Oscillatory Circuit

1. Definition:

• An oscillatory circuit is an electric circuit consisting of a capacitor with capacitance C connected in series with an inductor with inductance L, forming a closed loop.

2. Ideal Oscillatory Circuit:

• An ideal oscillatory circuit is a circuit with negligible resistance, considered to be zero.
• Note: In reality, all oscillatory circuits have resistance, so the energy of the circuit will gradually dissipate over time. However, in many cases, we can ignore resistance to simplify the problem.

3. Variation of Charge and Current:

• The charge q on one plate of the capacitor and the current i in the oscillatory circuit vary sinusoidally with time.
• Phase Relationship: i leads q and u by π/2.

4. Free Electromagnetic Oscillation:

• The electric field strength E is proportional to the charge q of the capacitor. The magnetic induction B is proportional to the current i in the coil.
• The sinusoidal variation with time of q on the capacitor and i in the oscillatory circuit is called free electromagnetic oscillation.

5. Period and Frequency of Natural Oscillation:

• The period T and frequency f of natural oscillation of the oscillatory circuit are the period and frequency of free electromagnetic oscillation.
• Formula:
  • T = 2π√(LC)
  • f = 1/(2π√(LC))
• Note:
  • If L is measured in millihenries (mH) and C is measured in picofarads (pF), then f is measured in megahertz (MHz).
  • The period and frequency of natural oscillation of the oscillatory circuit depend only on L and C, not on the amplitude of oscillation.

6. Electromagnetic Energy:

• The electromagnetic energy of the oscillatory circuit is the sum of the electric field energy and magnetic field energy of the circuit:
  • W = Wc + Wl = 1/2.Cu^2 + 1/2.Li^2
• Note:
  • During oscillation, there is a conversion between electric field energy and magnetic field energy, but the total electromagnetic energy of the circuit REMAINS CONSTANT.
  • Wc and Wl vary with angular frequency 2ω, frequency 2f, and period T/2.

7. Effect of Factors on Oscillation Period:

• If the number of turns of the inductor coil is increased, then the inductance L increases, leading to an increase in the period T of the electromagnetic oscillation.

8. Other Formulas:

• Formula relating charge q, current i, voltage u, and electromagnetic energy W:
  • W = 1/2.Cu^2 = 1/2.Li^2 = 1/2.q^2/C = 1/2.L.i^2
• Formula relating period T, frequency f, and angular frequency ω:
  • ω = 2πf = 2π/T

Note:

Oscillatory circuits are widely used in electronic devices such as radio transmitters, radio receivers, pulse generators, computer memory, etc.

In addition to the above content, you can learn more about related concepts regarding oscillatory circuits, such as:

• Damped oscillation: Electromagnetic oscillation in a circuit with resistance.
• Forced oscillation: Electromagnetic oscillation in a circuit when a periodic external force is applied.
• Electrical resonance: A phenomenon that occurs when the frequency of the periodic external force is equal to the natural frequency of the oscillatory circuit.