# 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) :

# 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.