In a series circuit of resistors, inductors, and capacitors, the phenomenon of the circuit terminal voltage and total current being in phase is called series resonance.
We know that in the R-L-C series circuit, the terminal voltage U can only be in phase with the current I when the inductance XL is equal to the capacitance Xc. Therefore, the condition for series resonance is: ω L=1/ω C. When the circuit parameters L and C are constant, the frequency can be changed to make the circuit resonate. The resonant frequency is fo=1/2 π√ LC fo, also known as the natural oscillation frequency.
When the power frequency is constant, by changing the inductance or capacitance, the circuit can also resonate. The inductance or capacitance that causes the circuit to resonate are L=1/ω 2C C=1/ω 2L. The characteristic of series resonance is that the circuit is purely resistive, and the terminal voltage and total current are in phase. The reactance X is equal to zero, and the impedance Z is equal to the resistance R. At this point, the impedance of the circuit is the smallest and the current is the largest, which may generate high voltages on the inductance and capacitance that are many times greater than the power supply voltage. Therefore, series resonance is also known as voltage resonance.
When in series resonance, the ratio of the inductor voltage UL or capacitor voltage UC to the terminal voltage U is called the quality factor of the circuit, represented by the symbol Q, that is, Q=UL/U=UC/U=ω L/R
Due to the fact that the voltage across the inductor and capacitor during resonance is Q times the power supply voltage, the resonant circuit of the radio can use this to select a signal of a certain frequency. However, in power engineering, due to the occurrence of overvoltage and high current caused by series resonance, which can damage electrical equipment, it is important to avoid series resonance.
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