What is the resonant frequency of a series RLC circuit, if R is 47 ohms, L is 4 microhenrys and C is 20 picofarads?

The resonant frequency of any RLC circuit is determined entirely by the inductance (L) and capacitance (C). The resistance (R) only affects the bandwidth and Q-factor, not the resonant frequency itself. The formula to calculate the resonant frequency is f = 1 / (2 * π * √(L * C)). First, ensure your values are in base units: L is 4 × 10^-6 henrys and C is 20 × 10^-12 farads. Multiplying L and C gives 80 × 10^-18. Taking the square root and multiplying by 2π yields approximately 5.62 × 10^-8. Dividing 1 by this result gives 17.79 × 10^6 hertz, which rounds to 17.8 MHz. Distractors using "kHz" instead of "MHz" are common if you forget to properly account for the micro and pico prefixes.