$A$ resistor and a capacitor are connected in series with an $AC$ source of angular frequency $\omega$. If the frequency is changed to $\omega / 3$ while keeping the voltage constant,the current becomes half. What is the ratio of the reactance to the resistance at the initial frequency?

If $E = 200\,V$,$R = 25\,\Omega$,$L = 2\,H$,and $C = 2\,\mu F$ and the frequency is variable,then the current at $f = 0$ and $f = \infty$ will be respectively:

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 $\omega$.

$A$ virtual current of $4 \, A$ and $50 \, Hz$ flows in an $AC$ circuit containing a coil. The power consumed in the coil is $240 \, W$. If the virtual voltage across the coil is $100 \, V$,its inductance will be:

$A$ lamp is connected in series with a capacitor and an $AC$ source. What happens if the capacitance of the capacitor is reduced?

In an $LCR$ series circuit,if ${X_C} < {X_L}$ and ${X_C} > {X_L}$,determine whether the current in the circuit leads or lags the voltage.