Series L-C-R Resonance Circuit:
A series LCR circuit is said to be resonance when the current has its maximum value. Before deriving let us understand the meaning of few terms.
Resonance is quite a common phenomenon in the system which have a tendency to oscillate at a particular frequency known as the natural frequency of the system. Now, if such a system is driven by an energy’ source at a frequency close to the natural frequency of the system, the amplitude of oscillations becomes high and this condition is termed as resonance.
A very common example is that of child swinging back and forth at a natural frequency. Now, if by pushing the swing at regular intervals such that the frequency of pushes is close to that of the swing makes the amplitude of swing very large. The impedance for an LCR circuit is given by the formula.
The frequency f0 of the applied voltage for which the current in a LCR series circuit becomes maximum is called the resonant frequency.
The current amplitude at resonant frequency is
Resonance Curve: In the condition of resonance, XL = XC, then current flowing in the circuit, I is maximum and the frequency at which this condition is meet, is called resonance frequency fr.
If XL ≠ XC then (XL – XC) ≠ 0
Thus, (XL – XC)2 > 0
and Z > R
Thus, the value of current I = V/Z will be less than the resonant current. Figure shows the changes in current due to frequency. This is called resonance curve.
Resonance circuits have wide variety of applications as in tuning system of radio or of a TV set. The antenna accepts signals form various broad casting stations which act as a source in the tuning circuit of the radio. Thus the circuit can be driven by many frequencies. To tune a one particular radio station, the capacitance of the capacitor in the tunning circuit is varied. By doing so, the resonant frequency of the circuit becomes nearly equal to the frequency of the received radio signal. At this point the current amplitude corresponding to the frequency of the signal of the particular radio station in the circuit is maximum and is received on the set. The series resonant circuit is also known as acceptor circuit, because out of the number of frequency feed to it, it accepts only one frequency and rejects the rest.
Remember : The resonance phenomenon occurs in a circuit only if L and C are both part of it as the voltage across L and C are out of phase they cancel out each other and the current amplitude becomes Im = Vm / R. This means that RL or RC circuit cannot exhibit resonance.
