In a general a.c. series circuit containing resistance, inductance and capacitance in series, the impedance of the circuit is given by,
Now, if inductive reactance XL is equal to capacitive reactance XC, the resultant reactance is zero, and the impedance of the circuit is equal to ohmic resistance, i.e., Z = R ohm. Current flowing through the circuit I = V/R ampere and is in phase with V. Under this condition the circuit is said to be in Electrical Resonance or in Series Resonance. The Current is maximum at this stage, as the impedance is minimum.
Resonance is the result of coincidence of the applied frequency with the natural frequency of the circuit. Under this condition voltages across the coil and the capacitor may be many times greater than the normal applied voltage. Hence, there may be breakdown of the apparatus.
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As the voltage across inductance (VL) is equal to the voltage across capacitance (VC), the circuit is said to be in Voltage Resonance. The circuit accepts the frequency to which it resonates. Therefore it is also called Accepter Circuit. The circuit as a whole behaves as a purely resistive circuit, as the inductive influence of the circuit is totally neutralized by the capacitive influence.
Resonant Frequency (fr):
The particular value of frequency for which resonance takes place in an R – L – C series circuit is called Resonant Frequency. It is usually denoted by fr.
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Its value may be derived as follows:
