# Resonance as applicable to simple RLC series circuit? effect on circuit performance

## Series resonance

A series circuit is said to be at electrical resonance when its net reactance is zero.The frequency (Fr) at which 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
• Phase angle at resonance is zero.
• Therefore,power factor is unity (cos 0 = 1 )
• XL =XC

Resonance frequency

fr =

• Quality factor (Q factor) :

# Q: Current in AC series R-L-C circuit at resonance

The net reactance in R-L-C 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 resonance is shown in figure (d). It means that impedance of the circuit equals the ohmic resistance R, so that current is maximum in AC series R- L-C circuit.