Compute the resonant frequency for a series RLC circuit with L = 8 mH and C = 40 µF (standard formula f0 = 1 / (2π√(LC))).

Introduction / Context:
Resonant frequency is the cornerstone of tuned-circuit design. For a given L and C, f0 indicates where series reactances cancel and current peaks, which is vital for filters, oscillators, and matching networks.

Given Data / Assumptions:

• L = 8 mH = 8 × 10^−3 H.
• C = 40 µF = 40 × 10^−6 F.
• Ideal, linear, time-invariant components.

Concept / Approach:

Use the standard formula: f0 = 1 / (2 * π * √(L * C)). Carefully handle unit conversions to avoid decade and decimal errors.

Step-by-Step Solution:

Verification / Alternative check:

Back-of-envelope: √(LC) ~ 5.65e−4 s ⇒ period ~ 3.55 ms ⇒ frequency ~ 1/3.55 ms ≈ 281 Hz—consistent.

Why Other Options Are Wrong:

2,810 Hz is an order-of-magnitude (×10) error. 28.1 Hz is a ÷10 error. 10 kHz is unrelated to LC values given.

Common Pitfalls:

Forgetting milli and micro conversions; misplacing decimal points; swapping series vs. parallel intuition (resonant frequency formula is the same).

Final Answer:

281 Hz