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.
-
ABoth A and R are correct and R is the correct explanation of A
-
BBoth A and R are correct but R is not the correct explanation of A
-
CA is correct but R is wrong
-
DA is wrong but R is correct
-
EBoth A and R are wrong
Answer
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