Single-phase full-wave AC voltage controller (AC regulator) using two antiparallel SCRs In practical operation, the firing angles used in the positive and negative half-cycles of the input supply ___.

Introduction / Context:
A single-phase full-wave AC voltage controller (AC regulator) typically uses two SCRs in antiparallel (or a TRIAC) to control the RMS output voltage delivered to a load by phase-angle control. A common doubt is whether the firing angles applied in the positive and negative half-cycles must always be identical.

Given Data / Assumptions:

• Single-phase supply and a pair of antiparallel SCRs (or an equivalent TRIAC).
• Gate pulses can be independently timed each half-cycle.
• Load may be resistive or inductive.

Concept / Approach:
For ideal symmetrical control, designers choose equal firing angles in both half-cycles so that the average output (DC component) is zero and electromagnetic effects are minimized. However, the controller hardware and control algorithm can impose different firing delays in each half-cycle (intentional or due to tolerances), so equality is not a hard requirement of operation—only of good practice when symmetry is desired.

Step-by-Step Solution:
Define α+ as the firing angle in the positive half-cycle and α− in the negative half-cycle.Symmetrical operation: α+ = α− to avoid DC offset and reduce transformer/core saturation issues.Asymmetrical operation: α+ ≠ α− can occur due to gating circuit design, sensor phase errors, or deliberate control strategies.Therefore, in general, the firing angles may be equal or unequal; equality is preferred but not mandatory.

Verification / Alternative check:
Waveform simulations with α+ ≠ α− show unequal positive/negative half-cycle areas, producing a DC component. Controllers are usually calibrated to set α+ ≈ α− for power-quality reasons, but operation is still possible otherwise.

Why Other Options Are Wrong:
Always equal / never equal: Too absolute; both can occur.
Sometimes equal: Vague and not as general as “may be equal or unequal.”
Must differ by 90°: No such general rule exists.

Common Pitfalls:
Assuming equality is enforced by physics. It is a control choice to ensure symmetry and reduce harmonics.

Final Answer:
may be equal or unequal