An inductor of inductance $L$,a capacitor of capacitance $C$,and a resistor of resistance $R$ are connected in series to an $ac$ source. The quality factor of the circuit is

In a series resonant $LCR$ circuit,the voltage across $R$ is $100 \, V$ and $R = 1 \, k\Omega$ with $C = 2 \, \mu F$. The resonant frequency $\omega$ is $200 \, rad/s$. At resonance,the voltage across $L$ is......$V$.

$A$ series $LCR$ circuit is connected to an ac voltage source. When $L$ is removed from the circuit,the phase difference between current and voltage is $\frac{\pi}{3}$. If instead $C$ is removed from the circuit,the phase difference is again $\frac{\pi}{3}$ between current and voltage. The power factor of the circuit is:

In a series resonant $R-L-C$ circuit, the voltage across $R$ is $100 \, V$ and the value of $R = 1000 \, \Omega$. The capacitance of the capacitor is $2 \times 10^{-6} \, F$; the angular frequency of the $AC$ source is $200 \, rad \, s^{-1}$. Then the potential difference across the inductance coil is: (in $V$)

In a series resonant $L-C-R$ circuit,the voltage across $R$ is $100 \, V$ and $R = 1 \, k\Omega$ with $C = 2 \, \mu F$. The resonant frequency $\omega$ is $200 \, rad \, s^{-1}$. At resonance,the voltage across $L$ is.....$V$

$A$ series $LCR$ circuit is connected across a source of alternating emf of changing frequency and resonates at frequency $f_0$. Keeping capacitance constant,if the inductance $(L)$ is increased by $\sqrt{3}$ times and resistance is increased $(R)$ by $1.4$ times,the resonant frequency now is