What is series resonant circuit?

An electrical circuit consisting of passive and active elements undergoes resonance when current or voltage in the circuit is maximum or minimum with respect to the magnitude of excitation at a partcular frequency. Also the circuit impedance is minumum or maximum at unity power factor. The phenomenon of resonance is observed in both series or parallel a.c circuits comprising of R, L and C and excited by an a.c source.

Series resonance takes place in an ac circuit which has all the elements connected in series with one another. Let us consider an a.c series circuit with R,L,C.

rcIn this circuit current I is represented as, I = V / Z Amperes
where Z = equivalent impedance of the circuit.
Voltage across the resistance R , inductor L and capacitor C is VR , VL and VC respectively.
We know that impedance Z = R + j ω L + 1 / jω C
= R + j ω L - j / ω C
= R + j ( XL - XC )
where XL = ωL and XC = 1 / ω C
= R + j X , where X = the net reactance

Resonance condition is obtained when XL = XC in series circuit .

Properties of resonance at RLC circuit :

    The applied voltage and resulting current are in phase

    P.f of series resonant circuit is unity

    Net impedance is zero at resonance

    Current in the circuit is maximum

    At resonance line current in series LCR circuit is maximum hence it is called an acceptor circuit.

    At resonance , the circuit has got minimum impedance and maximum admittance

    Resonating frequency f0 = 1 / 2 π √ LC.