Single-phase full-wave AC voltage regulator (purely resistive load): If the RMS load current is 20 A, compare per-thyristor average current and per-thyristor RMS current with 20 A (consider each SCR conducts for alternate half-cycles).

Difficulty: Medium

average thyristor current will be less than 20 A but rms thyristor current will be more than 20 A
both the average and rms thyristor currents will be less than 20 A
both the average and rms thyristor currents will be more than 20 A
rms thyristor current will be 20 A and average thyristor current will be 10 A
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Correct Answer: both the average and rms thyristor currents will be less than 20 A

Explanation:

Introduction / Context:
AC voltage controllers (AC regulators) use antiparallel thyristors to control the RMS voltage applied to a resistive load. Each thyristor conducts on alternate half-cycles. This question probes understanding of how device-level current (per SCR) compares with the total RMS load current reported at the terminals.

Given Data / Assumptions:

Single-phase, full-wave AC regulator with two antiparallel SCRs.
Load is purely resistive; load RMS current IL,rms = 20 A.
Symmetrical firing so each SCR conducts on its half-cycles only.
We compare a per-device average over a full mains cycle and a per-device RMS over a full cycle.

Concept / Approach:

Because each SCR conducts for only half of the time (its own polarity half-cycles), the current through each device is time-shared. For a sinusoidal resistive current, distributing conduction across two devices reduces both the per-device average current (over a full cycle) and the per-device RMS current relative to the total load RMS current.

Step-by-Step Solution:

Let i(t) be the instantaneous load current. For a resistive load, i(t) follows the applied voltage shape within the conduction interval.Over a full cycle, SCR1 conducts during positive half-cycles only; SCR2 conducts during negative half-cycles only.Per-device average current over one full cycle is the average of its half-cycle conduction and zero during the other half → average per device < average of the rectified load current, hence < 20 A.Per-device RMS over one full cycle is RMS of half-cycle conduction combined with zero in the other half. For symmetric conduction, I_rms,device = IL,rms / √2 for sinusoidal halves, which is less than 20 A.

Verification / Alternative check:

For an ideal full-conduction case on a resistive load: if IL,rms = 20 A, each SCR carries the same waveform but only half the time. Time-sharing lowers both RMS and average when computed over the full period per device.

Why Other Options Are Wrong:

Option A: Claims device RMS > 20 A, impossible with half-time conduction.
Option C: Both higher than 20 A contradicts power balance and time-sharing.
Option D: Assigns fixed numbers without basis; device RMS ≠ 20 A for half-cycle conduction averaged over full period.

Common Pitfalls:

Confusing per-device RMS (over full cycle with zero current for half the cycle) with the instantaneous half-cycle RMS; forgetting that averaging window matters.

Final Answer:

both the average and rms thyristor currents will be less than 20 A

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Single-phase full-wave AC voltage regulator (purely resistive load): If the RMS load current is 20 A, compare per-thyristor average current and per-thyristor RMS current with 20 A (consider each SCR conducts for alternate half-cycles).

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