What is the resonant frequency of an RLC circuit if R is 33 ohms, L is 50 microhenries, and C is 10 picofarads?

The resonant frequency of an RLC circuit depends only on the inductance (L) and capacitance (C). The resistance (R) has no effect on the resonant frequency, so the 33 ohms in the prompt is a distractor. The formula is f = 1 / (2 * pi * sqrt(L * C)). First, convert the values to standard units: L = 50 x 10^-6 henries, and C = 10 x 10^-12 farads. Plugging these into the formula yields f = 1 / (2 * 3.14159 * sqrt(50e-6 * 10e-12)). Calculating the square root of (500e-18) gives approximately 2.236e-8. Multiplying by 2 * pi yields 1.405e-7. Finally, taking the reciprocal (1 / 1.405e-7) gives approximately 7,117,625 Hz, which simplifies to 7.12 MHz.