What is the resonant frequency of a series RLC circuit if R is 47 ohms, L is 50 microhenrys and C is 40 picofarads?

The resonant frequency of a series RLC circuit is determined entirely by its inductance (L) and capacitance (C). The standard formula is f = 1 / (2 * π * √(L * C)). The resistance (R) of 47 ohms is a distractor; while it affects the bandwidth and Q-factor of the circuit, it is not used in calculating the resonant frequency itself. First, convert the given values into standard base units: L is 50 × 10^-6 henrys and C is 40 × 10^-12 farads. Multiplying L and C gives 2 × 10^-15. Taking the square root of that result yields approximately 4.472 × 10^-8. Finally, multiply that square root by 2π (which gives about 2.81 × 10^-7) and take the reciprocal (1 / x) to find the frequency. The result is approximately 3,558,812 Hz, which converts to 3.56 MHz.