If in an AC circuit containing series connected capacitors, inductors, and resistors

The phase angle between current and voltage disappears (j=0), indicating a change in the phase between current and voltage. Frequency meets the conditions

In this case, the total resistance of circuit Z becomes the smallest, equal to the active resistance R of the circuit, and the current in the circuit is determined by this resistance, taking the maximum value (for a given U m). In this case, the voltage drop across the active resistor is equal to the external voltage applied to the circuit (U R=U), while the voltage drop across the capacitor (U C) and inductor (U L) is the same but opposite in phase. This phenomenon is called series resonance or variable frequency resonance, with the frequency being the resonance frequency. The vector diagram of series resonance is shown in the figure. In the figure, the dependence of current amplitude on w has been shown.

When voltage resonance occurs

By substituting this formula into the resonance frequency and voltage amplitude on the inductor and capacitor, we obtain

Where Q is the quality factor of the circuit, determined by the expression. Due to the Q factor of ordinary oscillating circuits being greater than 1, the voltage on the inductor and capacitor exceeds the voltage applied to the circuit. Therefore, voltage resonance phenomenon is used in technology to amplify voltage fluctuations of any specific frequency. For example, in the case of resonance between the two ends of a capacitor, a voltage Um with amplitude can be obtained (Q in this case is the Q factor of the circuit, which can be much greater than ù m). This voltage amplification is only possible within a narrow frequency interval near the resonant frequency of the circuit. When calculating the insulation of wires containing capacitors and inductors, it is necessary to consider the phenomenon of series resonance, otherwise their breakdown will be observed.