Question
What is the resonant frequency of an RLC circuit if R is 22 ohms, L is 50 microhenries, and C is 40 picofarads?
Answer Options
- A) 44.72 MHz
- B) 22.36 MHz
- C) 3.56 MHz
- D) 1.78 MHz
Correct Answer: C
Explanation
The resonant frequency (f_r) of a series or parallel RLC circuit is the frequency at which the inductive reactance (X_L) equals the capacitive reactance (X_C). At this frequency, the reactive components cancel out, defining the circuit’s fundamental tuning point. The value of the resistance (R) does not affect the resonant frequency itself.
The resonant frequency is calculated using the formula: f_r = \frac{1}{2\pi\sqrt{LC}}. Plugging in the given values, L = 50 \times 10^{-6} \text{ H} and C = 40 \times 10^{-12} \text{ F}: f_r = \frac{1}{2\pi\sqrt{(50 \times 10^{-6})(40 \times 10^{-12})}} \approx 3,558,819 \text{ Hz} This converts to approximately 3.56 MHz. This frequency falls in the 80-meter amateur band, suggesting the circuit could be used for a filter or tuner in that range.
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