Single-phase full-wave AC voltage regulator with R–L load If a single-phase full-wave AC voltage controller (full-wave regulator) feeds an R–L load whose load power-factor angle is θ (radians), what is the permissible control range of the firing angle α for proper natural commutation and non-overlapping conduction?

Introduction / Context:
AC voltage controllers (also called AC regulators) adjust the RMS voltage delivered to a load by delaying the firing of thyristors. With an R–L load, current lags voltage by the load power-factor angle θ, which impacts the allowable firing angle range to ensure natural turn-off and avoid commutation overlap into the next half-cycle.

Given Data / Assumptions:

• Single-phase full-wave regulator (anti-parallel thyristor pair or bridge).
• Load is R–L with power-factor angle θ.
• Natural (line) commutation; no forced commutation circuits.
• Objective: avoid overlap between successive half-cycles and ensure current has decayed to zero before the next gating instant.

Concept / Approach:

In R–L loads, the current lags the applied voltage and persists after the instantaneous voltage crosses zero. If the firing angle α is too small relative to θ, the outgoing current from one half-cycle may still be flowing when the next device should be triggered, risking commutation failure or uncontrolled overlap. To guarantee natural extinction before the next half-cycle firing, α must not be set earlier than the lag-induced extinction boundary.

Step-by-Step Solution:

Verification / Alternative check:

Textbook conduction diagrams for full-wave R–L regulators show a practical bound α ∈ [θ, π], ensuring turn-off without auxiliary means.

Why Other Options Are Wrong:

(a) Allows α < θ, risking overlap. (c) 0 to (π − θ) is for different continuity considerations and does not guarantee extinction. (d) Extending above π is not possible in a single-phase line-commutated regulator.

Common Pitfalls:

Confusing rectifier constraints with AC regulator constraints; ignoring lagging current tail in inductive loads.

Final Answer:

θ ≤ α ≤ π