Half Power Frequencies

(Series RLC circuit)
The frequencies for which current in a series RLC (or a series tuned) circuit is equal to 1/√2 (i.e. 70.71%) of the maximum current (current at resonance)are known as Half Power Frequencies.

At the half power frequencies RMS power consumed by the circuit can be computed by the relation

P = I2 * R = (I0/√2)2 * R  = P0/2 where, P0 = Power at resonance I0 = Current at resonance R = Resistance of the circuit I = Current in the RLC series circuit

Therefore at the Half Power Frequencies the RMS power consumed by the circuit is half of the power consumed by the circuit at resonant frequency due to this fact the frequencies are called Half Power frequencies