ASVAB (Armed Services Vocational Aptitude Battery)Electronics Information (EI)Hard
A 100 µH inductor is part of an LC resonant circuit. If the resonant frequency needs to be 1 MHz, what capacitance (approximately) is required?
- A0.25 pF
- B25 pF
- C250 pF
- D2.5 nF
Show answer & explanationAnswer & explanation
Correct answer: C. 250 pF
The resonant frequency (f) of an LC circuit is given by f = 1 / (2π√(LC)). To find C, rearrange the formula: C = 1 / ( (2πf)² * L ). Given f = 1 MHz = 1x10^6 Hz and L = 100 µH = 100x10^-6 H. C = 1 / ( (2π * 1x10^6)² * 100x10^-6 ) = 1 / ( (6.283x10^6)² * 100x10^-6 ) = 1 / ( 39.478x10^12 * 100x10^-6 ) = 1 / ( 39.478x10^8 ) ≈ 2.53 x 10^-10 F = 253 pF. The closest option is 250 pF.
Why the other options are wrong
- A. This is too small by several orders of magnitude.
- B. This is incorrect, likely due to a calculation error or incorrect unit conversion.
- D. This is too large by an order of magnitude (2.5 nF = 2500 pF).
LC Resonant Circuit
An electrical circuit consisting of an inductor (L) and a capacitor (C) that resonates at a specific frequency.
- Resonant frequency (f) is where inductive reactance equals capacitive reactance.
- Formula: f = 1 / (2π√(LC)).
- Used in tuning circuits, filters, and oscillators.
Memory trick: Resonance: 2 Pi Radian Frequency, Root of LC.