Qstnid -21- Obtain The Resonant Frequency And <I>q</i>-factor Of A Series <I>lcr </I>circuit With <I>l </I>= 3.0 H, <I>c </I>= 27 Μf, And <I>r </I>= 7.4 ``\Omega``. It Is Desired To Improve The Sharpness Of The Resonance Of The Circuit By Reducing Its &Lsquo;full Width At Half Maximum’ By A Factor Of 2. Suggest A Suitable Way. - 07: Alternating Current - Neet-xii-physics

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NEET-XII-Physics

07: Alternating Current

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#21
Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, C = 27 μF, and R = 7.4 ``\Omega``. 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.

Ans : Inductance, L = 3.0 H

Capacitance, C = 27 μF = 27 × 10^-6 F

Resistance, R = 7.4 ``\Omega``

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

Q-factor of the series:

To improve the sharpness of the resonance by reducing its ‘full width at half maximum’ by a factor of 2 without changing, we need to reduce R to half i.e.,

Resistance =