What is the resonant frequency of a series RLC circuit, if R is 47 ohms, L is 50 microhenrys and C is 10 picofarads?

To find the resonant frequency, we use the standard resonance formula: f = 1 / (2π√(LC)). The 47-ohm resistance is included as a distractor and has no mathematical effect on the resonant frequency of the circuit. First, convert the given values to standard units: L = 50 × 10^-6 H and C = 10 × 10^-12 F. The product of L and C is 5 × 10^-16. The square root of this value is approximately 2.236 × 10^-8. Multiplying by 2π gives 1.405 × 10^-7. Dividing 1 by this number yields 7,117,625 Hz, which rounds nicely to 7.12 MHz. The kHz options are common mistakes made when students mishandle the powers of 10 in their calculators.