Series RLC step/impulse behavior — match resistance conditions to the qualitative response (assume the standard form R compared to 2sqrt(L/C)). List I (Condition) A. R = 0 B. R < 2sqrt(L/C) C. R = 2sqrt(L/C) D. R > 2sqrt(L/C) List II (Response) 1. Undamped oscillation 2. Damped oscillation (underdamped) 3. Critically damped response 4. Non-oscillatory overdamped response

Introduction:
The damping nature of a series RLC circuit depends on the relative magnitude of R to the critical value 2sqrt(L/C). Recognizing underdamped, critically damped, overdamped, and ideal undamped cases is essential for filter, timing, and surge design.

Given Data / Assumptions:

• Standard series RLC with resistance R, inductance L, capacitance C.
• Natural frequency ω0 = 1/sqrt(LC).
• Critical damping threshold at R = 2sqrt(L/C) (in SI units for series form).

Concept / Approach:

The characteristic equation roots determine the impulse/step response: underdamped (complex conjugate), critically damped (repeated real), overdamped (distinct real), and undamped (pure imaginary when R=0). Matching each region of R to its qualitative response follows directly from the discriminant of the second-order system.

Step-by-Step Solution:

Verification / Alternative check:

Compute damping ratio ζ = R / (2sqrt(L/C)). Then ζ < 1 underdamped, ζ = 1 critical, ζ > 1 overdamped; ζ = 0 gives undamped oscillation.

Why Other Options Are Wrong:

• Swapping 2 and 4 confuses underdamped with overdamped behavior.
• Assigning A ≠ 1 implies oscillation even with resistance, contradicting R = 0 only.

Common Pitfalls:

Mixing the series and parallel RLC criteria; always check which topology is assumed. Also ensure consistent SI units when using 2sqrt(L/C).

Final Answer:

A-1, B-2, C-3, D-4