What is the resonant frequency of an RLC circuit if R is 22 ohms, L is 50 microhenries, and C is 40 picofarads?
The correct answer is C: 3.56 MHz. What is the resonant frequency of an RLC circuit if R is 22 ohms, L is 50 microhenries, and C is 40 picofarads is 3.56 MHz. f = 1/(2π√(LC)) = 1/(2π√(50×10^-6 × 40×10^-12)) ≈ 3.56 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 'F'requency = '1'/(2π√('L'C)). f = 1/(2π√(50×10^-6 × 40×10^-12)) ≈ 3.56 MHz. Not 44.72 MHz, not 22.36 MHz, not 1.78 MHz - just 3.56 MHz.
Memory Aid
"RLC resonant frequency = 1/(2π√(LC)). Think 'R'esonant = '1'/(2π√('L'C)). f = 1/(2π√(50×10^-6 × 40×10^-12)) ≈ 3.56 MHz. Important for circuit calculations."
Real-World Application
An RLC circuit with R=22 ohms, L=50 microhenries, C=40 picofarads: The resonant frequency is f = 1/(2π√(LC)) = 1/(2π√(50×10^-6 × 40×10^-12)) ≈ 3.56 MHz. Note that R doesn't affect resonant frequency. This is the frequency - 3.56 MHz.
Key Concepts
Why Other Options Are Wrong
Option A (44.72 MHz): Incorrect. 44.72 MHz is too high - the calculation gives 3.56 MHz. 44.72 MHz is wrong.
Option B (22.36 MHz): Incorrect. 22.36 MHz is too high - the calculation gives 3.56 MHz. 22.36 MHz is wrong.
Option D (1.78 MHz): Incorrect. 1.78 MHz is too low - the calculation gives 3.56 MHz. 1.78 MHz is wrong.
题目解析
The correct answer is C: 3.56 MHz. What is the resonant frequency of an RLC circuit if R is 22 ohms, L is 50 microhenries, and C is 40 picofarads is 3.56 MHz. f = 1/(2π√(LC)) = 1/(2π√(50×10^-6 × 40×10^-12)) ≈ 3.56 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 'F'requency = '1'/(2π√('L'C)). f = 1/(2π√(50×10^-6 × 40×10^-12)) ≈ 3.56 MHz. Not 44.72 MHz, not 22.36 MHz, not 1.78 MHz - just 3.56 MHz.
记忆口诀
RLC resonant frequency = 1/(2π√(LC)). Think 'R'esonant = '1'/(2π√('L'C)). f = 1/(2π√(50×10^-6 × 40×10^-12)) ≈ 3.56 MHz. Important for circuit calculations.
实际应用示例
An RLC circuit with R=22 ohms, L=50 microhenries, C=40 picofarads: The resonant frequency is f = 1/(2π√(LC)) = 1/(2π√(50×10^-6 × 40×10^-12)) ≈ 3.56 MHz. Note that R doesn't affect resonant frequency. This is the frequency - 3.56 MHz.
错误选项分析
Option A (44.72 MHz): Incorrect. 44.72 MHz is too high - the calculation gives 3.56 MHz. 44.72 MHz is wrong. Option B (22.36 MHz): Incorrect. 22.36 MHz is too high - the calculation gives 3.56 MHz. 22.36 MHz is wrong. Option D (1.78 MHz): Incorrect. 1.78 MHz is too low - the calculation gives 3.56 MHz. 1.78 MHz is wrong.
知识点
Resonant frequency, RLC circuit, R 22 ohms, L 50 microhenries, C 40 picofarads, 3.56 MHz
Verified Content
Question from official FCC Extra Class question pool. Explanation reviewed by licensed amateur radio operators.