resonance for RLC series circuit? effect on circuit performance

Question: Define the term ‘Resonance’ as applicable to a simple RLC series circuit. Discuss briefly the effect of Resonance on circuit performance. OR Explain resonance condition RLC parallel circuit.

Q: what is resonance in electrical circuits?

Series resonance

A series circuit is said to be at electrical resonance when its net reactance is zero. The frequency (Fr) at which electrical resonance occurs is called Resonant frequency ( Fr).

Resonance conditions for series circuit

  • Impedance of resonance is only resistance i.e Z=R
  • Net reactance is zero

therefore, X =XL – Xc  = 0

XL = Xc

  • VL -Vc = 0

VL = Vc

  • Maximum current i.e line current, Imax = V/R
  • The phase angle at electrical resonance is zero.
  • Therefore,power factor is unity (cos 0 = 1 )
  • XL =XC

Resonance frequency

fr =

  • Quality factor (Q factor) :

The resonance condition in RLC Parallel circuit

Current in AC series RLC circuit at electrical resonance

The net reactance in RLC circuit shown in figure is,

If for same frequency of the applied voltage  XL   =  XC (in magnitude) then X = 0 and Z = R as shown in figure (c). From figure (c), VL = IXL and  VC = IXC, and these two are equal in magnitude but opposite in phase. Hence, they cancel each other. The applied voltage, V drops entirely across R. So that V =  VR. The circuit impedance Z = R. The phasor diagram for series electrical resonance is shown in figure (d). It means that impedance of the circuit equals the ohmic resistance R so that current is maximum in the AC series RLC circuit.


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