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. Suggest a suitable way.

Solution

Given,

Inductance, L = 3.0 H
Capacitance, C = 27 $μF = 27 \times 10^{- 6} F$
Resistance, R = 7.4 $Ω$

Therefore,
Resonant frequency,
$ω_{r} = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{3.0 \times 27 \times 10^{- 6}}} = 111 rad s^{- 1}$

Q-factor of the circuit,

$Q = \frac{ω_{r} L}{R} = \frac{111 \times 3.0}{7.4} = 45$

For improvement in sharpness of resonance by a factor of 2, Q should be doubled. To double Q with changing ω_r, R should be reduced to half, i.e., to 3.7 Ω.

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Electrostatic Potential And Capacitance

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. Suggest a suitable way.

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