Series resonance
One of the most important phenomena in ac circuits, especially in radio-frequency engineering, is the property of resonance. You’ve already learned that resonance is a condition that occurs when capacitive and inductive reactance cancel each other out. Resonant circuits and devices have a great many different applications in electricity and electronics.
Recall that capacitive reactance, XC, and inductive reactance, XL, can sometimes be equal in magnitude. They are always opposite in effect. In any circuit containing an inductance and capacitance, there will be a frequency at which XL = −XC. This is resonance.
Sometimes XL= −XC at just one frequency; in some special devices it can occur at many frequencies. Generally, if a circuit contains one coil and one capacitor, there will be one resonant frequency.
Refer to the schematic diagram of Fig. 1. You might recognize this as a series RLC circuit. At some particular frequency, XL = −XC. This is inevitable, if L and C are finite and nonzero. This is the resonant frequency of the circuit. It is abbreviated fo.
Fig. 1: A series RLC circuit.
At fo, the effects of capacitive reactance and inductive reactance cancel out. The result is that the circuit appears as a pure resistance, with a value very close to R. If R=0, that is, the resistor is a short circuit, then the circuit is called a series LC circuit, and the impedance at resonance will be extremely low. The circuit will offer practically no opposition to the flow of alternating current at the frequency fo. This condition is series resonance.
