By hvhipot 
A series resonant circuit includes an inductor and a capacitor, in which electrical resonance can be excited. If a capacitor is charged to a voltage of V 0 at a certain point in time, the energy concentrated in the capacitor’s electric field is equal to
Among them, C is the capacitance of the capacitor. When the capacitor discharges, the current I will flow in the coil and increase until the capacitor is completely discharged. At this point, the electrical energy K, E c=0, and the magnetic energy is concentrated in the coil
Among them, L is the inductance of the coil, and I0 is the maximum current value. Then the current in the coil begins to decrease, and the absolute value of the voltage across the capacitor increases, but with opposite signs. After a period of time, the current flowing through the inductor will stop and the capacitor will be charged to a voltage of V 0. The energy of K will once again be concentrated in the charged condenser. In addition, the process is repeated, but the direction of the current is opposite. The voltage on the capacitor board varies according to the law V=V 0 cos w 0 t,
The current in the inductor is I=I 0 sin w 0 t, which means that in K, the natural harmonic resonance of voltage and current is excited at a frequency w 0=2 p/T 0, where T 0 is the natural resonance period equal to T 0=2 p. During this period, energy is transferred from the electric field of the capacitor to the magnetic field of the inductor, and vice versa.
However, in actual K., some energy will be lost. It is used to heat wires with active resistors, emit electromagnetic waves and dielectric losses into the surrounding space, resulting in resonance attenuation. The amplitude of resonance gradually decreases, so the voltage on the capacitor board has changed according to the following pattern:
The coefficient d=R/2L is the attenuation index (coefficient),
The frequency of damping resonance. Therefore, the loss not only causes a change in the resonance amplitude, but also a change in its period T=2 p/w. K. The quality is usually characterized by a quality factor
The value of Q determines the number of resonances that K. will perform after charging its capacitor once, before the series resonance amplitude decreases by e times (e is the base of the natural logarithm).