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

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.....$W$

Which one of the following graphs correctly represents the variation of impedance $(Z)$ of a series $LCR$ circuit with the frequency $(v)$ of the applied $a.c.$?

In an $LCR$ series circuit,if $R = X_L = 2X_C$,find the impedance and the phase difference between the current and the voltage.

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 parallel $AC$ circuit with $R_1 = R_2 = R$ and $X_L = X_C = X$. An $AC$ source $V = V_0 \sin(\omega t)$ is connected across the circuit as shown in the figure. The $RMS$ value of the potential difference $V_A - V_B$ will be: