The impedance of LCR is
In expression (1), Io has different values for different frequencies. But Io has a maximum value when Z is minimum.
i.e., when XL = XLc or Z = R
since w = 2pf
This frequency for which the current in AC circuit reaches a peak value and the A.C circuit behaves like a pure resistive circuit is called resonant frequency. The following diagram shows the variation of frequency with Io. Notice that as the value of R decreases, the value of Io increases.
Since the circuit behaves like a pure resistive one, the current and voltage are in phase. This fact helps in tuning our TV and radio sets. The antenna circuit consists of LCR circuit. The value of C is varied till the resonant frequency is equal to the particular frequency from any radio station. At this stage, the current through the circuit is maximum and the receiver responds to the incoming signals. For this reason, such circuits are called acceptor circuits, as these accept those signals for which current reaches peak value.
