In a series $LCR$ circuit,the $rms$ voltage across the resistor and the capacitor are $30 \ V$ and $90 \ V$ respectively. If the applied voltage is $V = 50 \sqrt{2} \sin \omega t$,then the peak voltage across the inductor is

In a series $L-C-R$ circuit,the frequency of a $10 \, V$ $a.c.$ voltage source is adjusted in such a fashion that the reactance of the inductor measures $15 \, \Omega$ and that of the capacitor $11 \, \Omega$. If $R = 3 \, \Omega$,the potential difference across the series combination of $L$ and $C$ will be.....$V$.

$A$ series $LCR$ circuit consists of $R = 80\,\Omega$,$X_{L} = 100\,\Omega$,and $X_{C} = 40\,\Omega$. The input voltage is $V = 2500 \cos(100\pi t)\,V$. The amplitude of current in the circuit is $................A$.

An $A.C.$ circuit contains a resistance of $12 \ \Omega$ and an inductive reactance of $5 \ \Omega$. The phase angle between the current and the potential difference will be

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

$A$ sinusoidal voltage $V_0 \sin \omega t$ is applied across a series combination of resistance $R$ and inductance $L$. The amplitude of the current in this circuit is