Question
What is the resonant frequency of an RLC circuit if R is 33 ohms, L is 50 microhenries, and C is 10 picofarads?
Answer Options
- A) 7.12 MHz
- B) 23.5 kHz
- C) 7.12 kHz
- D) 23.5 MHz
Correct Answer: A
Explanation
The resonant frequency (f_r) of a tuned circuit is determined only by the values of the inductor (L) and the capacitor (C), not the resistance (R). The relationship is defined by the formula: f_r = \frac{1}{2\pi\sqrt{LC}}. The units must be converted to standard Henries and Farads for the calculation.
Plugging in the component values, L = 50 \times 10^{-6} \text{ H} and C = 10 \times 10^{-12} \text{ F}: f_r = \frac{1}{2\pi\sqrt{(50 \times 10^{-6})(10 \times 10^{-12})}} \approx 7,117,605 \text{ Hz} This frequency is approximately 7.12 MHz. This frequency falls directly in the middle of the 40-meter amateur band, suggesting the circuit is tuned for operation in that range.
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