Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, C = 27 μF, and R = 7.4Ω. 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.
Given: L = 3.0 H
C = 27 μF,
In Farad, capacitance C = 27 × 10-6F
R = 7.4Ω
Angular frequency is given by the relation:
ωR = 1/√LC
ωR = 1(√27 × 10-6F × 3 H)
On calculating, we get
ωR = 111.11 rad/s
Q factor can be calculated as follows:
Q = ωRL/R
Q = (111.11(rad/s) × 3H)/7.4(Ω)
⇒ Q = 45.0446
The sharpness of the resonance of the circuit by reducing its ‘full width at half maximum’ by a factor of 2 by reducing R to half.
i.e. R = R/2 = 7.4(Ω)/2 = 3.7Ω