What is the value of capacitance (C) in a series R-L-C circuit, if the circuit resonant frequency is 14.25 MHz and L is 2.84 microhenrys?

To solve for capacitance when you know the resonant frequency and inductance, you must rearrange the standard resonant frequency formula to: C = 1 / (4π²f²L). First, convert your knowns to standard units: f = 14.25 × 10^6 Hz and L = 2.84 × 10^-6 henrys. Square the frequency, then multiply by 4π² (approx 39.478) and the inductance. The denominator becomes approximately 2.276 × 10^10. Dividing 1 by this denominator yields roughly 4.39 × 10^-11 farads, which smoothly converts to 44 picofarads. The microfarad options are incorrect by a factor of one million.