How can you improve the quality factor of a parallel resonance circuit. Obtain the resonant frequency and quality factor of a series L-C-R circuit with L = 4 H, C = $64 μ F$ and R = $20 Ω$ .

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Solution

Resonant frequency $f_{o} = \frac{1}{2 π \sqrt{L C}}$
$⟹ f_{o} = \frac{1}{2 π \sqrt{4 \times 64 \times 10^{- 6}}} = 9.95 H z$
Quality factor $Q = \frac{X_{L}}{R} = \frac{2 π f_{o} L}{R}$
$⟹ Q = \frac{2 π \times 9.95 \times 4}{20} = 12.5$

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How can you improve the quality factor of a parallel resonance circuit. Obtain the resonant frequency and quality factor of a series L-C-R circuit with L = 4 H, C = 64μF and R = 20Ω.

Resonant frequency fo=12π√LC⟹ fo=12π√4×64×10−6=9.95 HzQuality factor Q=XLR=2πfoLR⟹ Q=2π×9.95×420=12.5

How can you improve the quality factor of a parallel resonance circuit. Obtain the resonant frequency and quality factor of a series L-C-R circuit with L = 4 H, C = $64 μ F$ and R = $20 Ω$ .

Resonant frequency $f_{o} = \frac{1}{2 π \sqrt{L C}}$
$⟹ f_{o} = \frac{1}{2 π \sqrt{4 \times 64 \times 10^{- 6}}} = 9.95 H z$
Quality factor $Q = \frac{X_{L}}{R} = \frac{2 π f_{o} L}{R}$
$⟹ Q = \frac{2 π \times 9.95 \times 4}{20} = 12.5$