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.

In an LCR series ac circuit `R=10Omega` , L=50 mH and `C=5muF`. Find o

1.	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.
Answer» 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`

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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.

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