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

The power factor of an $L-R$ series circuit is $0.6$ and that of a $C-R$ series circuit is $0.5$. If the elements ($L, C,$ and $R$) of the two circuits are joined in series,the power factor of this circuit is found to be $1$. The ratio of the resistance in the $L-R$ circuit to the resistance in the $C-R$ circuit is:

The impedance of the given circuit is......$\Omega $

In the given circuit,the peak voltages across $C$,$L$,and $R$ are $30 \,V$,$110 \,V$,and $60 \,V$,respectively. The rms value of the applied voltage is (in $\,V$)

In an $LCR$ series $ac$ circuit,the voltage across each of the components,$L, C$ and $R$ is $50\,V$. The voltage across the $LC$ combination will be........$V$.

In an $LCR$ circuit,the capacitance is changed from $C$ to $4C$. For the same resonant frequency,the inductance should be changed from $L$ to: