1.

Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, C = 27 muF , and R= 7.4Omega. It is desired to improve the sharpness of the resonance of the circuit by reducing its 'full width at half maximum' by a factor of 2. Suggest a suitable way.

Answer»

Solution :`omega_r= (1)/(sqrtLC) = (1)/(sqrt(3 xx 27 xx 10^(-6) ) = 111 rad//s `
`Q = (X_L)/(R ) = (omega_r L)/ ( R) = (111 xx 3)/(7.4) = 45`
For doubling Q for the same `omega_r` , R should be REDUCED to half and is EQUAL to`3.7 Omega `


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