(A) The quality factor $(Q)$ of a series $LCR$ circuit at resonance is given by the formula:$Q = \frac{1}{R} \sqrt{\frac{L}{C}}$Given values:Resistanc

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(A) The quality factor $(Q)$ of a series $LCR$ circuit at resonance is given by the formula:$Q = \frac{1}{R} \sqrt{\frac{L}{C}}$Given values:Resistance $R = 100\,\Omega$Inductance $L = 1\,H$Capacitance $C = 6.25 \times 10^{-6}\,F$Substituting the values into the formula:$Q = \frac{1}{100} \sqrt{\frac{1}{6.25 \times 10^{-6}}}$$Q = \frac{1}{100} \sqrt{\frac{10^6}{6.25}}$$Q = \frac{1}{100} \times \frac{1000}{2.5}$$Q = \frac{10}{2.5} = 4$Thus,the quality factor of the circuit is $4$.

Class 12 Physics Alternating Current Half Power Frequency , Quality Factor ,Resonance in AC Circuit

Medium

$A$ series combination of a resistor of resistance $100\,\Omega$,an inductor of inductance $1\,H$,and a capacitor of capacitance $6.25\,\mu F$ is connected to an $AC$ source. The quality factor of the circuit will be $.............$.

JEE MAIN 2023 All JEE MAIN

A
$4$
B
$3$
C
$2$
D
$1$

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Alternating Current

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Half Power Frequency , Quality Factor ,Resonance in AC Circuit

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$A$ series combination of a resistor of resistance $100\,\Omega$,an inductor of inductance $1\,H$,and a capacitor of capacitance $6.25\,\mu F$ is connected to an $AC$ source. The quality factor of the circuit will be $.............$.

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