Question

In a single-phase semi-converter without a freewheeling diode, for discontinuous conduction and extinction angle \( \beta>\pi \), each SCR conducts for the period:

• A. \( \pi - \alpha \)
• B. \( \beta - \alpha \)
• C. \( \alpha \)
• D. \( \beta \)

Hint:

In discontinuous conduction mode of a semi-converter, the conduction period of an SCR is given by \( \beta - \alpha \), where \( \alpha \) is the firing angle and \( \beta \) is the extinction angle.

Answer 1

The Correct Option is B

Step 1: In a single-phase semi-converter, SCRs (Silicon-Controlled Rectifiers) are used for controlled rectification of AC power. 
Step 2: The firing angle \( \alpha \) determines when the SCR turns on, and the extinction angle \( \beta \) defines when it turns off. 
Step 3: Without a freewheeling diode, the SCR remains conducting until the current naturally falls to zero, which occurs at the extinction angle \( \beta \). 
Step 4: The total conduction period of each SCR is given by: \[ \text{Conduction time} = \beta - \alpha \] 
Step 5: Evaluating options:
- (A) \( \pi - \alpha \) (Incorrect): This is valid only for continuous conduction mode.
- (B) \( \beta - \alpha \) (Correct): This correctly accounts for the discontinuous conduction mode where conduction stops at \( \beta \).
- (C) \( \alpha \) (Incorrect): The firing angle does not directly indicate conduction time.
- (D) \( \beta \) (Incorrect): The conduction duration is relative to \( \alpha \), not just \( \beta \).