In a series RLC circuit there is a frequency at which the inductive reactance of the inductor becomes equal in value to the capacitive reactance of the capacitor. The point at which this occurs is the Resonant Frequency point, ( fr ) of the circuit, in a series RLC circuit this resonance frequency produces a Series Resonance.

Series Resonance circuits are one of the most important circuits used electrical and electronic circuits. They can be found in various forms such as in AC mains filters, noise filters and also in radio and television tuning circuits producing a very selective tuning circuit for the receiving of the different frequency channels.

Consider the simple series RLC circuit shown above. Total circuit impedance is

Z = R + jX

Resonance occurs when Z_L = Z_C, that is

ωL =

1 / ωC

where ω = 2πf , so 2πfL =

1 / 2πfC

or 4π²f² =

1 / LC

and f_r =

1 / 2π √LC

So the total impedance of the series circuit becomes just the value of the resistance and therefore: Z = R. At resonance the impedance of the series circuit is at its minimum value and equal only to the resistance, R of the circuit.

At frequencies above ft, because inductive reactance Z_L > Z_C, there is a positive phase shift. Similarly, when frequencies are below ft, becase Z_C >Z_L , there is a negative phase shift

If the series RLC circuit is driven by a variable frequency at a constant voltage, then the magnitude of the current, I is proportional to the impedance, Z, therefore at resonance the power absorbed by the circuit must be at its maximum value as P = I²Z.
If the frequency is now reduced or increased until the average power absorbed by the resistor in the series resonance circuit is half that of its maximum value at resonance, two frequency points are produced called the half-power points which are -3dB down from maximum, taking 0dB as the maximum current reference.