Question

Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, C = 27 μF, and R = 7.4 W. 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 1

Given :

Inductance=L= 3.0 H  

Capacitance=C = 27 μF = 27 × 10−6 F  

Resistance=R = 7.4 Ω  

At resonance, angular frequency of the source for the given LCR series circuit :

ωr=1/$\sqrt{LC}$

=1/√(3x27x10⁻⁶)

=10 ³/9

=111.11 rad/s

Q factor :

Formula = Q= ωr L/R

=111.11x3/7.4=45.044

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

= R/2

=7.4/2

= 3.7 ohms

Answer 2

Answer:

Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, C = 27 μF, and R = 7.4 Ω. 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. ... To double Q with changing ωr, R should be reduced to half, i.e., to 3.7 Ω.