An inductance of $\left(\frac{200}{\pi}\right) \text{mH}$,a capacitance of $\left(\frac{10^{-3}}{\pi}\right) \text{F}$,and a resistance of $10 \, \Omega$ are connected in series with an $AC$ source of $220 \, \text{V}, 50 \, \text{Hz}$. The phase angle of the circuit is:

$A$ coil is connected to an $AC$ source with peak emf, $8 \, V$ and frequency $\frac{30}{\pi} \, Hz$. The coil has a resistance of $8 \, \Omega$. If the average power dissipated by the coil is $0.4 \, W$, then the inductance of the coil is (in $, H$)

An inductor of inductance $L$,a capacitor of capacitance $C$,and a resistor of resistance $R$ are connected in series to an $AC$ source of potential difference $V$ volts as shown in the figure. The potential difference across $L$,$C$,and $R$ is $40 \, V$,$10 \, V$,and $40 \, V$,respectively. The amplitude of the current flowing through the $LCR$ series circuit is $10 \sqrt{2} \, A$. The impedance of the circuit is .......... $\Omega$.

An oscillating circuit consists of a capacitor with capacitance $C = 10 \, \mu F$, a coil with inductance $L = 6.0 \, \mu H$, and active resistance $R = 10 \, \Omega$. The mean power that should be fed to the circuit to maintain undamped harmonic oscillations with an external driving source of frequency $f = 50 \, Hz$ and peak voltage $V_m = 280 \, V$ is:

In a given series $LCR$ circuit,$R = 4\,\Omega ,$ $X_L = 5\,\Omega $ and $X_C = 8\, \Omega ,$ the current:

In an $LCR$ series $ac$ circuit,the voltage across each of the components,$L, C$ and $R$ is $50\,V$. The voltage across the $LC$ combination will be........$V$.