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Series Resonance Circuit



RESONANCE


DEFINITION:
                        �A condition exists when an oscillating circuit responds with maximum amplitude of an external source of angular frequency �?� called resonance.�


RESONATING CIRCUITS:

DEFINITION:
                        �The circuits that contain both inductors and capacitors along with a resistor so arranged that the circuit is capable of resonance are called resonating circuits.�


                            
SERIES RESONATING CIRCUIT:
                                                        Consider a resister, inductor and capacitor which are connected in series with A.C. source whose frequency can be varied. When current flows through inductor, the inductive reactance becomes:
 XL = ?L
and when current flows through capacitor, the capacitive reactance becomes:
XC = 1/ (?C)

  1. At High Frequency:
    Inductive Reactance  XL  is greater than capacitive reactance XC due to which circuit behaves as R-L Series Circuit in which voltage V leads to the current I by 90� or p/2 (As, f ? XL and f ? 1/XC. So, when f increases  XL  > XC  ).

  2. At Low Frequency:
    Capacitive Reactance XC is greater than inductive reactance  XL due to which circuit behaves as R-C Series Circuit in which voltage V lags to the current I by 90� or p/2 (As, f ? XL and f ? 1/XC . So, when f decreases  XL< XC ).

  3. At Intermediate Frequency
    In between these frequencies, there will be a certain value of frequency at which XL becomes equal to XC and this frequency is called resonance Frequency.  

Characteristics:
  • At resonance,  XL = XC, so they are equal and opposite to each other and cancel each other�s effect and circuit behaves as resistive circuit.      
                                 
  • By changing frequency if  XL= XC,This circuit becomes the resonant circuit.
1/(?rc)=?rL
?r 2=1/LC
?r=1/v(LC)
2pfr=1/v(LC)
fr=1/v(2p(LC))
�fr� is known as �resonant frequency�.

  • Impedance of circuit becomes minimum and is equal to R (resistive circuit).

  • Power loss at resonance is maximum.
P=IV cos?
?=0
Hence, power factor cos0� =1

  • The variation of current with frequency is giver by the graph given below:

    At resonance frequency fr, if the amplitude of source voltage Vo remains constant, the current becomes maximum and is given as:
                                                                    Ir= Vo/R.





  • V = VC + VL + VR 
There are 3 cases :

  1. VC > VL (At high frequency)
  2. VC= VL (At resonance frequency)
  3. VC < VL (At low frequency)

  1. At Vc>VL:
                        
By applying Pythagoras Theorem,
V=[VR 2 + (VC - VL ) 2]^1/2
(At resonance frequency, VC = VL )
V=[(VR) 2 + 0]^1/2
 V= VR

ii. At Vc<VL:
                       

By applying Pythagoras Theorem,
V = [VR 2 + (VL  - VC) 2] ^1/2
(At resonance frequency, VC = VL )
V=[(VR) 2 + 0]^1/2
V= VR

Therefore, at resonance, the voltage drop across inductance VL and the voltage drop across capacitance VC may be much larger than the source voltage VR .

Entry # 11
By Rabia Khalid

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