If capacitors and inductors are connected in series with a generator, series resonance will occur as long as the reactance is equal. In this case, the effective part of Z should be as small as possible.
It should be noted that in ideal examples, inductors and capacitors only have reactive quality. In practical circuits and components, the active resistance of conductors is always very small, even though the active resistance is small.
During resonance, energy is exchanged between the inductor and the capacitor. In an ideal example, when the energy source (generator) is initially connected, energy accumulates in the capacitor (or inductor), and after disconnection, continuous resonance occurs due to this exchange.
According to Ohm's Law, the voltage across an inductor and a capacitor is roughly the same:
Where X represents Xc capacitor or XL reactance respectively
A circuit composed of inductors and capacitors is called a resonant circuit. Its frequency is calculated by the following formula:
The resonance period is determined by Thompson's formula:
Since reactance depends on frequency, inductance and resistance increase with increasing frequency, while capacitance decreases. When the resistance is equal, the total resistance will significantly decrease, as reflected in the graph:
The main characteristics of a circuit are quality factor (Q) and frequency. If we consider the circuit as a four port network, after simple calculations, its transmission coefficient will be reduced to quality factor: K=Q
Moreover, the voltage at the circuit terminals increases proportionally to the transmission coefficient (quality factor) of the circuit.
In series resonance, the higher the Q factor, the higher the voltage across the circuit components will exceed the voltage of the connected generator. The voltage may increase by tens or even hundreds of times. As shown in the figure:
The power loss in the circuit is solely attributed to the presence of active resistors. Only obtain energy from the power source to maintain resonance.
The power factor is:
Losses are caused by active power:
