In a single-phase half-wave AC voltage regulator supplying a purely resistive load via a series thyristor (phase control on one half-cycle only), which statement best describes the RMS load current sign?

Introduction / Context:
Half-wave AC regulators use a single series-controlled device to pass a portion of one half-cycle of the source to a resistive load. The RMS (root mean square) value is a magnitude measure of heating effect and cannot be negative by definition.

Given Data / Assumptions:

• Resistive (R) load.
• Half-wave phase control (typically on the positive half-cycle only).
• Standard definition of RMS.

Concept / Approach:
Instantaneous current follows the applied half-cycle waveform scaled by R. Although instantaneous current is zero during blocked intervals and positive during conduction, the RMS value computed over the full period is a non-negative magnitude reflecting equivalent heating in a resistor.

Step-by-Step Solution:
1) Instantaneous current i(t) = v(t)/R when thyristor is ON; i(t) = 0 when OFF.2) RMS is sqrt( (1/T) * ∫ i(t)^2 dt ) over one period T.3) Because i(t)^2 ≥ 0 at all times, the RMS result is non-negative; with any conduction the RMS is strictly positive.
Verification / Alternative check:
Even if conduction angle is small, the RMS remains a positive magnitude proportional to the square-root of mean power delivered.
Why Other Options Are Wrong:

• Negative RMS has no physical meaning; RMS is a magnitude.
• Zero RMS would imply no conduction at all (thyristor never fires).
• “Alternates sign” pertains to average or instantaneous values, not RMS.

Common Pitfalls:

• Mixing up average current (which can be zero for symmetric waveforms) with RMS.
• Confusing instantaneous polarity with RMS sign.

Final Answer:
It is always positive.