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......$V$.

Alternating current is flowing in an $LR$ circuit with inductance $L$ and resistance $R$. The frequency of the source is $f = \omega / 2\pi$. Which of the following statements is correct?

In the given circuit,the $rms$ value of current $(I_{rms})$ through the resistor $R$ is: $..........\,A$

An $AC$ source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current flowing in the circuit is found to be $I$. Now,the frequency of the source is changed to $\frac{\omega}{3}$ (maintaining the same voltage),and the current in the circuit is found to be halved. What is the ratio of reactance to resistance at the original frequency?

$A$ $10\, V, 60\, W$ bulb is to be connected to a $100\, V, 50\, Hz$ $AC$ source. To operate the bulb at its rated power,an induction coil is connected in series with it. Calculate the required self-inductance of the coil.

The adjoining figure shows an $AC$ circuit with resistance $R$,inductance $L$ and source voltage $V_s$. Then