$A$ series $R-L-C$ circuit consists of an $8.0\ \Omega$ resistor,a $5.0\ \mu F$ capacitor,and a $50.0\ mH$ inductor. $A$ variable frequency source applies an $emf$ of $400\ V\ (rms)$ across the combination. The power delivered to the circuit when the frequency is equal to one-half the resonance frequency is.....$W$

$A$ series $AC$ circuit containing an inductor $(20\,mH),$ a capacitor $(120\,\mu F)$ and a resistor $(60\,\Omega)$ is driven by an $AC$ source of $24\,V$ and $50\,Hz.$ The energy dissipated in the circuit in $60\,s$ is

In an $LCR$ circuit,$R = 100 \ \Omega$. When the capacitor $C$ is removed,the current lags behind the voltage by a phase of $\pi / 3$. When the inductor $L$ is removed,the current leads the voltage by a phase of $\pi / 3$. What is the impedance of the circuit in $\Omega$?

For the circuit shown in the figure,the current through the inductor is $0.9\,A$ while the current through the capacitor is $0.4\,A$. Then

The power factor of the given $LCR$ circuit is $1/\sqrt{2}$. Find the capacitance $C$ of the circuit in $\mu F$.

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: