Схема последовательного RLC-контура

A series RLC circuit connects a resistor and an inductor in series with a charged capacitor.

In a closed circuit, the capacitor discharges through the resistor and inductor. Due to energy losses in the resistor, the magnetic field energy acquired by the inductor is less than the electric field energy of the fully charged capacitor.

On recharging the capacitor, energy is again lost in the resistor, leading to lower electric field energy than the original magnetic energy. These energy oscillations continuously decrease in amplitude and are called damped oscillations.

The decrease in total electromagnetic energy with time is equal to the energy dissipated in the resistor.

On differentiating the equation and replacing the current, the equation of the damped RLC circuit is obtained.

For small resistance, the charge oscillations on capacitor plates die out slowly, and the circuit is called underdamped.

If the resistance reaches a critical value, the circuit no longer oscillates and is called critically damped.

For very large resistance, the circuit becomes overdamped with a slow decrease in the charge of the capacitor.