What is the resonant frequency of a series RLC circuit, if R is 47 ohms, L is 40 microhenrys and C is 200 picofarads?

The resonant frequency of an RLC circuit is calculated using the formula f = 1 / (2π√(LC)). Notice that the resistance (R) of 47 ohms does not factor into this equation; it determines the circuit's Q factor and bandwidth, but not the resonant frequency itself. Plugging in the given values, we convert the units to standard Farads and Henrys: L = 40 × 10^-6 H and C = 200 × 10^-12 F. Multiplying L and C gives 8 × 10^-15. Taking the square root and multiplying by 2π yields approximately 5.62 × 10^-7. Finally, dividing 1 by this result gives 1,779,380 Hz, or 1.78 MHz. The distractors in kHz are simply magnitude errors resulting from incorrect conversions of the micro and pico prefixes.