Question

What is necessary condition for series resonant oscillation?

Answer 1

In LCR series circuit voltage ac source v(t)=v(0)sinwt , where v(t) is voltage at t instant v(0) is peak value of the voltage & w be angular frequency at thatinstant,impedance is given by

Z=R+jwL+(1/jwC), j is the phasor.

Z=R+j{wL-(1/wC)}

Z=|Z| e^j@

Where @=tan^-1{wL-(1/wc)}/R

|Z|=Sq rt{R^2+(wL-1/wC)^2}

Now at a certain angular frequency at w=w(0) circuit becomes resonant. And this frequency is called resonance frequency.

At resonance frequency power of the circuit becomes maximumP=I(rms)V(rms)cos@;So at @=0° ,at resonance frequency current & voltage remains in same phase & for this cos@=1

Now tan@=0

{w(0)L-1/w(0)C}/R=0

w(0)L=1/w(0)C

w(0)^2=1/LC.

At this frequency power of the circuit becomes maximum.A and |Z|=R so at resonance frequency circuit is purely resistive and peak value of the current becomes maximum.

I(max)=v(0)/R