Voltage resonance phenomenon is observed in aseries resonantcircuit composed of capacitors, inductors, and resistors. In order to ensure the energy supply of the resonant circuit, the series circuit also includes an electromotive force source E, which generates an alternating voltage with a frequency of W. During resonance, the circulating current in the series circuit must be in phase with the electromotive force. If only the total resistance of circuit Z=R+J (WL-1/W C) is activated, it ensures effective Z=R. Equality:

（L-1 /WС）= 0（1）

It is the mathematical condition for resonance in a resonant circuit. In this case, the current in the circuit will be I=E/R. If we transform equation (1), we obtain:

WL = 1 /WС。

In this expression, W is the resonant frequency of the circuit.

Importantly, during the resonance process, the voltage across the inductor is equal to the voltage across the capacitor, and is:

UL = U = WL * I = WLE / R 

The total amount of energy in inductance and capacitance (magnetic and electric fields) is constant. This is due to the fact that there is resonant exchange of energy between these fields. Its total number has not changed at any time. In this case, there will be no energy exchange between its source E and the chain. On the contrary, there exists a continuous conversion of one type of energy to another.  

For resonant circuits, the term Q factor is used to represent the relationship between the voltage on the reactive element (capacitor or inductor) and the input voltage of the circuit. The quality factor is calculated using the following formula:

Q = WL / R 

For an ideal series circuit with zero resistance, resonance occurs with undamped resonance. In fact, compensating for the attenuation of resonance is achieved by feeding the resonant frequency from the resonator to the circuit.