Concept:In a center-tapped transformer, each half of the secondary winding conducts for only one half-cycle, resulting in a lower utilization factor than a bridge rectifier.
Formula:$$\text{TUF}_{\text{center-tap}} = \frac{\text{TUF}_{\text{primary}} + \text{TUF}_{\text{secondary}}}{2}$$
Solution:- The primary winding carries full AC current (\( \text{TUF}_{\text{primary}} = 0.812 \)).
- Each half-secondary conducts like a half-wave circuit (\( \text{TUF}_{\text{secondary}} = 0.287 \times 2 = 0.574 \)).
- Averaging the primary and secondary utilization yields:
- $$\text{TUF}_{\text{avg}} = \frac{0.812 + 0.574}{2} \approx 0.693$$
Why other options are incorrect:- Option A: \( 0.812 \) is the \( \text{TUF} \) of a bridge rectifier.
- Option B: \( 0.287 \) is the \( \text{TUF} \) of a half-wave rectifier.
- Option D: \( 1.210 \) is the ripple factor of a half-wave rectifier.
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