What is the resonant frequency of a series RLC circuit, if R is 47 ohms, L is 25 microhenrys and C is 10 picofarads?

The formula for determining resonant frequency is f = 1 / (2π√(LC)). As with all ideal series RLC circuits, the resistor value (47 ohms) determines the bandwidth but does not shift the center resonant frequency. Using the provided values of L = 25 × 10^-6 H and C = 10 × 10^-12 F, we first multiply them to get 2.5 × 10^-16. Taking the square root gives about 1.581 × 10^-8, and multiplying by 2π results in 9.934 × 10^-8. Taking the reciprocal (1 / x) of this denominator yields exactly 10,066,000 Hz, or 10.1 MHz. Distractors involving 63.7 or values in kHz stem from either dropping the 2π from the formula or mismanaging scientific notation.