Consider a basic series resonant circuit with Vs=1angle0degrees and L=20 microHe

Question

Consider a basic series resonant circuit with Vs=1angle0degrees and L=20 microHenry, R=14.14 ohms, and C=1000 picoFarad.

Compute the resonant frequency. Compute the bandwidth. Compute the half-power frequencies fH and fL.

Assuming the frequency of the source is the same as the resonant frequency, find the phasor voltage Vc.

Assuming the frequency of the source is the same as the resonant frequency, find the phasor voltage VL.

Assuming the frequency of the source is the same as the resonant frequency, find the phasor voltage VR.

Explanation / Answer

resonance frequency=1/(2*pi*sqrt(LC))=1.125 MHz

quality factor=(1/R)*(sqrt(L/C))=10

bandwidth=resonance frequency/quality factor=112.5 KHz

fH=1.125 MHz+112.5/2 KHz=1.181 MHz

fL=1.125 MHz-112.5/2 KHz=1.068 MHz

at resonance frequency,

Xl=Xc

so VR=1<0

Vc=-141j*(1/14.14)=10<-90

Vl=10<90

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