ASVAB (Armed Services Vocational Aptitude Battery)Electronics Information (EI)Hard
A radio receiver circuit uses a tuned circuit consisting of an inductor and a capacitor to select a specific frequency. If the inductance is 10 mH and the capacitance is 100 pF, what is the resonant frequency of this circuit? (Use π ≈ 3.14)
- A159 kHz
- B1.59 kHz
- C1.59 MHz
- D15.9 kHz
Show answer & explanationAnswer & explanation
Correct answer: A. 159 kHz
The resonant frequency (f) of an LC circuit is given by the formula f = 1 / (2π√(LC)). L = 10 mH = 10 × 10⁻³ H C = 100 pF = 100 × 10⁻¹² F LC = (10 × 10⁻³ H) × (100 × 10⁻¹² F) = 1000 × 10⁻¹⁵ = 1 × 10⁻¹² √(LC) = √(1 × 10⁻¹²) = 1 × 10⁻⁶ f = 1 / (2 × 3.14 × 1 × 10⁻⁶) = 1 / (6.28 × 10⁻⁶) = 0.1592 × 10⁶ Hz = 159.2 kHz. Option C is the closest.
Why the other options are wrong
- B. Incorrect calculation, likely an error in magnitude or units.
- C. Incorrect calculation, likely an error in magnitude or units.
- D. Incorrect calculation, likely an error in magnitude or units.
LC Resonant Frequency
The specific frequency at which an inductor (L) and a capacitor (C) in an LC circuit achieve maximum energy transfer, calculated by f = 1 / (2π√(LC)).
- Determines the natural oscillation frequency of the circuit.
- Used in tuning circuits for radios and filters.
- Dependent on both inductance (L) and capacitance (C).
Memory trick: Frequency Finds Fun with Fancy LC.