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Assertion–Reason in DC choppers: Assertion (A): If the duty cycle of a chopper is low, the current would not become discontinuous. Reason (R): If the load time constant L/R is low, the current may become discontinuous.

Difficulty: Medium

Both A and R are correct and R is the correct explanation of A
Both A and R are correct but R is not the correct explanation of A
A is correct but R is wrong
A is wrong but R is correct
Both A and R are wrong

Correct Answer: A is wrong but R is correct

Explanation:

Introduction / Context:
Chopper-fed inductive loads can operate in continuous or discontinuous current mode depending on switching parameters and the load time constant. This assertion–reason item probes how duty cycle and L/R affect current continuity.

Given Data / Assumptions:

Chopper with R–L load.
Duty cycle D can be low or high.
Load time constant τ = L / R sets current decay rate during OFF time.

Concept / Approach:
Low duty cycle implies longer OFF time fraction, giving current more time to decay. A small τ (low L/R) also causes faster decay. Both conditions favor discontinuous current. Hence, the assertion that low duty cycle prevents discontinuity is wrong; the reason that small L/R can cause discontinuity is correct.

Step-by-Step Solution:

During OFF time, i(t) decays approximately as i * exp(−t/τ).Lower duty cycle → larger OFF interval → more decay → more likely i reaches zero → discontinuous mode.Smaller τ = L/R → faster exponential decay → increased chance of discontinuity.Therefore: Assertion (A) is wrong; Reason (R) is correct.

Verification / Alternative check:

Simulation or timing diagrams confirm that elongated OFF periods and small τ values produce discontinuous current at moderate loads.

Why Other Options Are Wrong:

Any option claiming A is correct contradicts chopper current decay physics.Saying R is wrong ignores the well-known impact of τ on decay.

Common Pitfalls:

Assuming duty cycle only changes average voltage, not current mode; overlooking the exponential nature of inductor current decay.

Final Answer:

A is wrong but R is correct

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Assertion–Reason in DC choppers: Assertion (A): If the duty cycle of a chopper is low, the current would not become discontinuous. Reason (R): If the load time constant L/R is low, the current may become discontinuous.

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