In the adjoining figure,the impedance of the circuit will be $... \Omega$.

In the circuit shown,$C = \frac{\sqrt{3}}{2} \times 10^{-3} \, F$,$R_2 = 20 \, \Omega$,$L = \frac{\sqrt{3}}{10} \, H$,and $R_1 = 10 \, \Omega$. The current in the $L-R_1$ branch is $I_1$ and in the $C-R_2$ branch is $I_2$. The voltage of the $A.C.$ source is given by $V = 200\sqrt{2} \sin(100t) \, V$. The phase difference between $I_1$ and $I_2$ is:

$A$ circuit has a resistance of $11\,\Omega$,an inductive reactance of $25\,\Omega$,and a capacitive reactance of $18\,\Omega$. It is connected to an $AC$ source of $260\,V$ and $50\,Hz$. The current through the circuit (in amperes) is:

As shown in the figure,a series circuit connected across a $200 \,V, 60 \,Hz$ line consists of a capacitor of capacitive reactance $X_C = 30 \,\Omega$,a non-inductive resistor of $R_1 = 44 \,\Omega$,and a coil of inductive reactance $X_L = 90 \,\Omega$ and resistance $R_2 = 36 \,\Omega$. The power dissipated in the coil is.....$W$

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:

$A$ series $LCR$ circuit containing an $AC$ source of $100 \ V$ has an inductor and a capacitor of reactances $24 \ \Omega$ and $16 \ \Omega$ respectively. If a resistance of $6 \ \Omega$ is connected in series,then the potential difference across the series combination of inductor and capacitor only is (in $V$)