The frequency at which a circuit with a capacitor and an inductor oscillates is sometimes referred to as what?

The frequency at which a circuit with a capacitor and an inductor oscillates is sometimes referred to as what?

• A. The applied frequency
• B. The imaginary frequency
• C. The cutoff frequency
• D. The natural, or resonant, frequency

Answer: (D)

In an LC circuit the capacitor and inductor exchange energy back and forth, so the system tends to ring at its own natural rate. The math shows the charge on the capacitor (and the current in the loop) varies with angular frequency ω0 = 1/√(LC), giving a regular frequency f0 = 1/(2π√(LC)). This intrinsic frequency is what the circuit would oscillate at if it weren’t driven by an external source and unless some resistance damps it. That makes it the natural, or resonant, frequency. It’s not the external (applied) frequency, and terms like cutoff relate to filters rather than the free oscillation, while imaginary frequency isn’t a physical description of this real oscillator.

In an LC circuit the capacitor and inductor exchange energy back and forth, so the system tends to ring at its own natural rate. The math shows the charge on the capacitor (and the current in the loop) varies with angular frequency ω0 = 1/√(LC), giving a regular frequency f0 = 1/(2π√(LC)). This intrinsic frequency is what the circuit would oscillate at if it weren’t driven by an external source and unless some resistance damps it. That makes it the natural, or resonant, frequency. It’s not the external (applied) frequency, and terms like cutoff relate to filters rather than the free oscillation, while imaginary frequency isn’t a physical description of this real oscillator.