Which is closest to the resonant frequency of a series resonant circuit with L = 1 mH and C = 10 nF?

Answer: A. About 50 kHz

The resonant frequency is f0 = 1/(2π√(LC)). Since LC = 1×10⁻³ × 10×10⁻⁹ = 1×10⁻¹¹, √(LC) ≈ 3.16×10⁻⁶ s and f0 ≈ 1/(2π × 3.16×10⁻⁶) ≈ 50.3 kHz. At this frequency the inductor and capacitor reactances are equal, both √(L/C) ≈ 316 Ω. The resonant frequency is inversely proportional to the square root of LC, so making C 100 times larger lowers it to 1/10.

• A. Correct. 1/(2π√(LC)) ≈ 50.3 kHz.
• B. About 316 kHz mistakes the angular frequency ω0 = 1/√(LC) ≈ 3.16×10⁵ rad/s for the frequency.
• C. About 5 kHz is the result if C were taken as 1 µF (100 times larger).