What is the resonant frequency of an RLC circuit if R is 33 ohms, L is 50 microhenries, and C is 10 picofarads?
The correct answer is A: 7.12 MHz. What is the resonant frequency of an RLC circuit if R is 33 ohms, L is 50 microhenries, and C is 10 picofarads is 7.12 MHz. f = 1/(2π√(LC)) = 1/(2π√(50×10^-6 × 10×10^-12)) ≈ 7.12 MHz. For amateur radio operators, this is important for circuit calculations. Understanding this helps when designing resonant circuits.
Exam Tip
RLC resonant frequency = 1/(2π√(LC)). Think 'R'esonant = '1'/(2π√('L'C)). f = 1/(2π√(50×10^-6 × 10×10^-12)) ≈ 7.12 MHz. Not 23.5 kHz, not 7.12 kHz, not 23.5 MHz - just 7.12 MHz.
Memory Aid
"RLC resonant frequency = 1/(2π√(LC)). Think 'R'esonant = '7'.12 MHz. f = 1/(2π√(50×10^-6 × 10×10^-12)) ≈ 7.12 MHz. Important for circuit calculations."
Real-World Application
An RLC circuit with R=33 ohms, L=50 microhenries, C=10 picofarads: The resonant frequency is f = 1/(2π√(LC)) = 1/(2π√(50×10^-6 × 10×10^-12)) ≈ 7.12 MHz. Note that R doesn't affect resonant frequency. This is the frequency - 7.12 MHz.
Key Concepts
Why Other Options Are Wrong
Option B (23.5 kHz): Incorrect. 23.5 kHz is too low - the calculation gives 7.12 MHz. 23.5 kHz is wrong.
Option C (7.12 kHz): Incorrect. 7.12 kHz is too low - the calculation gives 7.12 MHz. 7.12 kHz is wrong.
Option D (23.5 MHz): Incorrect. 23.5 MHz is too high - the calculation gives 7.12 MHz. 23.5 MHz is wrong.
题目解析
The correct answer is A: 7.12 MHz. What is the resonant frequency of an RLC circuit if R is 33 ohms, L is 50 microhenries, and C is 10 picofarads is 7.12 MHz. f = 1/(2π√(LC)) = 1/(2π√(50×10^-6 × 10×10^-12)) ≈ 7.12 MHz. For amateur radio operators, this is important for circuit calculations. Understanding this helps when designing resonant circuits.
考试技巧
RLC resonant frequency = 1/(2π√(LC)). Think 'R'esonant = '1'/(2π√('L'C)). f = 1/(2π√(50×10^-6 × 10×10^-12)) ≈ 7.12 MHz. Not 23.5 kHz, not 7.12 kHz, not 23.5 MHz - just 7.12 MHz.
记忆口诀
RLC resonant frequency = 1/(2π√(LC)). Think 'R'esonant = '7'.12 MHz. f = 1/(2π√(50×10^-6 × 10×10^-12)) ≈ 7.12 MHz. Important for circuit calculations.
实际应用示例
An RLC circuit with R=33 ohms, L=50 microhenries, C=10 picofarads: The resonant frequency is f = 1/(2π√(LC)) = 1/(2π√(50×10^-6 × 10×10^-12)) ≈ 7.12 MHz. Note that R doesn't affect resonant frequency. This is the frequency - 7.12 MHz.
错误选项分析
Option B (23.5 kHz): Incorrect. 23.5 kHz is too low - the calculation gives 7.12 MHz. 23.5 kHz is wrong. Option C (7.12 kHz): Incorrect. 7.12 kHz is too low - the calculation gives 7.12 MHz. 7.12 kHz is wrong. Option D (23.5 MHz): Incorrect. 23.5 MHz is too high - the calculation gives 7.12 MHz. 23.5 MHz is wrong.
知识点
Resonant frequency, RLC circuit, R 33 ohms, L 50 microhenries, C 10 picofarads, 7.12 MHz
Verified Content
Question from official FCC Extra Class question pool. Explanation reviewed by licensed amateur radio operators.