$A$ 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?

The power factor of an $R-L$ circuit is $\frac{1}{\sqrt{2}}$. If the frequency of $AC$ is doubled,the power factor will now be

$A$ series $R-C$ circuit is connected to an $AC$ voltage source. Consider two cases: $(A)$ when $C$ is without a dielectric medium and $(B)$ when $C$ is filled with a dielectric of constant $K = 4$. The current $I_R$ through the resistor and voltage $V_C$ across the capacitor are compared in the two cases. Which of the following is/are true?

$A$ $12\,\Omega$ resistor and a $0.21\,H$ inductor are connected in series to an $ac$ source operating at $20\,V$,$50\,Hz$. The phase angle between the current and the source voltage is.....$^o$

An e.m.f. $E = E_0 \cos \omega t$ is applied to an $L-R$ circuit. The inductive reactance is equal to the resistance $R$ of the circuit. The power consumed in the circuit is:

$A$ resistance of $300 \ \Omega$ and an inductance of $\frac{1}{\pi} \ H$ are connected in series to an $AC$ voltage of $20 \ V$ and $200 \ Hz$ frequency. The phase angle between the voltage and current is