Half-wave controlled charger for a 50 V battery A single-phase half-wave converter is used to charge a 50 V battery. The thyristor gate is driven continuously (DC gate drive). The input is v(t) = Vm sin(ωt). Over what interval(s) does the thyristor conduct?

Introduction / Context:
Battery charging with a phase-controlled rectifier depends on the source instantaneous voltage exceeding the battery EMF (plus small drops). A continuously applied gate drive merely ensures the SCR will trigger whenever forward anode-to-cathode conditions exist; it does not force conduction when the source cannot forward-bias the SCR against the battery voltage.

Given Data / Assumptions:

• Single SCR half-wave converter.
• Battery emf ≈ 50 V (assume negligible series resistance for the decision threshold).
• Continuous DC gate drive available at all times.
• Input v(t) = Vm sin(ωt) on the same polarity half-cycle as the SCR.

Concept / Approach:

For current to flow into the battery, the instantaneous supply voltage must exceed the battery voltage. With continuous gating, the SCR will turn on immediately once v(t) exceeds 50 V in the forward half-cycle, and will continue to conduct until v(t) falls back below 50 V or current naturally goes to zero near the end of the half-cycle.

Step-by-Step Solution:

Verification / Alternative check:

If Vm < 50 V, no conduction occurs (even with continuous gate), validating that the battery EMF sets the threshold. If Vm ≫ 50 V, conduction occupies a central portion of the positive half-cycle only.

Why Other Options Are Wrong:

• 0–180° suggests full positive half-cycle conduction, which is false unless Vm is infinite and the drop negligible.
• 0–90° arbitrarily limits conduction; actual turn-off occurs after the peak when v drops below 50 V.
• “When v < 50 V” contradicts the forward-bias requirement.

Common Pitfalls:

Assuming gate drive alone guarantees conduction regardless of source EMF; forgetting that an SCR needs sufficient forward anode voltage.

Final Answer:

when v > 50 V