$A$ series combination of resistor $R$ and capacitor $C$ is connected to an a.c. source of angular frequency $\omega$. Keeping the voltage same, if the frequency is changed to $\omega/3$, the current becomes half of the original current. Then the ratio of capacitive reactance and resistance is

When an $AC$ generator of $120 \, V$ is connected in series with a capacitor and a resistor of $30 \, \Omega$,the circuit carries a current of $1.5 \, A$. The potential difference across the capacitor will be ..... $V$.

$A$ resistor and a pure inductor are connected to an $AC$ supply of $120\,V$ and $50\,Hz$. The current in the circuit is $3\,A$. If the power consumed in the circuit is $108\,W$,then the resistance in the circuit is.....$\Omega $

An $a.c.$ 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 $\frac{\omega}{3}$ (while maintaining the same voltage),the current in the circuit is found to be halved. The ratio of reactance to resistance at the original frequency $\omega$ is:

The following series $L-C-R$ circuit,when driven by an emf source of angular frequency $70 \text{ krad/s}$,behaves effectively as:

$A$ circuit is made of $1 \Omega$ resistance and $2.5 \text{ mH}$ inductance in series. If an alternating source of $200 \text{ V}$ and $50 \text{ Hz}$ is connected to the circuit,then the phase difference between current and voltage is . . . . . . .