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Calculate the resonent frequency of Q-fa...

Calculate the resonent frequency of Q-factor (Quality factor) of a series L-C-R circuit containing a pure inductor of inductance 4H, capacitor of capacitance 27 `muF` and resister of resistance `8.4Omega`.

Text Solution

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Given :L=4H,C=`27muF,R=8.4 Omega,Q=?`
Resonant Frequency
`omega_(r)=(1)/(sqrt(LC))`
`omega_(r)=(1)/(sqrt(4xx27xx10^(-6)))`
`(1)/(sqrt(108xx10^(-6)))`
`=(1)/(10.39xx10^(-3))`
`=0.0962xx10^(3)`
`omega_(r)=96.2 rads^(-1)`
Quality factor
`Q=(omega_(r)L)/(R)=(96.2xx4)/(8.4)=45.80`
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