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......$V$.

In an $AC$ circuit,the potential differences across an inductance and a resistance joined in series are $16 \, V$ and $20 \, V$ respectively. The total potential difference of the source is .......... $V$.

$A$ coil of inductance $0.50 \; H$ and resistance $100 \; \Omega$ is connected to a $240 \; V, 50 \; Hz$ $AC$ supply.
$(a)$ What is the maximum current in the coil?
$(b)$ What is the time lag between the voltage maximum and the current maximum?

An $AC$ source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current registered is $I$. If the frequency of the source is changed to $\omega/3$ (maintaining the same voltage),the current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$.

In an $LR$ circuit of $3 \text{ mH}$ inductance and $4 \text{ } \Omega$ resistance,an $\text{emf } E = 4 \cos(1000t) \text{ V}$ is applied. The amplitude of the current is:

An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega/4$,(keeping the voltage unchanged) the current is found to be $I/3$. The ratio of resistance to reactance at frequency $\omega$ is