$A$ 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 $.............$.

In a series $LCR$ circuit,the frequency of the source is half of the resonance frequency. The nature of the circuit will be:

$A$ series $L-C-R$ circuit containing a resistance of $120 \Omega$ has an angular frequency of $4 \times 10^5 \ rad \ s^{-1}$. At resonance,the voltage across the resistance and the inductor are $60 \ V$ and $40 \ V$ respectively. The value of the inductance is: (in $mH$)

For a series $LCR$ circuit at resonance,the statement which is not true is:

Obtain the equation of bandwidth for an $L-C-R$ series $AC$ circuit and deduce the equation of $Q$ factor.

In an $LCR$ circuit,the resonance frequency of the circuit increases to two times its initial value by changing the capacitance from $C$ to $C^{\prime}$ and the resistance from $100 \ \Omega$ to $400 \ \Omega$,while the inductance $L$ is kept constant. The ratio $C / C^{\prime}$ is: