In an LCR series ac circuit `R=10Omega` , L=50 mH and `C=5muF`. Find out the resonant frequency and Q-factor. Find also the bandwidth and half-power frequencies.

Explanation

Hence, L=50mH =`5times10^-2H`
`5 muF=5times10^-6F`
`therefore` Resonant frequency,
`f_0=1/(2pisqrt(Lc))=1/(2times3.4timessqrt((5times10^-2)times(5 times 10^-6)))`
`=10^4/(2times3.14times5)=318.5Hz`
and Q factor = `=1/Rsqrt(L/C)=1/10sqrt((5times10^-2)/(5times10^-6))=1/10times 100=10`
Now, `Omega=omega_e/(Deltaomega)=f_0/(Deltaf)`
`therefore` Bandwidth, `Deltaf=f_0/Q=318.5/10=31.85Hz`
Half- power frequencies are,
`f_1=f_0-(Deltaf)/2=318.5-31.85/2=302.6Hz`
and `f_2=f_1+(Deltaf)/2=302.6+15.92=318.52 Hz`