Half-wave controlled rectifier (positive half-cycle firing only) An SCR conducts only in the positive half-cycle. With firing angle α = 80°, the RMS anode current is 25 A. If α is increased to 160°, the expected RMS current will be:

Introduction / Context:
In a single-phase half-wave controlled rectifier (SCR triggered only on positive half-cycles), the firing angle α determines the conduction interval within each positive half-cycle. Increasing α reduces the conduction width, decreasing both average and RMS currents. This question asks for a qualitative comparison at α = 80° versus α = 160°.

Given Data / Assumptions:

• SCR fires in positive half-cycles only (half-wave control).
• RMS anode current at α = 80° is 25 A.
• Load is assumed unchanged (commonly resistive or predominantly resistive for this comparison).
• No change in supply amplitude/frequency.

Concept / Approach:

RMS current depends on the square of instantaneous current over the conduction interval. As α increases, the conduction window (α to π) narrows. Going from α = 80° (100° conduction) to α = 160° (20° conduction) dramatically reduces the area under i^2(t), so the RMS value falls much more than by a simple factor of 2; hence it will be less than 12.5 A (half of the original), not merely less than 25 A.

Step-by-Step Solution:

Verification / Alternative check:

Limiting behavior: as α → 180°, conduction interval tends to zero, and RMS current tends to zero; thus increasing α from 80° to 160° must decrease RMS current below half the former value.

Why Other Options Are Wrong:

25 A assumes no change with α; 12.5 A assumes linear halving with α, which is incorrect because RMS depends on the integral of sin^2 over the conduction window; “Less than 25 A” is true but not as informative as “Less than 12.5 A”.

Common Pitfalls:

Equating proportional change in α with proportional change in RMS; confusing average with RMS values; ignoring that conduction near π contributes very little to RMS due to low instantaneous values.

Final Answer:

Less than 12.5 A