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Home » 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.
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.
Alternating Current | CBSE | Class 12 | Guides | NCERT | Physics
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.

Inductance, L=3.0 \mathrm{H}

Capacitance, \mathrm{C}=27 \mu \mathrm{F}=27 \times 10^{-6} \mathrm{~F}

Resistance, \mathrm{R}=7.4 \Omega

The resonant frequency of the source in the LCR series circuit is

\omega=\frac{1}{\sqrt{L C}}

\omega=\frac{1}{\sqrt{3 \times 27 \times 10^{-6}}}=111.11 \mathrm{rad} / \mathrm{s}

Q-factor of the series

Q=\omega L/R

=(111.11\times 3)/7.4=45.04

We should reduce the resistance to half to improve the sharpness of the circuit’s resonance by reducing its ‘full breadth at half maximum’ by a factor of two.

=\mathrm{R} / 2=7.4 / 2=3.7 \Omega

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