In the circuit shown here,the voltages across $L$ and $C$ are respectively $300\, V$ and $400\, V$. The voltage $E$ of the $AC$ source is......$V$.

When an inductor $L$ and a resistor $R$ in series are connected across a $12 \, V, 50 \, Hz$ supply, a current of $0.5 \, A$ flows in the circuit. The current differs in phase from the applied voltage by $\frac{\pi}{3}$ radian. Then the value of $R$ is (in $\Omega$)

An alternating voltage is applied to a series $LCR$ circuit. If the current leads the voltage by $45^{\circ}$,then $\left(\tan 45^{\circ}=1\right)$:

What will be the reading in the voltmeter and ammeter of the circuit shown?

An alternating emf is applied across a parallel combination of a resistance $R$,capacitance $C$ and an inductance $L$. If $I_R$,$I_L$,and $I_C$ are the currents through $R$,$L$,and $C$ respectively,then the diagram which correctly represents the phase relationship among $I_R$,$I_L$,$I_C$,and the source emf $E$ is:

$A$ circuit connected to an $ac$ source of $emf$ $e = e_0 \sin(1000t)$,where $t$ is in seconds,exhibits a phase difference of $\frac{\pi}{4}$ between the $emf$ $e$ and current $i$. Which of the following circuits will exhibit this?