Physics Ncert Solutions Class 12th Alternating Current Overview Class 12th Physics Alternating Current

7.21 Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, C = 27 μF, and R = 7.4 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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Payal Gupta | Contributor-Level 10

8 months ago

7.21 Given values of the LCR circuit

L = 3.0 H, C = 27 $μ F = 27 * 10^{- 6}$ F, R = 7.4 Ω

At resonance, the angular frequency, $ω_{R}$ = $\frac{1}{\sqrt[]{L C}}$ = $\frac{1}{\sqrt[]{3 * 27 * 10^{- 6}}}$ = 111.11 rad/s

Q factor of the series, Q = $\frac{ω_{R} L}{R}$ = $\frac{111.11 * 3}{7.4}$ = 45.045

To improve the sharpness of the resonance by reducing its 'full width at half maximum' by a factor of 2 without changing $ω_{R}$ , we need to

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$I = Q_{0 . ω}$

$= \frac{C V}{\sqrt[]{L C}} = V \sqrt[]{\frac{C}{L}}$

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Physics Ncert Solutions Class 12th 2023

Physics Ncert Solutions Class 12th 2023

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