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:

An $AC$ source is connected in the given series $LCR$ circuit. The $RMS$ potential difference across the capacitor of $20 \mu F$ is . . . . . . $V$.
$V = 50 \sqrt{2} \sin 100 t$ volt

In the $LCR$ circuit shown in the figure,what will be the readings of the voltmeter across the resistor $(V_R)$ and the ammeter $(A)$ if an a.c. source of $220 \ V$ and $100 \ Hz$ is connected to it?

In a series $RLC$ circuit,the $r.m.s.$ voltages across the resistor and the inductor are respectively $400 \,V$ and $700 \,V$. If the equation for the applied voltage is $\varepsilon = 500 \sqrt{2} \sin \omega t$,then the peak voltage across the capacitor is ........... $V$.

In a radio receiver,the short wave and medium wave stations are tuned by using the same capacitor but coils of different inductance $L_s$ and $L_m$ respectively. Then:

$A$ 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.....$W$