$A$ charged capacitor discharges through a resistance $R$ with time constant $\tau$. The two are now placed in series across an $AC$ source of angular frequency $\omega = \frac{1}{\tau}$. The impedance of the circuit will be-

When an inductor $L$ and a resistor $R$ in series are connected across a $15 \, V, 50 \, Hz$ a.c. supply, a current of $0.3 \, A$ flows in the circuit. The current differs in phase from the applied voltage by $(\frac{\pi}{3})^c$. The value of $R$ is:
$(\sin \frac{\pi}{6} = \cos \frac{\pi}{3} = \frac{1}{2}, \sin \frac{\pi}{3} = \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2})$

$A$ 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 $\frac{\omega}{3}$,the current becomes half of the original current. Then the ratio of capacitive reactance and resistance at the former frequency is

$A$ circuit when connected to an $A.C.$ source of $12 \; V$ gives a current of $0.2 \; A$. The same circuit when connected to a $D.C.$ source of $12 \; V$,gives a current of $0.4 \; A$. The circuit is

$A$ $10\, V, 60\, W$ 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.

$A$ 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 statements is/are true?
$(A)$ $I_R^A > I_R^B$
$(B)$ $I_R^B > I_R^A$
$(C)$ $V_C^A > V_C^B$
$(D)$ $V_C^B > V_C^A$