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Resonance
The phenomenon of resonance is common among systems that have a tendency to oscillate at a particular frequency. This frequency is called the natural frequency of oscillation of the system. If such a system is driven by an energy source, whose frequency is equal to the natural frequency of the system the amplitude of oscillations becomes large and resonance is said to occur. For example a child one a swing has a natural frequency for swinging back and forth. If another child pushes the swing at regular intervals and the frequency of the pushes is almost the same as the frequency of swinging the amplitude of swing becomes very large. We say that resonance has occurred.
Series resonance circuit
A circuit in which inductance L, capacitance C and resistance R are connected in series, and the circuit admits maximum current corresponding to a given frequency of is called series resonance circuit.
The impedance (Z) of an RLC circuit is given by
Z = √R2 + (ω L – 1 / ω C)2
At very low frequencies, inductive reactance XL = ω L is negligible, but capacitative reactance (xC = 1 / ωC) is very high.
As frequency of alternating applied to the circuit is increased, XL goes on increasing and XC goes on decreasing. For a particular value of ω( = ω, say)
XL = XC
ω L = 1 / ω, C or
ωr = 1 / √LC
2 π vr = 1 / √LC or
Vr = 1 / 2 π √LC
At this particular frequency vr, as XL = XC.
Therefore from eq.,
Z = √R2 + 0 = R = minimum
Impedance of RLC circuit is minimum and hence the current I0 = E0 / Z = E0 / R becomes maximum. This frequency is called resonance frequency. 1/2 π √LC is the natural frequency of oscillation of an LC circuit containing no resistance.
The variation of circuit with the changing frequency f applied voltage is shown in (i) it is clear that for frequencies greater than or less then Wr the values of current are less than the maximum value (I0).
Further at w = w current is maximum (I0). The value of maximum current is inversely proportional ot R. for lower R values (I0) is large and vice- versa.
As series resonance circuit admits maximum current through it is called acceptor circuit. The practical application of series resonance circuit is in radio and. T. V receiver sets. The antenna of a radio t. V. intercepts signals from many broadcasting stations. To receive one particular radio station T.V channel we tune our receiver set by changing the capacitance of a capacitor in the tuning circuit of the set such that resonance frequency of the circuit becomes equal to the frequency of the desired station. Therefore, resonance occurs. The amplitude of current with the frequency of the signal form the desired station becomes maximum; and it is received in our set.
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