ω , X c = X L , and the impedance is minimum ( Z . This frequency is called the resonant frequency : or c L X X L or LC ω = ( . ) At resonant frequency, the current amplitude is maximum; i m = v m /R . Figure .
shows the variation of i m with ω in a RLC series circuit with L = . mH, C = . nF for two values of R : (i) R = Ω and (ii) R = Ω . For the source applied v m = V.
ω for this case is LC ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ = . × rad/s. We see that the current amplitude is maximum at the resonant frequency. Since i m = v m / R at resonance, the current amplitude for case (i) is twice to that for case (ii).
Resonant circuits have a variety of applications, for example, in the tuning mechanism of a radio or a TV set. The antenna of a radio accepts signals from many broadcasting stations. The signals picked up in the antenna acts as a source in the tuning circuit of the radio, so the circuit can be driven at many frequencies. FIGURE .
Variation of i m with ω for two cases: (i) R = Ω , (ii) R = Ω , L = . mH.