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Obtain the resonant frequency and Q-factor of series LCR circuit with L=3.0H, C = 27 muF, and R = 10.4 Omega. It is desired to improved the sharpness of the resonance of the circuit by reducing its 'full width at half maximum' by a factor of2. Suggest a sultable way. |
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Answer» Solution :Given, inductance L = 3H Capacitance of capaitor `C=27muF = 27xx10^(-6)F` Ristance `R =7.4 Omega` the resonant FREQUENCY of circuit `omega_(r )=(1)/(sqrt(LC))=(1)/(sqrt(3xx27xx10^(-6)))=(1000)/(9)` = 111.1 rad/s. Q-factor of a series LCR circuit Q-factor `= (omega_(r )L)/(R )=(111.1xx3)/(7.4)=45.04`. To reduce the width at half by factor Q, we have to reduce the value of R as R/2 `(R )/(2)=(7.4)/(2)=3.7 Omega` |
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