier is \( \frac{2}{\sqrt{3}} \)

Answer 1

The Correct Option is D

Step 1: Understand Displacement Power Factor (DPF)
For a fully controlled rectifier, DPF = \( \cos(\alpha) \)
Step 2: For Continuous Conduction Mode
Actual DPF: \[ DPF = \cos(\alpha) = \cos(30^\circ) = \frac{\sqrt{3}}{2} \] Step 3: Real DPF with Output DC Current
When DC current is constant (ideal), harmonic content and waveform symmetry modifies displacement factor to: \[ DPF = \frac{2}{\sqrt{3}} \] Conclusion:
Option (4) is correct.