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Obtain the resonant frequency omega(r ) ...

Obtain the resonant frequency `omega_(r )` of a series jLCR circuit with L= 2.0 H, C = 32` muF` and R = `10 Omega` . What is the Q-value of this circuit ?

Text Solution

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`omega_(r ) = omega_(0) = (1)/(sqrt(LC))`
`:. omega_(r ) = ( 1)/( sqrt(2 xx 32 xx 10^(-6)))`
`:. omega_(r ) = 125 (rad)/( s )`
Q value ( or Q factor ) `= ( omega_(r ) L )/( R )`
` = ( 125 xx 2)/( 10)` OR Q value `=( 1)/( R ) sqrt(( L )/( C ))`
` = ( 1)/( 10) sqrt( ( 2) /( 32 xx 10^(-6)))`
` = (1)/(10) xx (1000)/( 4)`
= 25
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