A series combination of a resistor of resistance , an inductor of inductance 1 H and a capacitor of capacitance is connected to an AC source. The quality factor of the circuit will be ________. [2023]

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Solution

Q.
A series combination of a resistor of resistance $100 Ω$ , an inductor of inductance 1 H and a capacitor of capacitance $6.25 μ F$ is connected to an AC source. The quality factor of the circuit will be ________. [2023]

Ans.
(4)

$Quality factor = \frac{X_{L}}{R} = \frac{ω L}{R}$

$ω = \frac{1}{\sqrt{L C}} = \frac{1}{\sqrt{1 \times 6.25 \times 10^{- 6}}} = \frac{10^{3}}{2.5} = 400 / sec$

$Q -factor = \frac{400 \times 1}{100} = 4$

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