In a series $LCR$ circuit, $R = 10 \ \Omega$ and the impedance $Z = 30 \ \Omega$. An $r.m.s.$ voltage of $210 \text{ V}$ is applied across the circuit. The true power consumed in the $AC$ circuit is: (in $\text{ W}$)

For a series $LCR$ circuit,$R = X_L = 2X_C$. The impedance of the circuit and the phase difference between $V$ and $I$ respectively will be:

In the given $A.C.$ circuit,the instantaneous currents through the inductor and capacitor are $0.8 \,A$ and $0.4 \,A$ respectively. The instantaneous current through the resistor is:

$A$ capacitor,an inductor,and an electric bulb are connected in series to an a.c. supply of variable frequency. As the frequency of the supply is increased gradually,the electric bulb is found to

In the given circuit,the magnitudes of $V_{L}$ and $V_{C}$ are twice that of $V_{R}$. Given that $f=50\,Hz$ and $R=5\,\Omega$,the inductance of the coil is $\frac{1}{K\pi}\,mH$. The value of $K$ is:

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