The frequency at which a circuit with a capacitor and an inductor oscillates is given by which equation? f = 1/2π√LC

The frequency at which a circuit with a capacitor and an inductor oscillates is given by which equation? f = 1/2π√LC

• A. f = 2π√LC
• B. f = 1/2π√LC
• C. f = √(LC)
• D. f = 1/(LC)

Answer: (B)

An LC circuit free to oscillate stores energy in the capacitor and the inductor, so the charge on the capacitor follows a simple harmonic motion. The equation for the charge ends up as q'' + q/(LC) = 0, which is the standard form x'' + ω^2 x = 0 for a harmonic oscillator. This means the angular frequency is ω = 1/√(LC). To get the ordinary frequency in cycles per second, divide by 2π: f = ω/(2π) = 1/(2π√(LC)). That’s why this form is correct for an ideal LC circuit. If resistance were present, the oscillations would be damped but occur near this frequency. The other forms don’t match the proper relation between L, C, and frequency.

An LC circuit free to oscillate stores energy in the capacitor and the inductor, so the charge on the capacitor follows a simple harmonic motion. The equation for the charge ends up as q'' + q/(LC) = 0, which is the standard form x'' + ω^2 x = 0 for a harmonic oscillator. This means the angular frequency is ω = 1/√(LC). To get the ordinary frequency in cycles per second, divide by 2π: f = ω/(2π) = 1/(2π√(LC)). That’s why this form is correct for an ideal LC circuit. If resistance were present, the oscillations would be damped but occur near this frequency. The other forms don’t match the proper relation between L, C, and frequency.